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Removed invalid castle solutions, closes #261

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Jay Boice
2022-12-19 16:06:21 -05:00
parent 7be2ef5e03
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5 changed files with 5 additions and 399 deletions
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riddler-castles/castle-solutions-2.csv
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@@ -60,7 +60,6 @@ As a final note, I also think it would be interesting to look at which strategie
0,0,2,5,14,22,29,0,6,22,I made an algorithm that weighted the placement 75% based on what would beat all submissions from last competition and 25% based on what would beat those placements.
2,6,11,16,16,21,3,3,11,11,"Looked at how troop placement was divided up in the previous run-through and tried to place an amount of troops in each castle which would win each one the majority of the time, while largely ignoring castle 7 and 8. Also tried to stay above multiples of 5."
0,2,11,11,16,3,21,5,26,5,"Targeting 28 by way of castles 9, 7, 5, 4, and 3. Wanted each of those castles to get at least 10 troops (to beat anyone who submits a strategy of 10s across the board, which I imagine will be at least somewhat popular)."
3,5,3,15,15,23,5,5,6,17,"I spent way too much time running genetic algorithms to do well against the strategies that did well last time, and then eventually randomly settled on this."
3,8,10,12,12,22,11,7,7,8,"I focused exclusively on the top five performers of the previous competition. I noted that among those competitors, the ordering was Brett>Jim>Ken>Lukas>Cyrus (ironically, Cyrus placed last among that group). I then assumed that this round's strategies would include the following: Brett clones, anti-Brett strategies, Cyrus clones, anti-Cyrus strategies, ""7 and 8 avoiders"", and old, ineffective strategies. Most of what followed was guesswork and I only spent about ten minutes actually dividing up my troops. I quickly decided to devote five more troops than Brett's strategy to each of castles 8, 9, and 10 in the hopes of outmaneuvering all of the Brett, anti-Brett, Cyrus, and anti-Cyrus strategies. I anticipated a flight from castle 7, which has a disproportionate number of troops but left a decent contingent there to mop up those who avoided the castle entirely. Castles 1 through 6 remain mostly unchanged from the first battle."
0,5,6,8,12,22,3,31,6,7,"Just a variant of the strategy I did last time. This time I am fighting for castles 6 and 8 and hope to pick up others that are not well defended. I expect people to put fewer 0,1, & 2, for castles on 9 and 10 and more 3, 4 and 5."
6,5,0,0,0,0,0,37,32,20,"heavy investment in most valuable positions, with some investment in least competitive battlefields"
@@ -228,7 +227,6 @@ d) My strategy loses against (10,10,10,..,10) but I don't think that is importan
1,2,7,13,14,16,5,24,9,9,"The equilibria of the previous tournament are almost ludicrously nonlinear. My approach is to start from the previous tournament's submissions (human nature hasn't changed much in the past few months) then add in the obvious strategies - a few dozen copycats of the top five and about a hundred copies of strategies tailored to beat the previous tournament (the best one I could find was 6-6-7-11-12-21-26-2-4-5). Once I found an optimal solution, I tweaked it some more. It's nothing like the Nash equilibrium strategy will look like; but a Nash equilibrium usually winds up in the middle of the pack and I want to win. Banzai!"
0,5,7,9,12,22,2,31,5,7,Modified basic data; optimalization.
5,6,11,12,12,16,4,4,4,26,"Punt on 7, 8, 9. Try to win the rest."
5,7,9,11,15,6,4,6,17,18,Intuition?
0,0,3,9,12,22,6,32,8,8,"Tried to place the numbers to fall in the abandoned distribution points. Either just ahead of the low end or just ahead of the high end. And I want Castle 8, 6, & 5 with the hope to steal 9 or 10 or (7 + 3 or 4)."
2,3,4,11,14,22,26,5,6,7,Modified the winners strategy but gave up on 8 and put more resources elsewhere. Figured a lot of people would follow the old results.
1,7,8,11,13,2,28,3,13,14,"I expect the ""abandon 9 and 10"" strategy to not be as widespread this time, so substantial resources have to be deployed there this time. I chose to abandon 8 and 6 with half-effort in 10 and 9 - the goal is to beat the people who mostly abandon 10 and 9, and split with people who fight hard for just 1 of those two castles."
@@ -246,7 +244,6 @@ d) My strategy loses against (10,10,10,..,10) but I don't think that is importan
2,6,9,9,12,5,5,5,14,33,Avi Mahajan
4,7,4,6,13,14,14,6,19,13,I assume the bulk of players aren't going to change their strategy. I then select levels that seem to be just to the right of a large area of the curve.
6,4,13,10,12,14,5,11,15,10,"This troop deployment was quasi-random with a slight bias towards low-value castles and a bigger bias towards high-value castles, mostly ignoring medium-value castles, since those will probably be hotly contested."
0,2,9,12,15,2,2,2,27,27,An adaptation of the previous winner's strategy.
7,8,10,13,14,3,7,20,7,11,Totally random distribution
4,5,7,11,15,18,24,4,6,6,"You only need 28 points to win, so I know that 1-7 equals 28 and I went for it."
2,2,9,2,7,6,27,19,10,16,geddylee1717@yahoo.com
@@ -362,7 +359,6 @@ I hope this split will grant me the extremes values of 10, 8, 2, 1 more often th
1,1,3,11,4,13,16,8,34,9,"(Please use this submission over the earlier one I submitted if only one submission is allowed per person) A correction to my earlier submission which ensures that I beat the winning distribution from the last competition (a likely choice for people who don't want to invest a lot of effort). Otherwise the main argument is the same - win at least one of top 3, spread out troops amongst all castles, try to capture a lot of the middle (4/5/6/7)."
0,7,8,6,13,9,6,35,11,5,Random solution meant to help my initial submission.
5,5,7,7,12,12,3,23,13,13,"I chose numbers like 13 and 12 in hopes of beating people who chose flat numbers, and beating people who went 1 over to beat flat numbers."
4,4,4,20,15,25,3,2,15,7,"i did it really quickly, almost randomly."
0,0,0,11,11,17,21,18,11,11,Fight for the big points.
1,7,5,4,17,8,2,13,8,35,GA battling itself. The top half is based on the best solutions and the bottom half of the population is random.
0,1,4,6,8,12,24,32,6,7,Arbitrary and malicious
@@ -532,7 +528,6 @@ I know some people will do that, and they likely will have run simulations and d
0,7,8,6,13,9,6,26,20,5,Random solution meant to help my initial submission.
5,5,0,0,0,0,0,30,30,30,Banking on people neglecting the highest point castles
3,4,5,9,13,10,16,29,5,6,Think people will model similar to last round so tweaked a little off that
1,1,6,6,6,6,17,32,17,6,Otautau
4,16,4,16,16,4,16,4,4,16,"Based on the previous results, it seems like there were a lot of instances where people placed a token 2-3 on castles that they did not see as decisive to their chances. So I decided to place a minimum of 4 on every castle hoping to be able to win against people who are taking a more concentrated approach. I donŠ—Èt think putting an even distribution of straight 10s is going to work because itŠ—Ès an easy strategy to counter. So I decided to arbitrarily select a pathway to 28 points (2+4+5+7+10) to be my concentration, trying to sidestep the relative popularity of 8 and 9, and evenly distributed the remaining soldiers to these five locations. I also made sure that my combination would at least beat the last winning combination, in case a bunch of people try to submit that strategy in particular. I doubt it will work, but it would be amusing if it did.
"
3,3,3,3,17,30,3,3,30,5,"My strategy is to stay one game theory step ahead. This time, I think stategies are going to converge. People will mimic the prior winner's and/or use the first dataset to develop and test strategies. I did exactly that, developed a set of strategies that did well against the first dataset; then I developed a strategy to beat those strategies."
@@ -571,7 +566,6 @@ With more time I might be able to find a more optimal strategy. looking just at
4,5,5,1,10,15,20,25,7,8,2cd level counter to the winning deployment previous.
0,6,7,12,12,21,3,31,4,4,"I ran a genetic algorithm to identify the optimal strategy based on prior submissions. If people deploy troops in a similar way this time, this strategy should perform well."
3,6,9,10,16,18,25,5,3,5,"Troop deployment was broken down by a number of factors. The risk/reward of placing a high number of troops for a x amount of points, the percentage chance with respect to past data on winning a battle for a castle with a certain number of troops, and the distribution of troop placement in the previous event."
3,4,5,10,2,17,20,26,6,6,Leave a decent chance to beat people how put 0-1 soliders in each castle.
5,7,0,0,0,0,22,22,22,22,"Top 4 castle get all the troops, higher than 20 deployment of the higher points castles to beat anyone else using my system, and another one added to beat those following my system with only one iteration. No point wasting troops on lower point castles, leftovers given to them to maybe snag a few points"
4,3,2,16,3,21,21,6,3,21,Assumed most people would avoid the castles that were ignored in the previous riddler in fear of others thinking they would be the obvious option.
0,0,3,6,13,9,6,23,35,5,Random solution meant to help my initial submission.
@@ -602,11 +596,9 @@ If this allocation was used in the previous tournament, it would have won 1272 b
I am making a (faulty) assumption that this tournament's distribution of group allocations will be the same as the previous tournament's distribution. We'll see if that assumption is good enough or if what worked last time no longer works."
1,1,1,15,21,22,5,24,5,5,No real strategy. SAC
0,6,7,12,12,21,3,32,3,4,someone told me this was a good combination
3,8,3,4,5,7,3,21,20,22,Random simulations
5,7,9,2,2,13,27,2,28,5,"Get to 28 points, by not conceding any castles but take avantange of others willingness to do so. Predicting 1-3 and 10 as most likely to be conceeded. Predicting 4-9 to be the highest invested in, I placed troops in a way to get the most points out of the middle numbers. Hoping that when I get beat for the middle numbers, I'll get castle 10 and 1-3, and when I win 6,7, and 9, I can win 1-3 or 10 to get me over the top."
0,0,0,0,5,30,10,40,5,10,idk
8,2,2,2,2,2,2,22,26,32,"There are 55 points available, so the way to win is to get at least 28 points. One way to get to 28 points is to get the three most valuable castles (8-10) and least valuable (1) castle. I put 2 soldiers at the other six to ensure a lone soldier can't capture them."
4,4,6,6,16,17,17,12,6,6,"gut feel alone, baby"
3,4,5,4,4,4,32,34,4,6,"4 is more than most are willing to use as token forces, also other reasons"
2,0,3,0,0,0,0,33,31,31,"Go for broke. Win 8,9,10 and either 1 or 3."
1,1,2,3,20,3,3,3,31,33,Deploy to beat my best startegy.
@@ -621,11 +613,9 @@ I am making a (faulty) assumption that this tournament's distribution of group a
3,5,6,10,9,18,24,12,8,5,"It was somewhat random, but I tried to use a general's intuition as to where my troops would be most needed."
1,3,5,9,11,13,17,18,12,11,"I wanted to cover 10 on most of the top castles. 8&7 seem underguarded, so I want to capture these. Hopefully I can win either 10 or 9, as well as 5 or 6 to win the game! I think this is a good distribution, I started with the number of the castle for each, and then I added with my intuition, with trying to get just enough to carry. If I do well though (like 60% or better) I'll be impressed."
6,6,6,6,6,6,6,46,6,6,Trying to steal a few other castles from most strategies that only send a few to 5-6 castles and loading up on the most popular choice
2,3,6,8,10,25,20,5,15,5,"I predict that people will still not send too many troops to castle 10, but more than before. Same for castle 9, but more so because it was undervalued last time. I think castle 8 will garner many more troops than last time, and so I will not waste troops there. Castle 7 and castle 6 might be overlooked... And the rest just a little to get a few extra points here and there."
3,3,3,8,15,25,31,2,5,5,"Most of the focus is on 7 and below, with some reserve troops on the high numbers for easy points if my opponent gives up on those completely. I figure most people taking the easy point strategy are going to go with 3 or 4 troops, so I lose some strength on the 8 and low numbers to get 5 on the 9 and 10."
4,4,0,0,0,0,0,27,31,34,"Win 8, 9, and 10 outright and either 1 or 2. This wins me 28 or 29 out of 55. Hope that others put their troops in the middle."
0,0,2,2,11,21,3,31,26,4,Brute force computation finding a deployment that did better than all of the entries in the last contest. I've described this here: http://blog.rotovalue.com/fighting-the-last-war/
0,12,6,3,1,28,32,1,5,11,Random solution meant to help my initial submission.
3,6,0,3,11,11,18,13,17,18,Because the prophet muhammad speaks through me
0,0,0,0,20,25,0,25,30,0,I wanted to consolidate my troops on the lowest possible combination to reach 28 pts.
2,2,2,2,2,13,26,2,24,25,"I considered the distribution of scores from the first time, and decided to give up on any major point getting on the first 5 castles. Instead focusing on four of the top 5 castles. I essentially randomly chose 8 to send a scouting party to (just in case) and leaned into castle 7, 9, and 10."
@@ -691,7 +681,6 @@ Based on these two principles, I think the best opportunities for points are Cas
2,6,8,8,16,17,13,21,2,7,"I put several on each castle to beat anyone who chooses to put none. Then, I selected some of the middle ground castles to get a good number of points up on."
2,4,4,12,17,23,27,3,4,4,"This is my don't overthink it too much battle plan. I figured out how many points each entry would score, and then took the top 699 entries (total points, not Winning percentage). I eliminated entries that used less than 100 soldiers and had 690 entries. Then, through a bit of trial and error, I think that I successfully maximised the amount of points a battle plan could earn against those soldiers. On to round 2."
4,4,4,5,12,12,23,25,6,5,"I considered the distribution results of the last war, assuming the distribution would remain pretty consistent. I chose a number that would beat most opponents no matter the point value of the castle."
0,0,6,8,0,17,19,0,23,25,"My plan was just to focus on getting 28 in some way. Basically, I took the proportional power of 10 (10/55, or roughly 18), and then add half of what I am sacrificing by ceding castle 8. I would give the other half to castle 9, along with its proportional power. Repeat the same for castles 5, 6, and 7, but this time, I also added the men I would originally have put in castle 1. Repeat the same for castles 2, 3, and 4."
2,2,0,8,5,19,14,20,14,16,It seemed robust against a variety of counter strategies.
2,3,4,5,11,11,20,31,8,5,I wanted to win.
4,1,6,4,1,1,19,30,19,15,I just want to win... and be victorious... and have my name live in GLORY ON THE 538 WEBSITE!! ARE YOU WITH ME?!?!!... AHHHHHHHHHHHH!!!! ~|--------------->
@@ -738,7 +727,6 @@ After 1000 tournaments, I had 1000 tournament winners. I played a final tournam
The winners of ""normal"" tournaments are mostly of the form, with a few castles heavily fortified and several with less fortification. But the winner of the ""tournament of champions"" is always of the form, with 28 points worth of castles heavily attacked and a few stray troops sent to other castles. So this seems to be a strategy to use when the other strategies have been ""battle tested"" to at least some extent.
"
3,3,9,3,3,3,22,23,3,28,"Need 28 points to win, 10+8+7+3=28. After distributing 3 soldiers to each castle, I was left with 70. I distributed the remaining 70 troops between my 4 vital castles by determining their importance. 10/28=35.7%. 35.7% of 70 is 25, so I added 25 troops to castle 10."
0,5,2,10,11,3,28,3,3,34,Need to get to 28. 10 + 7 + 5 + 4 + 2 = 28
2,2,2,4,20,20,20,20,5,5,"went for the middle high ones in hopes of winning more of those over people who went for the high values, but still wanted a chance at winning other castles"
4,4,13,17,23,23,4,4,4,4,Follow your heart to the very end
2,5,6,6,6,10,18,19,17,11,I asked my cat
@@ -752,7 +740,6 @@ The winners of ""normal"" tournaments are mostly of the form, with a few castles
1,5,4,5,5,12,10,15,16,27,"I am predicting others will try to emulate the previous winner's allocation, or try to -beat- the previous winner's allocation. I am trying to beat both of those pools of players at once."
2,2,6,6,11,11,16,16,21,9,"Roughly scaling with number of points (except for the last castle, which I figure people will either go for or not, so I just dumped the extra there). Hopefully people like round numbers (i.e. multiples of five) so I mostly made mine multiples of 5 plus 1 to try to edge people out. To glory!"
0,0,3,3,4,22,27,32,5,4,"I'm trying to one-up the last Riddler Nation Battle, then one-up that one."
1,6,7,12,12,21,2,31,3,4,Compared to previous winning distribution graph
4,6,9,11,15,21,26,1,3,4,i just want to win i have no plan to rule
0,0,0,1,7,20,3,13,28,28,"I chose this deployment because it gives me a high chance of winning. It is a lovely solution mathematically. Also, because I plan on getting a shout out, I would like to say ""I love you"" to my mother, Debbie Firestone in Tulsa, Oklahoma. Hi Mom!"
0,0,0,0,25,25,0,25,25,0,Maximise each soldiers worth so I have no wasted soliders in any battle that the match does not depend on. Maximise my force where it is needed.
@@ -781,11 +768,9 @@ The winners of ""normal"" tournaments are mostly of the form, with a few castles
4,4,4,4,4,4,34,4,34,4,Looks like 4 troops will winna castle most of the time. Put the remaining 60 troops randomly around in batch of 30.
3,4,6,2,22,23,28,4,4,4,Win or bust
4,6,8,10,15,22,27,2,3,3,"This is an adaptation of last tournament's bronze medalist (Brett Seymour's) strategy of punting the last three castles in favor of winning the first 7. I've slightly adjusted for the metagame, so to speak, by including 3 soldiers at the 9th and 10th castles, to anticipate many people placing 2 at each of these based on last tournament's results."
1.1,3.1,5.1,7.1,9.1,10.1,12.1,14.1,16.1,22.1,Weighted by value of castle with remainder added to Castle 10. Fractional troops to achieve victory where otherwise it would be a tie. Hopefully the programming allows that. Whole number troops may be assumed but not stated and not necessary in real life (roving soldier).
3,5,7,9,2,13,26,3,28,4,Another variation on the last winning strategy.
4,4,4,4,7,23,23,4,23,4,no
2,4,4,4,4,4,4,4,35,35,"Win 9 and 10 almost all the time, and hope to get the remaining needed points from putting 4s in the rest."
0,1,8,8,1,3,17,20,18,18,Just ran a random simulation and this won
0,4,5,9,10,4,28,32,4,4,A few more than the prior winner on the more valuable castles and a few less at the less valuable castles.
2,4,4,4,15,3,28,32,4,4,"I wanted to counter anyone who added a single troop to each of the big castles from the prior winning strategy. So, I added 2 troops to castles 5-10, and removed some from the lower castles."
8,9,10,11,12,15,3,15,0,17,eh
@@ -841,7 +826,6 @@ The winners of ""normal"" tournaments are mostly of the form, with a few castles
0,0,2,12,15,3,28,32,4,4,"Two above all winning deployments from last time, to get the troops I reduced the low value castles"
0,0,0,0,0,0,25,25,25,25,"In round 1, the higher castles were taken by much lower #s of troops. I'm going for the big ones."
1,1,1,1,1,19,22,24,27,3,"I want to win castles 6-9 because that adds up to 30 points, which wins automatically"
0,0,0,11,11,14,15,17,11,11,Be above average where point are above average.
2,2,3,3,4,4,20,20,21,21,Big Points!
1,1,7,10,12,15,2,25,2,25,Gut feeling
0,1,0,1,7,12,12,6,26,35,"I first created a randomized 2000 king tournament. I submitted the winner of that tournament but then realized an error in my ways, the randomized version created some deployments that would not be used by anyone. So I culled 50% of the deployments and re-ran the tournament, then culled 50% again etc. Until there was one clear champion."
@@ -870,7 +854,6 @@ The winners of ""normal"" tournaments are mostly of the form, with a few castles
6,7,10,13,16,20,28,0,0,0,I need 28 points. I'm going to take a high risk strategy of only trying win the 7 least valuable castles. And I'm going to make sure I have more troops at everyone of those than our last genius military strategist.
2,2,2,7,7,13,16,16,17,18,Because I'm the best there is. Plain and Simple. I wake up every morning and I piss excellence.
9,21,10,3,1,10,13,16,8,9,Random Number Generator
1,2,2,12,14,22,28,11,3,4,"I missed my chance to submit an answer in round 1, so this distribution is similar to what I would have submitted, with some minor adjustments based on the posted results. I focus on castles 4 through 8 because capturing them yields 28 points (a majority) and I assume many entries will focus on castles 9 and 10. Based on how hotly contested castle 8 was in round 1, I've shifted soldiers away from it and toward castles 4-7, 9, and 10. I've left a respectable force on castle 8 to counter strategies that leave it mostly empty, though. I've also shifted soldiers from castles 1-3 to the center, though I've left some stragglers to capture easy targets."
4,6,8,8,7,9,24,25,4,5,1/3 of my soldiers for Castles 1-5 and 2/3 of my soldiers for Castles 6-10
1,1,3,3,3,21,25,4,4,35,To get the castles 10/7/6 and maybe pick up a random other castle to round things out. And to defeat Cyrus. Down with tyranny
0,1,11,12,2,17,23,28,3,3,Win 5 castles worth 28 vp and make token bids for un-contested castles. Seems to be a local maximum against published strategies.
@@ -896,7 +879,6 @@ But I didn't go exactly the efficient route. I slightly overweigthed 2,5-8 beca
So this time I flipped that on it's head. Nice and simple. Go for the highest value castles (and castle 1) so that my point total, if I win them all, is 28, the minimum necessary to win."
1,1,2,5,6,6,4,20,25,30,because theres more pts in 7-10
1,4,5,9,15,15,20,20,1,10,Focusing in the middle
3,3,4,4,13,16,19,22,5,5,Gerrymandering + Expected value
0,0,0,10,0,0,0,30,30,30,"Have to win 28 VP, so go all in on the top 3 and then go for #4 as a random guess."
0,3,3,1,4,6,19,17,21,26,The strategy is to be correct.. and to be correct more than your enemies... and for 538 to give me a shout out as having won more than 95% of the matchups. BOOM BABY!
1,1,1,1,1,15,20,15,25,20,Looking at the previous year's deployments I realized that people did not go all in on the higher level one. My plan is to hopefully win 3 out of the top 5 and then hope that i get a few points from the bottom 5.
@@ -911,7 +893,6 @@ So this time I flipped that on it's head. Nice and simple. Go for the highest va
1,3,5,7,9,11,13,15,17,19,Proportional to possible points.
1,3,5,7,9,11,13,15,17,19,(2* number of points the castle is worth) - 1
0,0,0,7,11,21,22,31,4,4,tested configurations against previous submissions data set
0,1,3,20,25,30,4,4,4,5,Hoping for cheap wins on high-value castles vs low-allocations from opponents.
0,0,4,4,4,4,4,36,40,4,Targeted two wins and picked the rest to counter other targeted strategies.
2,3,4,7,11,11,18,21,18,5,"Looking at the averages, medians of the original dataset, I figured this would beat those who looked at the data set and try to beat the averages and medians. I think studies have shown most people don't go more than 2 steps out? So this is my two step out answer."
0,17,11,17,8,28,3,7,5,4,Random solution meant to help my initial submission.
@@ -920,7 +901,6 @@ So this time I flipped that on it's head. Nice and simple. Go for the highest va
1,3,5,7,9,10,12,14,19,20,analysis
0,4,7,9,10,0,0,0,30,40,High risk- high reward. Gotta lock in those big points then have enough of a chance to win the smaller castles to move past the 50% of available points needed to win.
4,4,4,1,16,11,21,2,2,35,Beats virtually any strategy? Maybe no.
2,4,6,3,10,10,3,18,19,20,"I focused on a capturing few set of casles that would put me over 28 points, with a few spread out in case my enemies were more concentrated than I, and tried to selected castles I thought would have been undervalued or avoided."
0,5,6,9,15,1,26,31,4,3,"Downloaded GitHub data from battle #1, ignored plans that were ""clear losers"" (couldn't score 28 points, didn't use all 100 troops, etc.), and optimized over the remaining 1313 plans. This deployment scored 1176 out of 1313 (1169 Wins, 14 Ties, 130 Losses). Can't say this is the best vs. those 1313, could be a local maximum rather than a global, just the best I could come up with."
4,6,9,11,14,17,30,5,2,2,"Focusing on winning the bottom 7, with a few troops on the top 3 to beat people with a similar strategy"
7,0,0,5,0,15,24,19,14,16,"Took starting point of old, using simulation against those answers to create some possible responses, then created a response to those"
@@ -951,7 +931,6 @@ So this time I flipped that on it's head. Nice and simple. Go for the highest va
11,11,19,19,20,5,4,1,5,5,We'll see?
1,2,6,6,12,13,31,21,4,4,Looking for dropoff points: https://github.com/nabraham/538-riddler/tree/master/2017.05.19_classic_battle
1,1,1,1,1,5,15,25,25,25,Best Placement
0,0,1,4,11,21,26,21,11,4,"It's a normal distribution centered around castle 7 based on last round's battle for Riddler Nation, arbitrarily spread ~5 to hedge my bets"
0,0,0,0,0,0,20,23,27,30,because no-one did it last time and I am curious if people will repeat that
1,1,1,1,1,18,19,19,19,20,"Last time, a ridiculous number of people split their troops evenly among the ten castles. Beating that strategy should earn a bunch of points in the head-to-head matchups."
5,7,9,11,15,21,25,2,2,3,"I analyzed the previous submissions and looked for patterns, then built a tool that let me try different combinations. I noticed that you usually needed to be able to 'pick' one or two castles from other leading submissions. This variant, 'pick'ing castles 6 and 7, had the best win total against the previous generation. While it loses to the ""classic"" solutions of 10s across the board and maxing 1/8/9/10, because of how obvious those solutions are, nobody actually ever chooses them."
@@ -971,9 +950,7 @@ So this time I flipped that on it's head. Nice and simple. Go for the highest va
2,4,7,9,12,2,27,31,3,3,"Looking at round 1 winner, just increased 1 troop to castles 6-10 and reduced 1 troop to castles 1-5. I hope the small trade off may pay out significantly."
2,2,6,2,10,18,26,26,4,4,"Last time I got really close to winning, so I'm going to switch it up a little bit and stick with the same strategy. Trying to win all the ones people throw away and then if people spread out too much trey and beat them too."
1,3,7,11,16,16,16,11,18,1,"Modified my previous submission, which would have fared quite well against the top-performers. But because I think a lot of people will change their strategy to compete against the last version's winners, I have zigged to their zag."
2,4,7,10,13,0,26,30,3,4,Minor tweaks to the previous winning strategy
0,3,5,17,17,17,17,17,5,2,Almost random ;-)
12,5,9,13,16,7,15,9,13,0,Because you asked me to.
0,0,1,16,20,20,18,19,3,3,Used a genetic algorithm to optimized based on previous reader responses (http://htmlpreview.github.io/?https://github.com/kloppen/riddler-castles/blob/master/solution.nb.html)
1,1,1,2,2,14,23,23,30,3,"To start off, it appears that for every castle, 30% of people did not send any troops there, so it makes sense to send a single troop to every castle.
@@ -1055,7 +1032,6 @@ It's not the winningest hypothetical from last round, however. (That was 0,5,7,1
1,1,3,9,18,23,22,19,1,3,"Reviewed all previous historical data to produce a model that would win the highest % of times. From there, knowing that many would use the same approach, and likely the same (somewhat simple) tools - the excel solver, I tweaked my final answer to beat the solution I found in the first step."
1,3,6,2,3,21,26,31,3,4,"Always include at least one, when possible go over multiples of 5 (higher concentrations shown there), don't sweat 9 and 10."
4,6,9,14,18,21,25,1,1,1,Tried to win the bottom 7 castles.
3,5,9,9,12,1,27,28,2,3,"Based on the previous strategy, I tried to improve it"
2,5,8,10,13,1,26,31,2,2,Slightly adjusted plagiarism.
2,5,8,10,13,1,26,31,2,2,previous winner solution++
0,18,18,1,1,1,1,20,20,20,To get 28
@@ -1073,7 +1049,6 @@ It's not the winningest hypothetical from last round, however. (That was 0,5,7,1
2,5,6,12,14,1,25,31,2,2,"Modified version of last winner, optimized against all previous entries"
3,4,4,7,10,13,25,28,3,3,At least 3 troops in each. Heavier near higher value.
2,5,8,11,14,17,20,23,0,0,"You need 28 points to win each engagement. I'm expecting most people will deploy their greatest number of soldiers to the highest-point castles. My intent is to concede those and instead deploy my soldiers to the lower-point castles, where each soldier should have greater incremental value. If one could consistently win castles 1 through 7, that would be just enough points to win the battle. I've decided to contest castles 1 through 8."
1,9,1,9,9,1,20,20,20,5,"Cede some, win some."
2,2,3,3,2,2,26,30,27,3,"Using prior competition data, largest area under the curve I could achieve without higher maths. (I used excel and simulated competitions)"
1,4,13,14,1,1,20,23,22,1,"Going for close wins and major losses. Hoping to win 7-9 and 3&4. Will lose to opponents who used more than placeholders anywhere, but hopefully get lots of wins in the two groups that can help reach 28."
1,2,2,3,11,21,22,32,3,3,Just take the points
@@ -1130,7 +1105,6 @@ It's not the winningest hypothetical from last round, however. (That was 0,5,7,1
0,12,12,12,12,12,0,40,0,0,"Last time I tried to minimize the number of castles needed to get 28 while getting as close to 28 as possible with some soldiers in other castles to pick up stragglers. This time I went for more castles than the minimum needed and didn't go for any stragglers to try and maximize my chance at my win condition. If I only go for what I need and someone else goes for stragglers, then I have more soldiers to work with where they count. Maybe."
13,21,5,5,14,16,10,8,5,3,"It looks like people left castle 10 open last time, so I put troops there, however, as most people will likely see that, I focused my efforts on the also under-exploited castle 9, while still spreading troops in order to pick up other castles."
4,6,8,2,16,0,28,32,2,2,to win. rp
0,0,10,10,12,12,26,26,0,0,I thought of a couple common strategies that I would like to beat and came up with this.
1,2,2,2,2,2,11,1,26,51,"This allows me to take advantage of those who completely ignore 1-6, and I believe the n+1 strategy will outfox likeminded competitors on castles 9 and 10. By essentially giving up competition at castle 8, I am making myself much more competitive for castle 7."
6,11,11,11,2,21,2,32,2,2,Blind Guess
2,1,5,4,48,5,19,5,2,9,I created a random plan generator that kept track of the best point expectation out of a small number of attempts. Then I ran it many times. The one that survived I tested against many random troop deployments.
@@ -1149,15 +1123,12 @@ I probably have no shot, but this is an interesting exercise, and I like seeing
4,4,31,25,3,9,9,8,5,2,Went a bit bigger than the winner's choice on the big castles and a bit smaller on the small castles.
2,2,2,30,30,20,5,5,2,2,middle castles will be underplayed
10,2,4,27,13,20,0,6,17,1,Random solution meant to help my initial submission.
28,1,17,6,5,4,3,9,2,21,Random solution meant to help my initial submission.
4,4,25,22,22,2,4,3,2,2,Wanted to see what would happen.
0,0,35,0,6,0,33,3,2,21,Random solution meant to help my initial submission.
1,1,2,2,2,6,6,4,3,73,(see my other try)
2,0,2,4,2,5,1,3,11,70,"Mostly ignored the previous tournament, though probably not a good idea because there are many ""joker players"" (players aiming only to create noise, with no intention to win, which quite unfortunately makes this more of a guessing social experiment, than a mathematical one). A simulation suggests that optimal mixed strategy should be randomising a plan around having some 50-80 men on castle 10, 0-25 on 9, 0-20 on 8, 0-10 on 7, and so on down to 0-3 on castle 1. This is one such random plan."
19,17,15,13,11,11,8,6,0,0,"I took the amount of points available and divided that by the number of troops so you'd get even troops per point available, and I rounded up and took some points from the bottom to reinforce the higher point value castles"
7,8,1,13,32,30,7,1,1,0,Random solution meant to help my initial submission.
0,4,31,27,14,0,12,8,3,1,Trying to defeat the winner from last round
3,0,0,7,12,4,2,12,5,5,Cuz
12,15,20,24,2,2,22,1,1,1,Wild Guessing
22,27,27,5,4,5,4,4,1,1,"I tried to hit as many high value castles while simultaneously giving myself a decent (>25%) chance of getting the smaller castles. I looked at last time's data and tried to stay out of the ""no-man's land"" where additional troops wouldn't have made a difference against most opponents"
0,0,0,0,0,0,7,0,32,61,Game theory is hard.
@@ -1168,11 +1139,10 @@ I probably have no shot, but this is an interesting exercise, and I like seeing
1,1,1,1,1,1,1,1,1,91,Why not.
1,1,1,1,1,1,1,1,1,91,HOLD THAT L!!
31,26,23,11,2,2,0,2,3,0,Because I like being right... and I can see the future. Crown me the victor 583!
1,1,1,1,1,1,1,1,1,1,bcs
0,0,0,0,0,0,0,0,0,100,"Because I am hoping nobody else would send 100 troops to castle ten, because they want to have stake in everything, or something else. They also wouldn't be stpid enough to take this calculated risk, like me. It is also hard to amass 10 victory points by a combination."
0,0,0,0,0,0,0,0,0,100,Just to see what happens
34,30,30,0,0,0,0,0,0,6,The top 3 castles and any other castle will win it. This strategy allows me to big bid on the high value castle.
32,26,23,0,19,0,0,0,0,0,"The deployment aims to get 3 out of four of castles 10,9,8,6, which always gives you over 23 points. I believe most people will spread their troops more evenly."
35,30,30,0,0,0,0,0,0,5,"You only need to win the top 3 castles and the last castle to claim victory (~51% of total points) and since these castles were way underdeployed last time, a big shot in the arm should be enough to take each of them. Since I am completely abandoning the rest, I should be able to over deploy the rest and win the castles that matter."
0,0,0,0,0,0,0,0,100,0,"Someone will try going for 10, just sending all their troops there. Heck, many people may try that. I want to guarantee to get castle 9, and hopefully split it among fewer people."
100,0,0,0,0,0,0,0,0,0,i am guaranteed one point
100,0,0,0,0,0,0,0,0,0,i am guaranteed one point
1 Castle 1 Castle 2 Castle 3 Castle 4 Castle 5 Castle 6 Castle 7 Castle 8 Castle 9 Castle 10 Why did you choose your troop deployment?
60 3 5 8 3 10 15 12 15 12 23 22 5 11 5 7 6 7 17 8 I spent way too much time running genetic algorithms to do well against the strategies that did well last time, and then eventually randomly settled on this. I focused exclusively on the top five performers of the previous competition. I noted that among those competitors, the ordering was Brett>Jim>Ken>Lukas>Cyrus (ironically, Cyrus placed last among that group). I then assumed that this round's strategies would include the following: Brett clones, anti-Brett strategies, Cyrus clones, anti-Cyrus strategies, "7 and 8 avoiders", and old, ineffective strategies. Most of what followed was guesswork and I only spent about ten minutes actually dividing up my troops. I quickly decided to devote five more troops than Brett's strategy to each of castles 8, 9, and 10 in the hopes of outmaneuvering all of the Brett, anti-Brett, Cyrus, and anti-Cyrus strategies. I anticipated a flight from castle 7, which has a disproportionate number of troops but left a decent contingent there to mop up those who avoided the castle entirely. Castles 1 through 6 remain mostly unchanged from the first battle.
61 3 0 8 5 10 6 12 8 12 22 11 3 7 31 7 6 8 7 I focused exclusively on the top five performers of the previous competition. I noted that among those competitors, the ordering was Brett>Jim>Ken>Lukas>Cyrus (ironically, Cyrus placed last among that group). I then assumed that this round's strategies would include the following: Brett clones, anti-Brett strategies, Cyrus clones, anti-Cyrus strategies, "7 and 8 avoiders", and old, ineffective strategies. Most of what followed was guesswork and I only spent about ten minutes actually dividing up my troops. I quickly decided to devote five more troops than Brett's strategy to each of castles 8, 9, and 10 in the hopes of outmaneuvering all of the Brett, anti-Brett, Cyrus, and anti-Cyrus strategies. I anticipated a flight from castle 7, which has a disproportionate number of troops but left a decent contingent there to mop up those who avoided the castle entirely. Castles 1 through 6 remain mostly unchanged from the first battle. Just a variant of the strategy I did last time. This time I am fighting for castles 6 and 8 and hope to pick up others that are not well defended. I expect people to put fewer 0,1, & 2, for castles on 9 and 10 and more 3, 4 and 5.
62 0 6 5 6 0 8 0 12 0 22 0 3 0 31 37 6 32 7 20 Just a variant of the strategy I did last time. This time I am fighting for castles 6 and 8 and hope to pick up others that are not well defended. I expect people to put fewer 0,1, & 2, for castles on 9 and 10 and more 3, 4 and 5. heavy investment in most valuable positions, with some investment in least competitive battlefields
6 5 0 0 0 0 0 37 32 20 heavy investment in most valuable positions, with some investment in least competitive battlefields
63 6 6 9 11 13 16 8 8 9 14 I assumed that the distribution would change a little from the previous round but not a whole lot. For the top castles I chose values a few more than what would have done well earlier. For 7 and 8 I went much lower than the winners of the previous round but still a reasonable amount. Then I went down from 6-1.
64 4 6 4 11 12 4 9 4 34 12 My first strategy was similar to the winner, but not quite as good. Seeing the distributions this time, I went for a more uniform distribution. I started with 4 at each castle, which is enough to win a lot of battles since some castles will have few soldiers so others could be loaded up on. Then, I shifted my remaining 60 troops to ensure that A) I could beat a equally distributed soldier allotment, B) I could beat someone who loaded up on the top 3 or 4 by most likely winning castle 9, and C) I could beat the previous winner.
65 1 0 9 12 15 4 21 5 28 5 Last round, many people who did not commit many troops to an attack sent fewer than four or five. My five each on castles ten and eight, and four on castle six could gain a large number of points against such players for a small price. The last winner committed most of his troops to castles totaling 30 points. I decided to try a similar number. I tried to avoid overinvesting in large castles because the last winner's arrangement suggested that people did so last time.
227 5 2 1 6 1 7 0 11 0 2 0 2 0 2 31 2 31 33 31 33 One needs at least 28 points to win. My first thought was to focus on the middle range -- castles 4 through 8, but then realized this could easily fall to a strategy that focused only on castles 10, 9, 8, and 1. The goal isn't to maximize your expected score, it's to maximize the number of times you score 28 or more. Looking at the overall distribution, this distribution looks like it will win a good portion of the time. I throw a soldier to 2 and 3 in case somebody beats me out for castle 1. Based on everyone targeting the 6-8 range last time, I decided to go all in on 9 and 10. If you lock those 2 up, then you only need another 9 point to win. I decided to target 4-3-2 to get those points. 2 points were put on all remaining numbers in order to guarantee a win on the rare 0 or 1 someone else puts up.
228 0 2 6 2 7 14 11 3 12 2 21 22 3 31 19 4 5 Always leave the most number of doors open. A bit modified basic game from the data with optimalization
229 1 0 1 0 9 11 11 14 16 11 3 15 21 12 3 15 31 11 4 I ran 29 random and weighted-random scenarios and optimized for maximum wins. This configuration along with some minor variations won 28 of 29. assumed people would gravitate to even castles, and round numbers.
2 6 7 11 2 2 2 2 33 33 Based on everyone targeting the 6-8 range last time, I decided to go all in on 9 and 10. If you lock those 2 up, then you only need another 9 point to win. I decided to target 4-3-2 to get those points. 2 points were put on all remaining numbers in order to guarantee a win on the rare 0 or 1 someone else puts up.
230 0 8 6 8 7 12 11 16 12 1 21 12 3 2 31 2 4 19 5 20 A bit modified basic game from the data with optimalization This whole strategy is entirely centered around beating people who try to use the predominant strategy from last year, while also attempting to beat most other teams. Since middle road castles like 8, 7, (6ish), and 5 were heavily contested by these competitors, I'm only sending several troops to each of these so no one gets any points for just sending 1 there, except 5 which they can tie. I then send 11 to six to beat those who only send 10 or less while not sending too many there as well, while sending 18 to 10 and 9 to guarantee their capture. That leaves me 48 troops for castles 1, 2, 3, and 4. So that would be 12, evenly divided, but I'm taking some away from 1 and 2 to bolster 4, so 1 will be 8, 2 will have 8, 3 12, and 4 20. Since I don't like sending the most troops to 4, I'm gonna make it 16 and send those extra 4 to 10, 9, and 6. Yippee.
231 0 3 0 5 11 7 11 16 16 13 3 21 21 22 3 31 5 4 5 assumed people would gravitate to even castles, and round numbers. Using the data from the first challenge (and my primitive Excel skills), I built a spreadsheet that helped me simulate battles against the original batch of responses. I used this to come up with several different deployments that were more successful than the first round's winner. I then identified, to the best of my ability, a deployment that allowed me the most wins against the original data while also beating all of the "optimized" strategies I identified for the first round.
232 8 4 8 6 12 8 16 11 1 11 12 10 2 13 2 11 19 14 20 12 This whole strategy is entirely centered around beating people who try to use the predominant strategy from last year, while also attempting to beat most other teams. Since middle road castles like 8, 7, (6ish), and 5 were heavily contested by these competitors, I'm only sending several troops to each of these so no one gets any points for just sending 1 there, except 5 which they can tie. I then send 11 to six to beat those who only send 10 or less while not sending too many there as well, while sending 18 to 10 and 9 to guarantee their capture. That leaves me 48 troops for castles 1, 2, 3, and 4. So that would be 12, evenly divided, but I'm taking some away from 1 and 2 to bolster 4, so 1 will be 8, 2 will have 8, 3 12, and 4 20. Since I don't like sending the most troops to 4, I'm gonna make it 16 and send those extra 4 to 10, 9, and 6. Yippee. Brilliance.
244 2 10 4 0 6 0 8 0 12 0 22 0 5 0 31 30 5 30 5 30 Ran a genetic algorithm to determine the optimal solution to beat previous submissions, fitness was weighted toward submissions with a higher win percentage. With the caveat that deploying 30 troops for the biggest three is very unlikely, I should guarantee myself 27 points (which is just under half available). I only need to win just one more point to triumph hence deploy the remaining to castle 1 (although there may be some game theory that in the event of others deploying this strategy I should deploy to castle 2 or 3 to take the win over them also).
245 10 4 0 6 0 1 0 18 0 20 0 23 0 1 30 2 30 2 30 23 I don't need big wins. All I need is 28 points. I figured that I would be able to win the 1-point castle most of the time with 10 troops there and then hope that most people won't be sending more than 30 troops anywhere. I tried to dominate in areas that I don't think will be strongly contested.
246 10 0 0 1 0 5 0 2 0 5 0 16 0 28 30 30 6 30 7 With the caveat that deploying 30 troops for the biggest three is very unlikely, I should guarantee myself 27 points (which is just under half available). I only need to win just one more point to triumph hence deploy the remaining to castle 1 (although there may be some game theory that in the event of others deploying this strategy I should deploy to castle 2 or 3 to take the win over them also). I ran a genetic algorithm against the previous submissions, which started to sub in its own creations to test against.
4 6 1 18 20 23 1 2 2 23 I tried to dominate in areas that I don't think will be strongly contested.
247 0 5 1 0 5 0 2 0 5 0 16 0 28 0 30 28 6 32 7 35 I ran a genetic algorithm against the previous submissions, which started to sub in its own creations to test against. I am trying to use the most efficient way to 28 points (minimum needed to win) assuming that most players will distribute their troops to more castles. The fastest way is to win castles 10, 9, 8, and 1. I've distributed my troops proportionally to their value.
248 5 8 0 8 0 9 0 9 0 10 0 10 0 11 28 11 32 12 35 12 I am trying to use the most efficient way to 28 points (minimum needed to win) assuming that most players will distribute their troops to more castles. The fastest way is to win castles 10, 9, 8, and 1. I've distributed my troops proportionally to their value. I don't know.
249 8 0 8 2 9 3 9 3 10 4 10 22 11 26 11 3 12 31 12 6 I don't know. Chose to focus on 3 of the top 5 castles to score most of the winning points with smaller bands to the lower castles to score the remaining points needed to win. Small bands were also sent to castles 10 and 8 in case of easy victories. Exact numbers were chosen based on the distributions from the previous competition. Since more than half of submissions in the previous competition had no more than 2 soldiers at castle 10, I would expect many competitors to now send 4-5 soldiers to castle 10. I sent 6 soldiers to castle 10 in hopes of beating that strategy.
359 0 5 7 6 8 7 6 8 13 9 9 11 6 12 20 13 26 14 5 15 Random solution meant to help my initial submission. The best way to keep someone from out-thinking you is to not think.
360 5 3 6 3 7 3 8 6 9 3 11 16 12 26 13 26 14 8 15 6 The best way to keep someone from out-thinking you is to not think. Ran against previous results to optimize results. Changed up some to based on assumption that people would do that same.
361 3 7 3 9 3 10 6 2 3 4 16 7 26 11 26 22 8 10 6 18 Ran against previous results to optimize results. Changed up some to based on assumption that people would do that same. Sam Holton
7 9 10 2 4 7 11 22 10 18 Sam Holton
362 1 3 5 7 9 20 25 10 10 10 Seems like a good idea at the time.
363 1 6 9 13 16 21 0 0 31 3 I saw that many strategies loaded up on boxes 7 and 8 (either focusing on the top 3 or the middle few), and that there was relatively less competition for 9 than for 10, so I allocated, roughly proportional to how much they contribute to getting me to 28, so I would win 9, 6, 5, 4, 3, 2. I saw that most people who put more than me on lower values left their higher values completely empty, thus my thinking that I can win castle 10 with just a few folks there on all those who totally ignore it.
364 7 10 12 13 14 14 0 0 15 15 Previous winner's solution was to focus on the middle part, while leaving 9 & 10 undefended and focusing on a select few castles. My assumption is that many others will try to copy this. Intent is to therefore leave the middle undefended and have a blanket defense for the others.
528 0 5 0 5 0 5 0 5 25 5 25 10 0 15 25 15 25 15 0 20 Putting all my eggs in one basket (winning all 4)--ceding the rest. Felt like i over-thought it last round.
529 1 2 2 11 3 13 4 16 16 1 21 20 24 20 21 1 6 15 Assigned enough troops to 6-10 in order to beat 60% of the previous Battle Royale for each castle. Assigned enough troops to 1-5 to vulture some of those. I designed several strategies that seemed good to me and then designed this one specifically to beat all of them.
530 4 6 6 7 6 7 6 25 6 25 6 10 26 5 4 5 32 5 4 5 fighting the last war - tested against the precedent war data with a touch of randomness to allow for the fact that others are doing the same I focused on strategies that would win a majority of wars against strategies that would be customized to win against the specific strategy of the past winner. Would you also accept a probabilistic distribution of armies?
0 0 0 0 25 25 0 25 25 0 I decided to go simple this time. If you win castle 9, 8, 6 and 5 you win so I am going all out for just those castles
531 0 4 0 6 0 9 0 11 25 14 25 3 0 27 25 18 25 4 0 4 Somewhat-randomized castle selection in the butter zone (adding to 28) Add 1 to the winning troops from last time, except for Castle 8 gets whatever is left over.
532 0 3 4 1 4 0 5 2 6 4 7 11 9 22 11 26 17 30 34 My strategy was selected so that if I get the shout out on 538, then I would like to say "Hi Mom!" to Debbie Firestone in Tulsa. I would also like to thank the 538 for the awesome Friday puzzles! I really like this one. I weighted castle N by approximately (1/N)/(1/1 + 1/2 + ... + 1/10), which could be thought of as an inverse harmonic distribution - a name I just made up. There is no deep theory about why I expect this to work, I just have a hunch.
533 0 0 4 4 8 12 10 15 13 20 1 24 26 1 30 1 3 23 5 10 was underutilized Computer Program on the last data set
566 0 5 4 7 8 10 12 12 1 2 26 31 28 4 4 Alteration of the best solution from the 1st time that would have performed better and won. Additionally, it beats most of the other top solutions. In antiquity those that excelled in warfare first made themselves unconquerable in order to await the moment when the enemy could be conquered. - Sun Tzu
567 2 3 2 3 15 10 17 22 22 27 3 4 4 4 I used a genetic algorithm in which randomly distributed troops were shuffled one at a time to different castles and compared to the Git Hub data and 30 of the distributions. (The major problem is that the best distribution depends on what it is being compared to, so there is no guarantee it will work, especially if other contributors do something similar. Ugh. But let's see how it goes.) This was the best distribution. n/a
568 2 4 6 4 8 5 14 5 20 10 28 10 10 5 15 3 35 There are two competing factors. Some castles are more valuable, but they engender higher competition. My goal is to commit enough resources to the medium-value castles to win them, thus outcompeting those who commit higher resources to the high-value castles, while maintaining a sufficient attack on the high-value castles to win them over other people who choose my medium-castle strategy. More troops on the bigger numbers
0 0 0 0 16 16 17 17 3 31 I'd like to pretend that there is some really sound reasoning behind this strategy but there honestly isn't. Mostly, the strategy hinges on if I can win Castle 10, as well as at least 3 of the 5 remaining castles that I've deployed soldiers to, that puts me at at least 28 points.
569 12 4 11 4 11 4 11 4 11 4 11 22 11 4 11 24 6 26 5 4 Have assumed many people will divide evenly, 10 soldiers per castle. Hence 11 will beat them and then for Castle 8 & 9 a lower number should score sufficient wins! Fingers are also crossed... I had a hunch
570 0 2 4 3 8 4 9 4 12 4 2 14 26 14 30 16 5 17 4 22 If you could make my crown a size 7-3/8 that'd be great. I started with the previous winner as my initial base strategy. I pitted this against all other submissions in the previous challenge. Then I simply experimented with the distribution until I seemed to get a maximum number of wins. Knowing the previous winner distribution is a new piece of information I didn't have before. I went with an assumption that even with this new info, game theory would still point me back to highly weighted Castles 7 & 8 as a winning strategy. Focus on higher half of numbers.
571 0 1 0 1 6 1 3 4 12 4 17 22 27 27 31 3 5 5 4 I looked at the values that others were placing from Round 1. When It made sense, I placed slightly more than where a mass of others where placing. I also did a bunch of math. Win probability maximization.
596 3 0 4 5 4 7 6 10 19 12 8 2 23 26 2 31 27 3 4 Need 28 points to win. Pick some minimum for each castle based on charts and hope I get 1/4 of the points I need. Then place leftover soldiers on castles that add up to 21 points. Plan: sum(2:5)+sum(7:8)=29
597 5 1 1 10 2 15 3 17 8 1 18 23 22 1 18 26 22 1 5 trying to get number 9 By analyzing the first dataset, primarily using the median number of troops sent to each location.
598 0 0 0 2 0 12 3 15 8 3 18 28 28 32 31 4 12 4 We chose the number of troops randomly starting with castle 10. Two above all winning deployments from last time, to get the troops I reduced the low value castles
2 3 6 9 9 3 28 32 4 4 slightly overweight castles with greater value versus previous winning strategy, slightly underweight castles with lower value versus previous strategy. Something to do with the number of winning combinations in which castle appears!
599 3 0 3 0 9 0 12 0 3 0 16 0 17 25 29 25 4 25 4 25 Random In round 1, the higher castles were taken by much lower #s of troops. I'm going for the big ones.
600 0 1 3 1 2 1 11 1 14 1 2 19 28 22 32 24 4 27 4 3 Try to win a few key castles without losing to many troops I want to win castles 6-9 because that adds up to 30 points, which wins automatically
601 1 2 2 3 4 3 10 4 15 4 15 20 15 20 20 21 15 21 Going for a balanced attack, yo. Big Points!
2 2 2 2 22 23 2 21 22 2 Yeah Boiz.
602 1 5 1 6 7 9 10 12 2 15 26 2 31 25 4 2 4 25 Andrew Simmons Gut feeling
603 0 5 1 7 0 10 1 12 7 2 12 26 12 31 6 3 26 4 35 Plan: sum(2:5)+sum(7:8)=29 I first created a randomized 2000 king tournament. I submitted the winner of that tournament but then realized an error in my ways, the randomized version created some deployments that would not be used by anyone. So I culled 50% of the deployments and re-ran the tournament, then culled 50% again etc. Until there was one clear champion.
604 1 1 5 2 1 3 11 8 2 18 19 22 2 18 25 22 2 5 32 By analyzing the first dataset, primarily using the median number of troops sent to each location. I chose to compete at all castles in case my opponent left one unguarded, but I chose to prioritize the even numbered castles based on their point value. Then, anticipating a similiar 1-soldier strategy among my opponents, I rebalanced the higher value odd castles with two soldiers, borrowed from the lower value castles.
613 6 0 14 0 10 0 8 0 10 0 7 25 17 25 11 25 4 25 13 0 I created two random number generators (RNG) for each castle, each for integers between 1 and 10. Then I ran the RNGs until the sum of all 20 generators equaled exactly 100. I added the two numbers for each castle and recorded them above. To win I just need the majority of points so if I 9, 8, 7, 6 castles win the battle.
614 2 4 2 5 2 8 19 11 2 4 2 17 22 20 23 24 4 2 4 I picked four castles to focus on that total 28 (the magic number). Put two armies on each of the remaining as insurance. 8/7/6 is greater than 10/9 as well as 8/7/5 from last time. Pick up any "punted" castles from others who did 3 or under.
615 5 0 4 1 5 8 4 9 14 2 14 16 16 26 29 31 3 6 4 In the data from the previous iteration, I looked for the biggest decrease between consecutive bars, and added 3 to that. 3rd submission. 1181.5 out of 1313 (same 1313 cases as first two submissions). 1179 W, 129 L, 5 T. This solution is light at Castle 5 and heavy at Castle 6 compared to the 1st two submissions.
0 0 6 3 12 17 27 27 4 4 I analyze the previous round's data and used the number of players who won by taking a castle with a certain number of troops. I then weighted it to also look at the point value expected per troop deployed.
616 1 0 2 0 5 0 5 11 5 0 6 0 15 25 18 31 20 32 23 1 Wanted to distribute based off of proportional weighting, but where's the fun in that? Hoping that people distribute more troops on ALL the higher value targets this time around, and that my troop deployment is enough to beat the distribution. Figure #10 is overvalued and #7 is undervalued, enough in #4 to beat even distributions, and 1 in #10 to beat those that abandon it.
617 20 2 8 1 19 8 0 8 0 9 2 0 28 0 8 22 8 20 7 30 Random solution meant to help my initial submission. Fight for the weak points compared to last time
618 1 7 1 1 3 12 4 1 20 19 3 1 31 26 3 1 31 31 3 I divided the 10 castles into 5 adjacent pairs, allocated troops based on the relative value of each pair, and then placed 1 troop in the odd-numbered (and lower-valued) castle to leave no castle uncontested with the rest of the troops in the even-numbered castle. Never leave a castle behind!. Going for the in between wins.
6 0 5 5 5 10 21 2 21 25 Game theory
619 0 3 0 4 0 5 0 6 0 9 25 11 25 13 25 15 25 17 0 17 To win I just need the majority of points so if I 9, 8, 7, 6 castles win the battle. Ehh, more troops for the bigger points but more of a general strategy to take as many castles as possible.
620 4 2 5 2 8 2 11 7 4 8 17 20 2 23 4 33 4 8/7/6 is greater than 10/9 as well as 8/7/5 from last time. Pick up any "punted" castles from others who did 3 or under. Who knows, man? Who really knows.
621 0 5 1 9 8 4 9 6 2 3 16 32 26 0 31 15 3 5 4 21 3rd submission. 1181.5 out of 1313 (same 1313 cases as first two submissions). 1179 W, 129 L, 5 T. This solution is light at Castle 5 and heavy at Castle 6 compared to the 1st two submissions. Random solution meant to help my initial submission.
681 4 1 4 2 4 3 1 4 16 10 11 12 21 14 2 16 2 18 35 20 Beats virtually any strategy? Maybe no. I doubled the number of points of castles 5-10 and sent that number of troops. For castles 1-4 I sent the corresponding number of troops.
682 2 3 4 3 6 3 3 13 10 18 10 3 3 23 18 3 19 28 20 3 I focused on a capturing few set of casles that would put me over 28 points, with a few spread out in case my enemies were more concentrated than I, and tried to selected castles I thought would have been undervalued or avoided. This strategy did well against a sampling of the last tournament's entries. Usually gets to 25 via 4+5+7+9, and usually wins a sufficient combination of 1, 2, and 3 to get to 28. If the strategy fails to do that, there's a good chance the opponent is under-represented in slots 6, 8, or 10, and can then be beaten there to compensate for surprise losses.
683 0 1 5 2 6 1 9 1 15 1 1 17 26 21 31 27 4 28 3 1 Downloaded GitHub data from battle #1, ignored plans that were "clear losers" (couldn't score 28 points, didn't use all 100 troops, etc.), and optimized over the remaining 1313 plans. This deployment scored 1176 out of 1313 (1169 Wins, 14 Ties, 130 Losses). Can't say this is the best vs. those 1313, could be a local maximum rather than a global, just the best I could come up with. I decided to just give up in 10, figuring everyone else would send a tin of resources there. I allocated to the next highest ones in descending order. I popped a few into 2 just to try to steal those.
4 6 9 11 14 17 30 5 2 2 Focusing on winning the bottom 7, with a few troops on the top 3 to beat people with a similar strategy
684 7 1 0 4 0 7 5 10 0 13 15 2 24 26 19 30 14 3 16 4 Took starting point of old, using simulation against those answers to create some possible responses, then created a response to those Basically the winner of the last game, a bit modified
685 1 0 1 0 3 0 3 6 3 8 3 11 22 16 2 16 31 16 31 27 Not too much thinking involved, but you fail to concur 100% of the kingdoms to you don't try to invade. I was able to distribute most troops to the castle that carry the highest percentages of the total points. By sacrificing the bottom three castles, I am trying to give myself a greater chance at winning the top castle, which I consider a swing "castle". As well, I still contribute points above the average amount for castles 4, 5, and 6 because they are worth 27% of the total points, and might swing battles for those who put all the soldiers in the top 4 castles. If I am able to split the top castle then I would be able to tie those matches.
686 3 5 2 5 5 8 12 7 15 10 11 3 7 23 23 30 19 5 3 4 I looked at the winning strategy from before, a strategy designed to perform optimally against that strategy, a typical strategy based on previous data, and a random/point-weighted strategy. I then tweaked the last strategy to perform optimally against the other 3 ( most cumulative points). I went against my better judgement which said to just stick with the random/point-weighted approach Similar to the winning strategy from last time, but a bit more effort on the highest two castles.
727 0 2 0 6 1 4 2 10 13 13 17 15 22 17 30 19 4 21 3 Like evenish (2n-1) deployment, but heavier on top In needing to get to 28 points, I figured I could largely ignore the top two targets, and focus heavily on 8,7,6,5 and 2, which gets to 28, and deploy some remaining troops to hedge on other targets in case they are ignored by players more heavily invested with the same strategy.
728 2 0 4 0 7 0 9 10 12 0 2 0 27 30 31 30 3 30 3 0 Selected for arrangement that would win the most total points (not necessarily wins) against the 1300 strategies from the first round (assuming people will not change too much) Get 28
729 2 4 2 7 2 9 5 12 2 21 27 22 31 26 3 4 3 4 Looking at round 1 winner, just increased 1 troop to castles 6-10 and reduced 1 troop to castles 1-5. I hope the small trade off may pay out significantly. Increase the 9 and 10 to capture the higher percentage and increase castle 6 at the expense of lower numbers
2 2 6 2 10 18 26 26 4 4 Last time I got really close to winning, so I'm going to switch it up a little bit and stick with the same strategy. Trying to win all the ones people throw away and then if people spread out too much trey and beat them too.
730 1 4 3 2 7 6 11 16 12 16 2 16 26 11 31 18 2 1 4 Modified my previous submission, which would have fared quite well against the top-performers. But because I think a lot of people will change their strategy to compete against the last version's winners, I have zigged to their zag. Attempted a numeric approximation of a linear optimization based on the historic cumulative frequency distribution. Then performed a Monte Carlo simulation by changing the cumulative frequency distribution to see if there were any improvements.
731 2 4 3 7 3 10 3 13 3 0 21 26 21 30 21 3 21 4 2 Minor tweaks to the previous winning strategy I figure for castles one to five, some people might put just one on to cover those who have none, but other than that don't care. So two beats them. But then people might think that and put two so I put three. Some people might also put 20 each on 6 to 10 to maximize points. So I put 21 on to beat them for 6-9 and one on 10, conceding it. I figure more people will concede one of the lower ones than 10 if they're doing the same thing. So I should win a lot of 6-9, some 1-5, and very few 10. But hopefully what I win is enough. And then I swapped one on 1 for one on 10 just so I could beat people who tried the same strategy but not much else. Disregard my previous submission, I added up wrong.
732 0 2 3 2 5 3 17 2 17 3 17 22 17 27 17 32 5 3 2 4 Almost random ;-) Optimal with the given opponents.
740 2 4 2 4 2 4 5 4 12 4 21 18 22 26 26 28 4 4 Increase the 9 and 10 to capture the higher percentage and increase castle 6 at the expense of lower numbers Old answers seem to suggest people leave some gaps in the deployment, hopefully I'll pick those up and be competitive in the middle.
741 4 1 2 6 5 11 6 12 3 2 21 26 27 31 27 2 5 4 3 Attempted a numeric approximation of a linear optimization based on the historic cumulative frequency distribution. Then performed a Monte Carlo simulation by changing the cumulative frequency distribution to see if there were any improvements. Similar to my original strategy but slightly refined based on data from first simulation. Trying to get a majority of the middle value castles and steal a few low and high value ones.
742 2 4 3 6 3 9 3 11 3 14 21 2 21 17 21 31 21 3 2 3 I figure for castles one to five, some people might put just one on to cover those who have none, but other than that don't care. So two beats them. But then people might think that and put two so I put three. Some people might also put 20 each on 6 to 10 to maximize points. So I put 21 on to beat them for 6-9 and one on 10, conceding it. I figure more people will concede one of the lower ones than 10 if they're doing the same thing. So I should win a lot of 6-9, some 1-5, and very few 10. But hopefully what I win is enough. And then I swapped one on 1 for one on 10 just so I could beat people who tried the same strategy but not much else. Disregard my previous submission, I added up wrong. I tried to barely beat the prior winner in as many places as possible.
2 2 3 2 3 22 27 32 3 4 Optimal with the given opponents.
743 2 1 7 5 2 8 2 10 12 13 15 1 21 26 33 30 3 3 version 2 I took last time's winner, and moved 2 troops out of Castle #1 and into Castles #9 & #10, thus ensuring I beat last time's winner. I figure most people will either just copy the previous winner, or replay their first, losing strategy.
744 2 3 2 4 3 5 3 7 3 10 22 15 27 3 31 25 3 25 4 3 Nothing fancy. This is the hypothetical troop placement with the highest margin of victory over the first round data (an average of 14.55 more points than my opponent). It's not the winningest hypothetical from last round, however. (That was 0,5,7,12,12,1,25,31,3,4, with a MOV of 11.83.) First try. Will think a bit more over the weekend but I am curious whether my snap guess is better or my actual thinking.
745 2 1 2 1 3 9 3 14 3 1 22 19 27 24 31 29 3 1 4 1 I used integer programming to maximize points against last year's submissions. It's not exactly the same as maximizing individual wins but it is a good proxy for battling against everyone. I ignored the ties and counted them as losses, which is a pessimistic approach and ties will bring even more points than I accounted for, hopefully. Got a total of 47058 points. IP is submitted here: http://imgur.com/a/6tHHI If I win 3,4,6,7,8, it would be 28 which is over half. I guessed it would be easier (solder deployed vs likelihood of winning) to win lower numbers. I added 1 per castle to ensure they sent troops in order to win points.
768 2 4 6 8 8 10 11 13 13 1 15 26 17 30 20 3 4 3 Keeping it simple! I assumed others would either overload high numbers or weight with 10 castles accordingly. I weighted for 9 castles and rounded all numbers down, then gave the leftovers to castle #10. Several ways to 28. Prey on unexposed extremes, make your money in the middle.
769 6 3 8 4 11 4 14 4 17 4 20 4 24 1 0 1 0 35 0 40 Take all the low value castles and gain 28 VPs Ran an analysis on the data you provided through some rudimentary regression and decided this was the best strategy.
770 1 1 2 1 2 2 3 2 10 3 15 5 20 10 31 35 13 40 3 I wanted castles 9 and 10 (: Tried different strategies (even balance, top heavy, linear progression) against others w/ computer simulation that varied the losing side slightly each time until it won. Tested against some of the common strategies used in round 1 this time and this distribution was generally successful considering how people might adapt this round.
7 7 15 15 15 16 16 3 3 3 Trying to win all the middle areas with everyone else going for the high value ones
771 3 4 4 5 5 7 11 8 19 10 25 2 26 27 1 31 3 3 Varying the best winning strategies of last time to find an optimal solution Just a small variation on the winning strategy from last time... lame I know.
772 5 2 7 3 10 3 2 8 16 18 23 20 2 20 2 20 30 3 3 I tried to come up with a distribution that would challenge for 28 points against both the average try and the winning strategies from the previous battle. I am banking on other players placing 1 or 2 troops on Castles 1, 2, 3, 9, and 10. The low-value incremental castles will hopefully push me over the top.
773 0 0 1 0 10 5 10 12 14 13 18 16 20 22 16 32 10 0 1 Maximize points. Assumes overload on Castle 10, but maximize down the ladder I prioritized castles 3-9 distributing troops based on a combination of weighing values of each castle and the results of the previous round.
2 3 3 3 3 12 14 26 31 3 The idea here is two fold. Best strategy is to think one step ahead. Most people are going to look at how many 1's there were and put 2's at castles. This will beat them. The second is most people overload castle 10. In a more balanced strategy we will never beat them so we relinquish castle 10 while still giving it 3 soldiers to win against armies that completely relinquish 10. The exception is lowering castle 1 from 3 to 2 in order to give an additional soldier to 6. This defeats the 11 across strategy. Games won will either involve winning 8 and 9 or sweeping bottom castles.
774 3 5 7 9 10 11 2 26 25 31 3 3 Variation on the winning strategy from last time. Only slightly changed from last times winner. I did a simulation for a previous submission and it gave pretty crazy data so I want to see if a more intuitive response will do better.
775 5 4 4 25 2 20 10 3 15 27 10 26 9 3 5 4 chenbesler@gmail.com Random
776 2 4 3 8 5 10 0 13 10 1 15 26 20 30 25 3 17 3 Several ways to 28. Prey on unexposed extremes, make your money in the middle. I wanted to win the game
826 2 1 3 1 3 7 13 10 18 14 3 18 25 22 30 18 3 3 For this one, I looked at the median data from the last round, and chose numbers that would put me above the median for each castle. The sum of the median numbers was 89, enabling me to put median+1 in all castles (with an extra +1 for castle #8, the most contested castle last time). Mach 1 eyeball.
827 0 1 1 2 12 10 14 12 31 15 31 17 1 19 1 21 4 3 4 Picking my battles on medium strength castles. I'm essentially just trying to beat the winner of the original submission at the same time as I'm beating the person trying to beat the original winner.
828 3 0 5 0 8 10 10 5 13 20 1 20 26 20 30 25 2 0 2 0 I figured that people would try and come up with new strategy to counter what they imagine will be the counter to last year's winning strategy, or they would go even further and try to counter the counter of the counter (etc). I decided to copy last year's winner and see if lightning would strike twice. to win
3 5 8 10 13 1 26 30 2 2 Last time's winning strategy. Maybe people don't change.
829 1 4 4 6 2 9 3 0 21 14 21 3 21 27 21 31 3 3 trying to beat the average bets, placing small ones on everything to pick up any additional ones I can old winning strategy +1 at the expense of castle 4
830 3 8 7 12 10 6 14 7 17 13 21 14 25 22 1 10 1 5 1 3 Fight where your enemy is weakest and take just enough to secure victory. Combination of intuition, randomness, and trying to match the winning deployment of last time.
831 3 0 6 2 1 14 12 14 15 2 18 14 21 25 24 29 0 0 It's necessary to win 28 castle points. I'm aiming for that with about an %18 cushion. 33 points. Only losing castles 6, 7, or 8,loses outright. And losing 6 is survivable if I get lucky and pick up castle 3. I divided the troops up evenly with 3 per castle point for the castles I attacked. And had 1 left over so I took a flyer on castle 3. Majority of strategies opted for 1-7, or 1,8-10 then some variant of uniform distribution. High amounts on 7 and 8 defeat first two, 14 each on 3, 4 and 6 brings total to 28 and counters even distribution. Castle 1 is not worth the troop for any strategy. 9 and 10 are more expensive than they are worth vs most opponents. 2 troops on 2 and 5 to beat 1 troop distribution. Wouldn't beat a computer, but I want to beat Riddler Nation.
854 11 1 7 1 12 1 10 2 15 2 20 4 25 12 0 14 0 13 0 50 It could beat many of the lower troop submissions tested 100 random distributions for best round robin result, then hand tuned a little.
855 2 1 6 1 1 6 2 12 3 13 4 26 5 30 11 2 21 2 51 Focusing on 7 and 8 while not sacrificing any with 0. I'm hoping I can beat the balanced people at 5 and 6 to and stealing where they put 0s or 1s. The ones who go heavy up top I hope to beat them at 8 and win most of the rest. I don't know
856 1 3 1 3 3 0 3 0 23 9 27 15 33 35 2 35 2 1 Castles 9 and 10 are too high risk, high reward, and not necessarily needed. 6, 7, 8 and any combination of 3 castles (except for Castle 1) would grant you a win. I sent them to ones that seemed like a good idea.
2 0 0 1 12 14 12 15 0 44 I spent a while playing around with genetic algorithms, this one ended up as the winner in a big run.
857 1 3 1 1 1 17 14 1 21 24 1 31 27 3 29 1 I want to get 28 points from castles 8,7,6,5,2. Then I win. Just need 28 points lads! Also, who goes for #10 anyway?
858 24 1 3 10 3 10 24 10 14 10 2 10 11 13 9 14 6 21 4 1 In general, I wanted to deploy more soldiers to higher value castles. I could see that the previous winner broke with this rule on three castles, so I adopted that part of his strategy, but with my sacrifices occurring at adjacent castles to his sacrifices. Basically, I started with the previous winner's strategy and then tried to anticipate how everyone else would react to the info provided. I gave up on castles 1 (low value) and 10 (high conflict). I distributed the extra troops to castle 9-7, focusing on trying to win castle 9.
859 0 6 2 0 11 16 6 20 3 0 30 1 2 46 12 1 34 6 0 4 Ground it out with an evolutionary approach. There is no stable point, of course, but it was getting pretty goofy when I got to 19k entries (mostly by perturbing the most successful ones of each iteration), so I had to stop it at some point. I stopped it when it looked... kind of neat... and I needed my CPU for other things. Random solution meant to help my initial submission.
879 1 2 2 2 2 30 17 30 19 20 21 5 36 5 0 2 0 2 Victory middle castles will be underplayed
880 4 10 2 24 4 28 27 2 13 12 20 14 0 6 5 17 3 1 Looked at deployment values from the inaugural battle & attempted to put myself above the 50th percentile for all castles. Random solution meant to help my initial submission.
881 1 0 1 0 1 35 1 0 17 6 21 0 26 33 30 3 1 2 1 21 I figure that too many people will overdeploy to castles 10 and 9, so it's not worth overdeploying to those castles. I also figure that Castles 1-4 just aren't worth enough to overdeploy there. But, I also want to capture any castle that anybody doesn't even try to defend. So, I'll put a single defender on the 6 castles that I don't want to overdeploy to in order to pick up some cheap wins or ties. As far as Castles 5-8, I figure those are the most valuable ones. I also figure that Castle 8 is worth the most. And, given that the winner last time put 30 there, I figure 30 seems to be about correct for that. Then I just divvied up the rest of my troops in a configuration that makes some type of sense. I probably have no shot, but this is an interesting exercise, and I like seeing the data that comes out of this. Random solution meant to help my initial submission.
3 3 21 21 21 21 4 4 1 1 I estimated where most people would distribute their troops, assumed they would plan what I would plan to combat that. Then I tried to maximise a way of beating my own plan against them.
882 18 1 16 1 15 2 13 2 11 2 9 6 7 6 5 4 4 3 2 73 If there is an optimal strategy for this game, it is beyond my modest abilities to figure out. Also, with 1000+ entrants, trying to pick what the other entrants will do seems like a shot in the dark even with the data from the first game. So I kept it simple and assigned soldiers proportionally to each castle's percentage of the total available points. Rounding standardly, this worked out to exactly 100 soldiers. (see my other try)
883 14 2 14 0 14 2 14 4 14 2 14 5 14 1 0 3 1 11 1 70 Getting 28 so that I can always have a majority amount of castle points. Mostly ignored the previous tournament, though probably not a good idea because there are many "joker players" (players aiming only to create noise, with no intention to win, which quite unfortunately makes this more of a guessing social experiment, than a mathematical one). A simulation suggests that optimal mixed strategy should be randomising a plan around having some 50-80 men on castle 10, 0-25 on 9, 0-20 on 8, 0-10 on 7, and so on down to 0-3 on castle 1. This is one such random plan.
884 0 19 1 17 1 15 1 13 1 11 2 11 21 8 31 6 41 0 1 0 Outwit the guys who max castle 10. And don't half any points for the small ones I took the amount of points available and divided that by the number of troops so you'd get even troops per point available, and I rounded up and took some points from the bottom to reinforce the higher point value castles
893 2 0 13 2 1 4 2 2 62 5 1 2 3 1 11 70 1 Mostly ignored the previous tournament, though probably not a good idea because there are many "joker players" (players aiming only to create noise, with no intention to win, which quite unfortunately makes this more of a guessing social experiment, than a mathematical one). A simulation suggests that optimal mixed strategy should be randomising a plan around having some 50-80 men on castle 10, 0-25 on 9, 0-20 on 8, 0-10 on 7, and so on down to 0-3 on castle 1. This is one such random plan. Random solution meant to help my initial submission.
894 19 1 17 1 15 1 13 1 11 1 11 1 8 1 6 1 0 1 0 91 I took the amount of points available and divided that by the number of troops so you'd get even troops per point available, and I rounded up and took some points from the bottom to reinforce the higher point value castles Why not.
895 7 1 8 1 1 13 1 32 1 30 1 7 1 1 1 0 91 Random solution meant to help my initial submission. HOLD THAT L!!
0 4 31 27 14 0 12 8 3 1 Trying to defeat the winner from last round
896 3 31 0 26 0 23 7 11 12 2 4 2 2 0 12 2 5 3 5 0 Cuz Because I like being right... and I can see the future. Crown me the victor 583!
897 12 0 15 0 20 0 24 0 2 0 2 0 22 0 1 0 1 0 1 100 Wild Guessing Because I am hoping nobody else would send 100 troops to castle ten, because they want to have stake in everything, or something else. They also wouldn't be stpid enough to take this calculated risk, like me. It is also hard to amass 10 victory points by a combination.
898 22 0 27 0 27 0 5 0 4 0 5 0 4 0 4 0 1 0 1 100 I tried to hit as many high value castles while simultaneously giving myself a decent (>25%) chance of getting the smaller castles. I looked at last time's data and tried to stay out of the "no-man's land" where additional troops wouldn't have made a difference against most opponents Just to see what happens
901 10 35 15 30 20 30 30 0 20 0 1 0 1 0 1 0 2 0 0 5 by gut feeling. You only need to win the top 3 castles and the last castle to claim victory (~51% of total points) and since these castles were way underdeployed last time, a big shot in the arm should be enough to take each of them. Since I am completely abandoning the rest, I should be able to over deploy the rest and win the castles that matter.
902 0 1 0 1 0 2 0 1 0 1 0 1 0 2 0 1 100 90 0 I had no strategy I just wanted to participate Someone will try going for 10, just sending all their troops there. Heck, many people may try that. I want to guarantee to get castle 9, and hopefully split it among fewer people.
903 2 100 13 0 1 0 2 0 62 0 5 0 2 0 1 0 11 0 1 0 Random solution meant to help my initial submission. i am guaranteed one point
1 1 1 1 1 1 1 1 1 91 Why not.
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riddler-castles/castle-solutions-3.csv
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@@ -11,7 +11,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,1,5,20,4,20,4,20,4,20,
1,4,12,14,7,16,18,20,3,5,"I focused on a combination that would get me to 28 points, but still tried to have above average on the castles that others might try to put 1-3 troops at."
1,2,1,3,5,20,21,33,7,7,
3,6,11,13,5,18,22,11,6,4,
4,0,0,0,0,0,0,32,32,32,You only need 28 to win
1,1,6,10,14,15,23,24,3,3,"I'm reverting to something closer to the winning strategy of this question's first instance. I'm sending few troops to the highest and lowest valued castles, instead focusing my parties on the middle-values."
1,1,1,2,1,15,21,26,31,1,"Goal is to maximize odds of winning 28 or more, and winning 6 through 9 seemed to have the easiest path of getting there. Skipping 5 and leaving 2 at 4 is because 4+6+7+8+9 is enough to win, happy to leave 5 behind to win 6-9."
@@ -21,21 +20,16 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,5,7,9,11,2,16,18,15,14,"I have optimised this strategy to beat the average deployment from the last iteration of the game, by sacrificing castle 6,which was not well contested last time, so I expect it to be hotly contested this time round."
1,1,1,1,23,23,24,24,1,1,Trying to capture the mid-high castles and sacrifice the others
3,3,3,3,3,10,15,20,30,10,"Just guessing based on the previous two events. 678 heavy vs 459,10 heavy, sort of a mix."
2,2,2,2,12,20,20,20,20,20,"I spread my troops on the five highest value castles, hoping that I can beat out some of them, and sent two to the lower value ones so I can beat someone who sends the minimum."
1,2,2,8,10,15,17,19,23,3,"I tried to look for a mix between the successful armies in 1 and 2. I targeted 4-9 because they total more than half the points, and dropping 1-2 of these castles wouldn't stop my victory. "
4,6,7,4,4,4,30,32,4,4,"mostly random TBH, just gut feeling"
2,2,3,14,2,16,2,4,32,23,Intuition.
2,3,4,5,7,9,26,33,6,5,It just felt *right*
4,4,4,4,16,4,16,28,16,4,To mess with the averages
6,6,7,0,0,0,21,25,0,35,"Castles 1-3 and 6-8 were the most ignored by the top 5 warlords in the last round. 4-5 and 9-10 were most popular. I figured if I can almost guarantee getting 10 by placing 35 soldiers, ignore 9 where most others will send a significant amount, capture 7-8 which look to be ignored by most, and capture 1-3 which will be ignored for low point value, I could total 31 points which is more than enough to win a majority of the battles. Maybe a simpleminded strategy but this is based purely off the results of the last round and it could be an obvious one. "
3,5,6,10,13,18,28,7,6,5,1 thru 7 are worth 28 points while 8-10 are worth 27. So sacrifice those for volume ;)
2,6,9,9,12,2,28,27,2,3,Just did a pretty similar strategy to Cyrus.
1,1,1,1,1,5,5,10,25,50,"I figured if I can guarantee a split or victory of high level castles, that can override the lower level ones--this is not very scientific. Also, the form doesn't allow us to send 0 soldiers to a given castle."
2,4,5,8,10,11,12,14,16,18,Impossible to say.
1,3,6,8,10,12,14,16,18,20,Linear
1,1,1,1,1,1,91,1,1,1,Banking on winning ALL the battles at Castle 7
1,1,1,2,14,15,2,28,32,4,"Winning 5, 6, 8, and 9 gives me just over half of the available points, so I went hard for those four."
4,5,7,9,11,13,14,16,13,11,Used the last answer and increased deployment for the first 5 by 1 and decreased the last 5 by 1 to account for evolution.
1,3,5,7,9,11,13,15,17,19,Linear
4,4,4,5,5,16,5,5,21,31,
1,6,6,11,11,16,16,16,11,6,"Figure 5x would be a popular number to distribute, so 5x+1 along a skewed curve based on intuition."
@@ -57,19 +51,13 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
4,4,4,4,4,24,24,24,4,4,"I figured at least 4 in each would pick off the people who sent out tiny forces, but still let me sink in a few in more strategic spots."
1,5,8,12,13,1,26,30,2,2,I copied the first winner one minor arbitrary change.
2,4,6,7,9,11,13,14,16,18,Weighted distribuation
1,1,1,1,1,17,17,20,40,2,"My line of thinking is that most other warlords would work to capture Castle 10 with the majority of their troops, so I avoid it completely and work with my forces to conquer the second-strongest castles.
If however, my opponent ignores castle 10 as I did, and goes after the lesser castles, I'd designate two soldier in the off chance they could conquer the castle alone. If I conquer Castles 6-9, I'd win the war even if I lose all the others. "
3,6,9,14,18,22,28,0,0,0,"Ignore the top ones, focus on minimum needed for majority of points"
1,1,1,1,2,7,10,20,35,22,"I went top heavy and ignored the low point castles due to their inefficiency as the are 1.8 digits
Soldiers per point. "
1,2,0,0,0,0,0,32,32,33,"The top 3 castles score 27 points in total, almost 50% of the point total. Assuming I can win all 3 and pick up a single unguarded low point castle, i will prevail."
1,1,5,10,1,15,16,17,1,26,
2,4,5,7,9,11,13,15,16,18,I took the ratio of the points for each castle against the total points possible (10/55) and multiplied it by 100 to determine the number of soldiers for each castle.
1,4,9,10,1,13,16,17,14,15,I assumed the number of soldiers necessary based a trend from the previous two events. I then added one soldier to castles 6 through 10 and subtracted one soldier from castles 1-5. I then decided to sacrifice castles 1 and 5 and minimize their defenses and put their soldiers on the other 8 castles.
4,0,1,1,1,0,0,31,31,31,My goal is to acquire 28 points. This is on permutations of castle attacks that makes it likely
15,1,1,1,1,1,30,30,25,24,"First, we have to find the minimum number of points to needed to win (28). Then we have look at the minimum amount of castles needed to secure that, which is 4. Holding the top 3 pts Castles will only get to 27 pts; however, holding point 7 will get 34 pts, but that an extra six points not needed. So, having strong defenders on the top 3 castles, of which in previous games few went above 30 to hold, and then holding castle 1 strongly, will give the best opportunity to hold the least castles with the least wasted points to win.
But if one is lost, all is lost. :)"
4,0,0,0,0,0,0,32,32,32,"I do have to win all 4 of my engagements, which doesn't leave any margin for error. I'm confident in castle 1, and 2/3 for 8-10. So I just have to get a little lucky that opponents spread their forces out too much."
2,2,9,11,16,10,30,5,8,7,Based on last year's deployments I observed that very few soldiers were deployed to the 9 and 10 castles so I send a force to that could take both of those. I sent a token force to the 1 and 2 castle as they are not worth that much. For the remainder I tried to get above last year's average except for castle 8 which I can afford to lose if I take either 9 or 10. However I may just be fighting the last war and be destroyed.
3,3,1,1,1,1,10,35,44,1,focus on castle 8 and 9 with the assumption that castle 10 is likely going to be taken and castle 1 and 2 will have 1 soldier brought to them
@@ -93,14 +81,11 @@ But if one is lost, all is lost. :)"
3,3,4,6,7,9,15,25,27,1,I've never actually participated in something like this before. I assumed most people would attempt to capture the castle worth the most points (10). I felt if I essentially sacrificed that castle and then stuck to a rather linear distribution of soldiers increasing from 1-9 I stood a greater chance of capturing those castles and thus winning the Game. I guess we'll see.
1,2,3,6,9,14,16,17,16,16,It slightly beat something that slightly beat May's average.
4,4,4,5,11,17,23,26,3,3,
17,17,17,17,17,5,0,0,0,0,overcome 6
1,1,4,8,10,13,16,19,16,12,seems plausible
3,6,6,11,11,1,27,30,2,3,"cluster forces around valuable castles most likely to be fought over (7 and 8), choose one middle but less valuable castle (6) to offer almost no defense of, give 11% of forces to next level valuable castles (4 and 5) assuming most will give 10% to those castles. Also assumes most will attempt to cluster forces proportionately to win larger castles in some ratio of all forces in the 10, 9, 8, 7 castles, keeping more than 25% in castles 8 and 7. "
1,1,7,1,18,20,2,23,25,2,"Go big on some, steal the rest with some 1>0s and hope for some luck!"
2,2,5,5,10,15,20,25,5,6,
2,4,5,7,9,11,12,15,16,19,"Direct mapping. Soldiers per castle = (points per castle / total points) * total soldiers, with rounding, and leftover soldier goes to castle 10. Trying to win by playing simpler than people expect. :)"
1,3,5,7,9,11,13,15,17,19,"Trying to be competitive at every single castle, without wasting too many soldiers."
1,1,1,1,14,20,30,30,2,2,
2,7,2,2,13,18,23,29,2,2,"I wanted to get 28/55 points by committing to castles 8,7,6,5 and 2. I deployed these troops to help obtain 8 most frequently and 2 the least. I deployed 2 troops on each other castle to not allow for my enemies to get an easy 1-0 victory on any castle. If I can win one or two of those, that would be great "
15,15,7,2,26,2,2,3,10,18,Last time winners focused on the middle. I'm focusing on the edges
1,1,1,1,1,5,10,15,25,40,
@@ -118,17 +103,11 @@ But if one is lost, all is lost. :)"
2,3,3,3,21,17,2,3,24,22,Last times winner but more even alignment
1,1,1,1,1,20,1,1,34,39,Ties are wins
1,1,1,2,4,5,36,36,12,2,"7 and 8 seem like a sweet spot for points vs competition, and I want to put in enough to beat most people who came to the same conclusion. At the same time, I want to make sure I don't get beaten by tiny troop commitments to the other castles. I figured 9 would be a nice bonus to sometimes get."
1,0,9,0,0,10,10,20,40,0,Adjustments to previous contest
5,5,5,3,3,19,1,2,27,30,"Based on the last two games, those with less troops were overwhelmed. I figure most people will leave 9 and 10 relatively open, and 1-5 will be given 4, to take out the 3's from round 2. Let's see what happens!"
2,2,2,2,2,19,19,20,24,28,
3,3,14,4,18,15,3,15,4,21,Randomish
1,2,2,16,19,3,3,3,26,27,Im fighting the ghosts of wars past
2,3,1,5,16,28,6,9,18,12,Troop deployments to low point castles are just enough to tie up enemy troops while focusing on the mid to upper range castles that are worth the most. Don't over dedicate to 10 as people are drawn to the easy number.
1,1,1,1,1,6,15,18,20,25,random
1,2,3,4,4,16,18,24,27,2,"Highly valuing castles 6-9, if one wins those 4 they win. Hoping to win many battles by having the opposing army massively overspend to win castle 10 while my force wins 6-9. "
1,9,20,29,15,10,2,8,5,1,"Distribute to all, try to find a place where numbers will be thin."
1,1,2,2,26,10,15,15,26,2,"The total point possibility is 55, so you need 28 to win. From there, troop (resource) distribution is a mix of math (what are the best combinations that can lead to 28?) and human behavior speculation (metagaming). Castle 10 is a trap and a good way to get your opponent to waste resources, since they are working with incomplete information, so I threw only 2 troops there (to minimize my investment while hedging against other players who choose 0 or 1). Castles 1-7 add up to 28, so a popular strategy may be to aggressively claim them. The 26 in Castle 5 is designed to disrupt that, as players who go for this strategy may emphasize their investments in Castles 6 and 7, and will be afraid to over-invest in 5 without hedging earlier castles accordingly. Meanwhile, there are enough troops in castles 6-9 to yield likely wins, while hedges in the lower castles may secure additional value. "
1,0,0,0,0,13,17,20,23,27,Win big (I only want 0 troops at castle 1 but it won't let me. Hoping I dont get disqualified.)
1,1,1,1,1,23,23,24,24,1,
2,2,2,11,16,16,26,16,5,4,"It seemed to me that the chance of winning castles 9-10 is relatively low, since many warlords will send more troops there. I focused more strength on the mid-range, castles 5-8. chose mostly uneven numbers (rather than rounding at 5, etc) in hopes of beating warlords who divided by 5s or 10s. And I sent at least some troops to every castle, since this guarantees a win against a warlord who sends 0 to any of them-- making that number greater than 1 for each castle, since many players will send a minimal force to those castles. "
2,3,4,4,21,21,21,22,1,1,I sacrificed 9 and 10 hoping that my enemy would focus a lot of soldiers on them and instead tried to capture a lot of of the mid value castles.
@@ -145,12 +124,10 @@ But if one is lost, all is lost. :)"
2,5,0,11,3,19,22,4,28,6,"Choose who I want in my main coalition based on trying to have some overlap and differences with both previous rounds, but come up with 2,4,6,7,9 without too much further thought. Allocate 85% of my army to this coalition to not leave others undefended (except 3, out of spite)."
1,0,0,0,0,0,0,99,0,0,"You need to get points, and probably the only way to do that is to win a house outright. I am guessing that someone will do 100 for 10 and 9, so guessing 8 will be the one where people don't apply 100."
2,2,2,10,1,1,25,25,30,2,"Maximize the troops that could take 28 points, and the others are 2 to cleanup places where my opponent sent only 1."
1,2,2,11,16,3,4,1,29,33,Why not?
1,1,1,1,10,10,2,20,20,34,Try to create as many options to get to 28 as possible. Goal is to win 2 out of the top 3 then pickup enough of the rest to get to 28+
2,2,2,2,11,11,2,22,44,2,"I was looking for four castles that would add up to 28 points, the minimum required to win. I found I could not do this without castle 9. I chose to leave out castle 7 because 5 and 6 should be easier to get. I sent token forces to 1, 2, 3, 4, 7, and 10 to force my opponent to keep those covered. That left me 88 troops. I sent half of those to castle 9, which I assumed would be contested heavily. Half of what was left was sent to castle 8. The remaining troops were split between 5 and 6."
2,2,4,7,9,11,14,15,17,19,"Added up all the VPs to be had (55) took 100 and divided it by 55 (1.8). This is how many soldiers each VP is worth. I then multiplied the castle number by 1.8, rounded and skewed it towards the high end a bit for people who employed the same strategy."
1,0,9,15,0,20,25,30,0,0,
1,0,0,4,11,14,21,26,24,0,"I started with zero at Castle 10, and a large chunk (25) at 8 and 9. I then gave 5 fewer troops to each Castle going down until I ran out. Then I went back and added in a bit of noise. Then I noticed it required >0 for Castle 1, so I put that in."
1,1,1,21,1,1,22,24,26,2,"I figured a lot of people would go 10 on each, and this would consistently beat those ones. I also guessed a lot of people would put two on each of the lower ones to beat out the one you are forced to put there, so I made sure to take that into account. The second question for me was the people who went a bunch in top half and left one each to the lower ones so I knew I would need to adjust the numbers to favor something would also win against someone who went 1-1-1-1-1-19-19-19-19-19 because that seemed like it would be like the second most common formidable strategy.
The last thing I considered was that because you need 28 points to win and the easiest way to there seems to be 9+8+7+6 the easiest way to get there. I ignore the ten because other people will dump a bunch of points there and either way I will need to get four numbers total as 10+9+8 only gets you to 27. This strategy pretty cleanly beats both those strategies. To beat this you would need to foresee it probably and get 9 at least. I think if you went for a 10-9-8 strategy and just low balled a bunch of other numbers hoping to get one you might beat me but you will lose to everyone playing 10 on everything so I think this is the most stable that I can come up with."
@@ -172,7 +149,6 @@ However, your entry form won't let me put 0 for castle 1, so I switched castle 1
1,1,15,1,15,1,20,2,20,24,"Focusing on the odd numbers offers fewer points than focusing on the even numbers, but if I can capture one even as well, I can pull ahead. "
8,10,7,5,11,13,3,15,26,2,"I wanted to have some troops at every castle to have a chance to win any of them. I think some people may try to just win the 4 most valuable castles, as that wins you a majority of points, so I wanted to make sure I hit one of them hard to pre-empt that. The rest was pretty much random!"
2,2,2,8,9,11,12,18,18,18,
3,2,3,3,15,18,3,24,27,3,"Needed 28 points to win, so I focused on 5, 6, 8, and 9. I avoided 7 because I thought 5 and 6 would be less contested. I included 2-3 points in all others to contest them in case other players submitted 0-1 soldiers to each one. With my placement of units, I figure I should take at least one of my goals to get to 28, and may be able to punish people for overcommitting."
1,1,1,11,13,4,29,32,4,4,"I picked two more than the winning deployment from a previous round for all the top castles, assuming that most other players would pick one more than the winning deployment. This made me run out of soldiers by the end though, so the least value castles are pretty weakly defended."
1,1,1,14,12,12,14,14,30,1,Not a lot of thought went into the deployment. trying to get castles 9-7 most of the time.
1,1,1,11,2,21,3,26,3,31,"I really decided to only focus on castles 10, 8, 6, and 4 since those would win it for me. I started thinking of doing 30, 25, 20, and 10 respectively, but if a lot of people like doing multiple of 5s, adding one more to each could give me a lot more wins. I figure some people would put 0 in 1, 2, and 3, so I put one in each just in case. The remaining 8 troops went pretty evenly into 5, 7, and 9."
@@ -195,7 +171,6 @@ This leaves me with 9 and 10. And 28 troops. If history tells us anything, its t
2,2,5,13,16,1,7,16,33,5,"I looked at the distributions of the two previous wars and picked out some forts that have a potential to be left unguarded and put a couple more troops in there, while approximately splitting the difference between the two sets of winners, hoping that others might have the same approach, allowing myself to have a couple more in those key forts mentioned above. "
1,1,1,1,1,3,33,20,20,19,"To achieve over 50% of the available points, you must either win either the lowest 7 or highest 4, or otherwise mix and match point values up to 28 points. I have chosen to fight hard for the 4 highest values, in hopes that most spread their troops more conservatively. Because Castle 7 is included in both of these combinations, it is likely to be highly contested, so I have placed a third of my troops there. 1 troop was distributed to all castles in the lower 6 to snag extra points in case of similar strategies, or to those which chose not to contest certain castles. This strategy only works if I am able to win all 4 top castles, so this beats the winning Feb 2017 strategy of aiming low, but not the Jun 2017 strategy of splitting between 9/10 and 4/5. That makes this strategy considerably more risky and dependent on what the general trends are among the other participants this time."
1,1,1,2,8,10,20,25,30,2,The Art of War
1,4,12,20,24,32,1,1,1,1,Guess Wildly
2,2,2,7,11,14,17,17,15,13,"Designed a strategy that would beat both the average strategies from the last 2 battle royales, without winning any castle with a high excess of troops."
1,1,9,9,1,15,2,2,29,31,"Mostly guessing. 6, 9, and 10 seems like an efficient way to get close to 28, and hardly anyone's going to put lots of troops to both 3 and 4."
3,3,11,11,4,4,19,20,21,4,"The past winners placed 2-3 troops at each of their worst bases, by placing 4 I could acquire those bases at a lower marginal cost of entry. I wanted to try and take 5 bases total, and wanted to make sure that each of those 5 bases had more than 10 so that I could beat out the average person who just runs 10's across the board. I avoided the 10 spot because I think the average person will overplace value on that and overallocate their troops there."
@@ -230,7 +205,6 @@ Round 1 winners went strong for upper-middle and low numbers to get to 28 -- som
------
I wonder if you could provide the average score for the previous winners, and other people who might have had a higher average result, but won fewer duels. "
2,17,9,19,17,3,4,16,15,1,Random numbers between 1 and 19
1,1,1,2,3,26,30,30,3,3,Highest value avoiding copy cats and those who will put everything on 10 and 9
1,1,2,2,2,16,16,30,3,27,Not too sure.
1,0,0,2,21,22,3,24,27,0,"Key is to get to 28. Wanted to stack as few castles as possible to increase probability of winning those. Left 7, 4, and 3 as contingency plans in case someone was doing the same."
@@ -238,19 +212,8 @@ I wonder if you could provide the average score for the previous winners, and ot
1,1,1,1,11,12,15,17,19,22,"I assumed that a reasonably common strategy would be trying to spread the troops proportional to the castle scores (so, basically scaling up from a 55 point triangular spread). The idea here is to cede 10 points every game to build a more top-heavy spread to specifically counter those players and some variations on that theme."
1,4,0,0,0,0,27,0,34,34,
2,2,2,5,9,11,11,11,11,36,trying to win the higher castles without leaving any empty and pick off the 10 on each strategy
1,2,6,3,23,18,1,23,21,1,Targeting slightly less attractive targets than last rounds winner
21,18,15,12,12,10,9,6,0,0,"I made three simplifying assumptions about my opponents' strategies: first, they want to hold as few castles as possible to get over the victory threshold; second, they understand that it is a waste to have more than the threshold of victory points needed; third, they ascribe the same strategic value to each of those castles, as their strategy fails without any one of them. This means that my average opponent will aim to hold four castles, worth 28 victory points and will deploy 25 troops to each.
There are (by my very quick, admittedly) count, 9 unique strategic combinations of four castles that get to the victory threshold. I assume that my opponents are indifferent about which one they choose and arrive at whichever one they wish to play randomly.
I use the frequency with which a castle worth a given number of victory points appears in one of the 9 unique four-castle strategies to generate the probability that my average opponent, within my simplifying assumptions, would place troops at that castle, and subsequently, how many soldiers (on average) I expect to be stationed at that castle.
I would then simply distribute my 100 soldiers so I had marginally more at each castle than my opponent. Noting the inherent risk of this strategy (every battle should be a draw if my opponents play as I do, or as I expect them to give or take a trembling hand or two), I (rather randomly) decide that the castles worth 1 or 2 victory points are of low strategic value, given how infrequently they are included in 4-castle strategy and redistribute the six troops I would have placed there in the purer form of my strategy to the castles worth 10, 9, 8, 7, 6 and 5 VPs.
Hooah!"
1,1,1,9,11,14,17,18,15,13,My goal was to build a strategy that beat the average of both of the previous two rounds of raiding.
5,5,6,19,23,7,7,19,4,5,I just picked a strategy that would beat the top 5 in the most recent battle and also the top 5 in the first battle
1,1,5,5,5,15,15,20,30,1,Defeat in detail
4,8,9,11,3,2,5,2,27,29,Trying to get undervalued castles for cheap while leaving highly contested ones on the board
1,1,1,11,16,21,21,26,1,1,I tried to win just enough castles to get a majority of points by focusing on winning the predicted least competitive castles by one person. I guessed that most people will use multiples of 5 more often than other values and made all my troop counts 1 more than a multiple of 5.
2,3,4,12,1,24,4,26,2,22,"Pretty random, some psychology"
@@ -258,8 +221,6 @@ Hooah!"
1,1,1,3,12,17,5,27,3,30,We're in the Endgame now.
2,2,2,2,10,10,28,12,30,2,"Somewhat randomly. Generally speaking, either try to win or don't. Not a lot of in between."
1,2,3,4,5,6,7,8,9,55,Tried to guarantee 10 and get what I could with the rest
12,12,12,12,12,12,12,0,0,1,Maximising castle wins
5,10,15,10,22,22,-10,2,2,2,
3,1,2,1,3,3,16,19,26,26,"Go with non-derivatives, sacrifice 5's and 6's for 7's and 8's. In the words of Brienne of Tarth, ""Don't go where your enemy leads you."""
3,6,7,8,2,13,15,1,33,12,It's what I submitted last time. I did a bunch of simulations two years ago but I'm not doing any more work today for this glorified rock-paper-scissors match.
2,5,10,1,1,16,3,31,27,4,Random to avoid overthinking the problem
@@ -267,22 +228,17 @@ Hooah!"
1,0,1,17,20,1,2,23,32,3,saw the best ones from the last 1 and combinated.
4,4,10,14,15,14,15,16,4,4,"4 each seems like it will win 9+10 pretty frequently based on past distributions. Then, big numbers at 8,7,6,5 all will lose to even bigger ones of course, but will do well against people who followed either of the strategies of the past two winners - big numbers on 7/8 or on 4/5 - and hopefully win enough of the castle 3 in addition to take the battle. "
2,2,5,10,14,15,20,20,10,2,"devalued the highest due to probability someone would pick those, and the lowest due to lower value. Centralized in the middle, hoping to win the majority of 4-8. Put at least 2 in all categories so if any are using a similar strategy but ""giving up"" certain castles I will win those, and used 2 instead of one to try and outsmart any with the same strategy using 1 soldier."
1,1,0,25,0,0,25,25,25,0,
1,1,1,18,1,1,1,1,33,34,
1,2,2,2,11,13,3,32,31,3,"Assume many will either go for 7/8 or 9/10, and those that do will weight heavier on the higher of the 2, so trying to split the difference and win one of each pair.
3s to try to pick up a few where people put 1 or 2, then using the majority of the rest to try for 5/6, which outweigh 1-4 combined."
1,1,1,2,16,20,24,2,30,3,"Focusing on 9, 7, 6, and 5 as they represent half of possible points"
1,1,1,1,1,12,12,24,1,46,I dunno
1,1,1,5,10,20,25,30,3,4,Shooting for mid numbers (adds up to more than the extremes put together). Still put a few in the top numbers in case of a steal.
1,0,0,14,22,2,2,24,33,2,Why did you force at least 1 unit to go to castle 1?
1,5,5,5,20,20,20,20,0,0,
1,1,1,1,1,1,4,20,20,50,
3,3,3,3,12,12,3,29,29,3,"I choose to concentrate on towers 8 and 9, hopefully winning them almost all the time. I should also win towers 5 and 6 much of the time making 28 points for a victory. If I miss one or both of 5 and 6, I hope to make it up with scouting forces of 3 soldiers which may be more than most scouts."
1,1,1,1,1,1,9,20,30,35,I want castle 10 baby!!!!!!!!!
1,0,0,0,0,9,10,10,35,35,"For the goal of winning 28 points, I plan to take castle 9 and 10. Then win any two among castle 7-9. I'm avoiding castle 4 - - 5 as they seemed to be hotly contested in prior matches"
0.00001,0,0,0,5,5,5,15,30,40,"the previous winners clearly picked a lane, some highs and mids, or some mids only, my lane is to go top heavy. As long as I can claim two top tier and two lower tier, I can win."
1,1,0,9,14,20,25,30,0,0,"Just give up on the biggest ones, probably a waste "
1,0,1,1,19,5,5,6,35,28,:)
1,1,4,12,20,2,2,6,30,22,"Randomly, kind of based off the previous renditions. "
1,0,0,0,0,0,0,22,37,40,
1,1,4,5,9,12,12,18,12,26,Seemed like a good idea at the time
@@ -306,7 +262,6 @@ Hooah!"
3,5,7,7,8,10,10,10,20,20,"Used the previous results, and tried to pick the opposite strategies"
2,2,3,4,8,11,12,28,29,1,"Have at least 1 at every castle, aim for capturing castles 6 - 9, much higher value than the lower value counts, and hopefully less contested than castle 10"
1,3,5,7,9,11,13,15,17,19,I reinforced the higher value castles with 1 army from each less-valued castle in the hopes that I could both win some high-value battles against warlords trying to win a greater number of low-value castles and some (more?) low-value battles against top-heavy warlords.
1,1,1,15,22,2,6,6,34,13,I hand-tuned to win against the previous 5 top warlords as well as the averages in the last two competitions.
4,4,4,4,4,22,13,22,21,2,In hic signo vinces
2,2,3,12,18,16,30,8,5,4,"I need 28 points of castles to win. I started by thinking I would sacrifice 8, 9, and 10 because IF I could win the rest, I'd hit my 28. Recognizing that putting more troops in the remaining high value castles left the low valued castles relatively weak I decided to further reduce the troop deployment at the low end to slightly increase deployment in the 8pt castle. This is an interesting game because I need to decide which bucket of castles I want to commit to while leaving a token force at the rest. There's a subtle rock paper scissors element to this this game but with an extra depth of how sharp are your scissors, how heavy the rock, and how thick the paper. I'd like to know how viewing past battle strategies of winners affects this outcome. If the previous results weren't published, would this third round have a distribution of troops similar to the first round?"
2,4,6,7,8,15,23,35,0,0,"Idk, could work"
@@ -334,14 +289,11 @@ Castles 4-8 are enough to win
Two troops at Castles 9 and 10, in case they are undefended."
2,3,5,8,2,22,23,4,27,4,"Well, I didn't use *actual* game theory, that's for sure!"
1,0,0,0,0,0,24,25,25,25,Control the four top castles that add up to more than the rest.
1,24,1,1,1,1,1,24,24,23,These are the intervals between notes on a piano I have a patent for.
4,7,5,21,21,12,20,7,3,0,"Took average of top 5 winners from first battle, average of top 5 winners from second, and guessed the trend of the top 5 from this battle would look like [0, 0, 0, 15, 16, 0, 0, 0, 39, 30]. Used evolutionary machine learning to find a strategy that would consistently give highest scores against slight variations on the predicted opponent strategy."
1,2,2,12,18,20,20,18,3,3,Just throwing something at the wall.
1,1,3,5,7,9,13,16,20,25,"Disregard game theory, and just kind of wing it?"
2,3,4,5,6,6,32,31,5,6,"Focused on 2 in the middle, never lower than 2 to beat the 1s deployed and heavier on two important"
1,0,0,3,3,21,22,23,24,3,Captain Chaos
1,0,0,6,17,17,6,4,23,26,War
1,6,11,14,14,14,17,20,1,1,It was obvious
1,1,1,22,9,22,1,22,1,20,guess work
1,2,2,2,3,18,18,26,26,2,"Avoid 10 as the most likely to be contested. Put 2 as a mininum to beat anyone just throwing 1's in. Focusing on 6, 7, 8 & 9 as together they defeat 1, 2, 3, 4, 5 & 10. "
1,4,5,5,5,10,10,20,20,20,
@@ -363,7 +315,6 @@ Thus, castles 6-8 got one extra soldier, who will provide The Edge To VICTORYYYY
1,1,2,1,20,5,2,1,32,35,"I suspect folks will counter the previous round(s) strategies, so I want to zig while they zag and capture the big prizes. "
1,1,1,19,19,17,17,18,3,4,idk tbh
2,10,10,2,20,2,2,24,2,26,This was all a fluke.
1,1,1,16,19,2,2,2,21,20,
1,1,1,2,1,15,20,3,29,27,"The trick seems to be strategically giving up on castles while committing the least number of troops to the ones I'm playing for in order to succeed. Four seems to be the best number to go after, while also strategically leaving 2-3 troops rather than one in a few locations in order to scoop up easy victories against foes committing 1-2. I'm a little concerned that I'm committing too few troops to Castle 6, but that's above the mean from each of the last two contests."
2,4,5,8,4,11,16,8,23,19,Macro economic model of optimizing against market inefficiencies as surmised from previous rounds
1,5,2,1,22,1,26,34,3,5,Trying to avoid over-spending on castles the opponent will deploy to.
@@ -371,12 +322,10 @@ Thus, castles 6-8 got one extra soldier, who will provide The Edge To VICTORYYYY
1,2,4,12,16,7,14,14,17,13,"For each castle, I took the average from the top 5 winners from the past two versions of this and rounded to the nearest integer. That total came to 102, so I used my judgement to bring 2 numbers down by 1. Because those two rounds differ greatly in winning strategy, this strategy is probably just bad against everything."
7,9,9,11,13,0,0,0,51,0,It adds up to >20 points and I don't think anyone's gonna care as much as I do about the ones I chose? Idk though
1,3,3,3,3,26,4,26,27,4,"Winning 6, 8 and 9 will all but assure me victory. If I lose one of them, I hope I have enough at castle 7 or 10 to pick up one of those instead"
1,4,5,15,17,3,2,1,26,27,"Maximize the deployments on castles 4, 5, 9 and 10 which appears to be better value than castles 6, 7, 8 from previous rounds. "
1,2,2,11,23,8,2,21,28,2,"Ensure I will win against all 0 deployments and try to dominate 9, 8 and 5."
5,6,8,10,13,15,5,28,6,4,"Lose the middle, win the ends"
3,4,6,11,11,21,11,11,11,11,"I didn't want to overthink it. The last rounds, switched based on where people loaded up, so I wanted to do a fairly even distribution to take the ignored categories while maintaining something in each category to not give anything away. I loaded up on 6 to try to win it since the best ones in the previous rounds each essentially gave away 2 of the top 4 so winning the 5th highest could be very beneficial."
3,3,11,15,18,11,22,6,4,7,Random numbers with the majority of troops deployed to castles with medium values (4-7).
10,1,1,1,2,1,5,23,23,29,yanggang2020
1,1,1,1,15,21,24,1,1,34,"Completely unscientific and eyeballed it based on the last two results. You need 28 points to win and at least four castles to make up that point total. I chose 10, 7, 6, and 5. It seemed like castle 10 was undervalued in the first round and corrected more in the second, so I'm anticipating that 10 will be more contested in this round. The other castles are the lowest value castles remaining that I need to get to 28 points. It appeared that the second round saw a greater emphasis on higher point castles and a more dispersed strategy (based, poorly, on averages). I put remaining troops in those castles assuming that enemy troops will drop off on castles 5 and lower. The remaining castles are just to cherry pick any undefended castles and force enemy troops to send at least 2 to capture."
5,5,10,15,10,20,24,5,3,3,"I wanted to prioritize taking castles 1-7. Taking every single one of these castles will provide me with 28 points, just over half. I chose to escalate with the number and hope others would focus on the ""big"" castles"", leaving me to win with the small ones. However, I still sent some troops to the small ones in case someone went all in on the same strategy. If they do, I'm hoping the small amount I sent+the variation in the troops I'm sending will allow me to win those matchups."
3,4,0,10,0,16,7,22,10,28,watching Game of thrones taught me to just go for it!
@@ -435,10 +384,8 @@ I did leave one soldier on castle 10 as a counter play for anyone who sends noon
1,6,1,13,1,21,24,1,31,1,"I chose 5 castles (9,7,6,4,2) to try and win 28 points most often and sorted my troops according to point values per castles. Then I took 1 troop from each castle and allotted to other 5 castles (just in case opponent sent 0 or 1 troops to those castles also)."
0,0,0,0,5,20,20,20,20,15,
1,1,2,7,3,12,7,22,8,37,"The crux of the 4 castle strat is taking castle 10. So if I get it, then have even deployment in the other castles, I'll beat everyone who tries it hinging on 10. If the majority of people hinge the 4 castle strat on 9, I'm screwed. "
2,2,2,2,10,12,14,16,18,20,The larger number castles are important to win but not that life changing to put 20+ troops. If you sell out for the three largest castles and end up splitting and losing the rest you will not win.
1,1,3,8,8,2,2,22,22,31,
0,0,1,3,1,1,22,23,24,25,"This is my second entry. I created it as the counterpoint to my strategy (sort of) in the first. Here, I must win 3 of the 4 largest and then pick up 4 more points."
1,5,6,8,10,10,21,27,1,1,I figured most people would go big on the first two and not on the others
0,0,0,0,20,23,0,30,27,0,"There's no way to win without at least four castles, so I focused on winning four and tried to optimize versus earlier distributions. "
0,2,3,11,14,15,5,5,35,10,
4,5,6,12,21,26,26,0,0,0,"I did the math and discovered that 28 points is the magic number. 8, 9, 10 get you 27, and 1-7 get you 28. So, I punted on 8,9,10, expecting most people to stock up on those and give them a free victory there while they use the majority of their troops. Meanwhile, I'll be happy to take all the smaller castles because 28>27. I debated going for 8,9,10 and 1 to take 28 points, or even 2,3,4,6,7,8 to make 28, but figured my first thought would win more often than the other two, which would be harder to distribute troops since 8 would take so many to guarantee the victory. "
@@ -453,10 +400,8 @@ I did leave one soldier on castle 10 as a counter play for anyone who sends noon
0,0,10,0,0,20,28,32,5,5,Because I'm the Grandmaster.
5,0,0,0,0,0,0,24,36,35,"limit losing troops, look for highest return on investment"
0,1,2,16,21,3,22,32,2,1,Savviness and wordsmithographyophillia
2,2,2,2,2,15,20,30,20,15,"Somewhat random, but trying to pick off low castles with 2 troops vs 1 and go for some larger numbers"
2,0,11,12,15,22,8,1,28,1,"Focusing on a few moderate-to-large castles. Expected to lose 2 every time, 8, 10 almost every time. About half of 1 and 7. Most 4, 5, 6, and 9."
3,4,6,11,13,7,6,21,26,3,"Many people are math adverse. When dealing with 100, people may be inclined to use numbers like 5, 10, 25. Numbers like 6, 11, 26 may get close wins and save more soldiers to put into other spots. "
2,5,3,20,8,36,6,12,3,4,"Exponential used to chose numbers (2^(1.2*n)). Focused on even numbers, weighted mostly to the middle value castles. crossed fingers"
5,8,11,1,1,17,21,1,34,1,Aim to get 28 points. Look to beat prior winners. Rely on intuition and a quick excel check (keep time invested at ten minutes).
2,3,4,20,26,15,10,10,5,5,"There are 55 points available for capture. The first to 28 points wins. No one can win unless they capture AT LEAST 4 castles. Most people would likely try to capture the most valuable castles first and weight their troops towards those objectives. But those who spend 50ish troops on castles 9/10 only have 50ish troops to spend on the remaining 8 castles, needing to win at least 9 points, between those 8 castles. I could see a 2, 7, 9, 10, strategy working well enough compared to last year's 4, 5, 9, 10, meta.
@@ -474,7 +419,6 @@ Trick: 36-19
6,3,3,16,3,22,31,4,4,8,"I found that having more troops at castles 1, 4, 6, 7, and 10 would be enough to win, so I focused on those. Also, those castles were not as heavily contested last time. I did just enough in those castles to win most games last time then allocated the rest of the troops to the other castles."
0,0,0,0,0,0,0,0,100,0,Nash Equilibrium
2,2,2,2,2,30,0,0,30,30,Felt like it.
1,2,5,7,7,7,7,7,34,24,random guessing
3,3,4,6,6,3,3,34,4,34,
0,11,12,0,16,18,2,3,2,36,
0,0,1,17,22,2,1,1,33,23,I slightly modified Vince Vatter's distribution from Round 2. I'm very original.
@@ -490,7 +434,6 @@ Trick: 36-19
1,1,1,1,4,6,21,21,22,22,"Just general intuition on how people will likely make their deployments. The low tier castles get one each, since about 30% of people send 0 to these, and most people that send any send more than one. Mid-tier receive few as well, but a few more, to win about 30% of battles there. The high tier castles receive more, but rather than clumping into 6-7-8 or 9-10, they are distributed closely between 7-8-9-10. I expect to win 2 of these 4 most of the time, and 3 of 10 quite a few times.
I know, not very scientific. But the best generals seek to understand to mindset of their opponents, and tailor their strategies to beat them. I am curious to see how this fairs."
3,2,0,0,0,0,0,25,35,36,I want to win 8-9-10 and either 1 or 2. Glass Cannon bby
1,2,2,2,13,13,20,7,27,13,i liked the numbers
3,4,5,17,3,19,3,19,3,24,"This is a defensive strategy. What is the most straightforward way to gain a majority (4+6+8+10) and then a defensive distribution to pick off lone scouts in the advent that you get overwhelmed in the core 4. As an added bonus, the strategy beat the top 5 of both previous years."
0,7,0,8,15,0,1,32,32,5,"I'm going for 2,4,5,8,&9 = 28 for the win... However... if someone is really going after 8 and 9 too, my 5 soldiers on 10 will hopefully be enough to carry the day."
@@ -500,7 +443,6 @@ I know, not very scientific. But the best generals seek to understand to mindset
2,4,4,1,2,24,26,3,31,3,Gotta take >half the points baby
1,0,19,1,1,21,0,23,0,34,
3,3,3,3,11,11,16,21,26,3,You’ll never know
1,1,1,1,10,20,30,35,1,1,IDRK
0,0,8,19,17,12,4,4,4,32,"Trying to win 10, 6, 5, 4, 3. Probably not a strategy to win the whole thing but should be good enough to be in top 50%."
1,0,19,1,1,21,0,23,0,34,
0,0,1,19,0,19,1,25,1,34,
@@ -510,7 +452,6 @@ Hopefully avoiding the high value castes will allow me to put more troops on low
Throwing 1 soldier to castle 10 in the event my opponent is thinking the same way."
5,7,9,3,8,5,27,31,2,3,
10,11,10,10,11,11,11,11,10,5,"Pretty much evenly distribute my forces winning any castle left undefended, while sending one extra guy to 5 castles that accumulate enough points to win on their own. Sacrifice Castle 10 as I don't need it to win and hope others will focus on it"
1,2,2,11,15,1,3,31,31,2,tried a hybrid model between the winning strategies of round 1 and round 2
6,6,5,15,20,20,28,0,0,0,Seed the top scoring castles and focus heavy on winning the middle ones. The castles worth few pointe I assumed few people would go for
1,1,2,3,5,8,13,21,34,12,"Starting with Castle 1, it is the first 9 terms of the Fibonacci Sequence (1,1,2,3,5,8,13,21,34). ΣF9=88, 100-88=12 troops remain for Castle 10. I don't think I'm likely to win, but isn't it more important to be beautiful?? https://www.youtube.com/watch?v=93lrosBEW-Q"
0,0,11,13,2,21,21,21,0,11,"Gut feeling, picking the less selected castles by either of the previous two rounds."
@@ -531,7 +472,6 @@ Throwing 1 soldier to castle 10 in the event my opponent is thinking the same wa
Probably suboptimal, but who knows."
0,0,0,16,1,1,25,28,28,1,
0,0,6,7,23,24,25,7,7,4,"go for the middling castles while not totally abandoning the higher ups, hopefully will win a number of battles while just winning 4 castles, but hopefully will get 5 & hopes it be the right 5. willing to concede 3 points..."
0,6,0,0,0,0,0,33,33,28,"I wanted to win 28 point by attacking as few castles as possible. By focusing as many troops as possible on castles 8, 9 and 10 and choosing a low value castle that people typically don’t commit many resources to, I hoped to win the majority of bouts. "
0,1,3,17,21,17,14,16,5,6,"I devised a strategy to beat all ten presented in previous iterations, then I added that strategy and devised the way to beat all ten plus that solution. I repeated several times adding improved solutions to my list to beat."
1,2,3,16,23,2,4,6,23,20,
@@ -553,17 +493,13 @@ Probably suboptimal, but who knows."
1,7,1,1,13,17,22,36,1,1,"At least 1 soldier at every castle to take easy points from undefended castles, but mainly focusing on castles 8,7,6,5, and 2 which yield enough points on their own to win a battle with half the points + .5"
2,4,5,7,9,11,13,15,16,18,"On average, you can deploy 1.8 troops per castle point. This strategy sends troops to each castle based on their values."
2,9,3,10,3,18,3,22,3,27,straight up guess
10,10,10,13,13,12,15,20,1,1,
1,10,13,13,13,15,2,27,3,3,"Think I need to send somebody to every castle, but potentially concede 10,9,7,1; hopefully sweep remainder."
0,0,0,20,20,0,0,8,26,27,"I tried to defend the minimum amount of castles needed to hold a majority of the hit points (assuming I understood the directions which, you know, 50/50), while another castle was defended with a small amount of troops to diminish attacking forces."
0,3,3,13,15,16,17,17,10,6,"The lower numbers are obviously less valuable. 10 and 9 I armed moderately, so that they could take a small force, but I didn't want to waste forces that could be used on the medium-high numbers. Those are the meat, and if past trends prevail, 10 and 6 may very well be good enough to beat many people anyway (for 9 and 10)"
2,10,2,15,20,30,15,1,1,2,Aim for the middle
0,0,7,5,6,17,16,17,16,16,
1,1,1,1,15,20,29,30,1,1,think it could work
1,1,1,1,15,15,15,15,15,21,Need to make sure you have someone at every castle. This beats most other combinations because it sends a man to every castle
1,1,2,2,2,2,20,20,20,30,"No strategy, just tried to weight the higher points castles higher"
3,3,8,3,21,5,26,10,10,11,"I wanted to defeat the previous champions. The first round winners won by going heavy in 4,5,9,10. The 2nd round they went heavy in some combination that didn't include 9,10. I went for go for 7, 5 and 3. With average values in 8,9,10 in hoping to get one or two of these."
3,5,11,19,2,19,19,17,2,4,"I wanted to optimize against previous winning strategies, to make sure I don't lose to uniform distributions (10, 10, 10, 10, 10, 10, 10, 10, 10, 10) or proportional distributions (like 2, 3, 5, 7, 9, 11, 13, 14, 17, 19). I also wanted to beat strategies that are directly written to beat previous winners (such as 4, 6, 7, 18, 2, 19, 21, 17, 2, 4, which is very similar to my winning combo). The hope is to win castles 3, 4, 6, 7, 8 to get to 28pts, while having enough soldiers in other categories to win castles that other strategies might punt. I can share some of the code I used for testing if that'd be interesting or helpful. "
0,2,1,1,19,22,25,28,1,1,"Stating the obvious first- there are 55 possible points, meaning you need 28 points to guarantee a victory. I feel like Castles 9 and 10 are overrated since Castle 10 is worth the same as Castles 8+2, 7+3, etc. My strategy was to win castles 5, 6, 7 and 8 for a total of 26 points. If accomplished, I only need to win ONE castle out of castles 2, 3, 4, 9 and 10 to guarantee a victory. I dedicated the vast majority of my soldiers (94) to get castles 5-8 while the rest only got 1 or 2 soldiers each. I actually put 2 soldiers on Castle 2 since it has the lowest value, I feel like putting a 2 there gives me the best chance of getting it. Putting 1 soldier each at 9 and 10 may seem silly but I still may get points against some other similar strategies. Even winning half of those castle 9 or 10 points would put me over the top. Anyway I have an English degree so the pressure is on you, math people! I wish you good fortune in the wars to come."
2,2,2,1,1,1,1,32,31,27,"Win the big castles, grab a couple other points somewhere."
2,4,7,9,17,19,30,4,4,4,With the power of my brain.
@@ -610,7 +546,6 @@ So I distributed my remaining 97 soldiers, giving slightly more to the higher-wo
10,10,10,10,20,20,5,5,5,5,"My strategy is people don't expect you to send troops to the small stuff, so they don't send troops there. The most troops are sent to the big ones, so your best chance of getting points is in the middle."
2,4,9,17,22,16,5,7,5,13,"I took the top 5 winners from the last 2 times, along with the averages for each castle from the last 2 times, then maximized the number of points scored if my distribution faced each of these 12 opponents. "
1,3,6,8,10,12,14,16,15,15,I split the difference between the average soldiers per castle from the previous iteration vs. roughly proportional #s of soldiers per castle value.
2,2,4,8,16,32,16,14,2,2,
5,5,5,6,12,12,16,9,12,18,Hoping other warlords don't put very many in the early castles
2,1,0,0,0,0,0,28,33,36,
1,1,2,15,19,0,11,14,17,20,"I tried to plan a balanced attack of the high-value castles (7-10) and the low-value castles (4-5) with increasing troops in each category. Since castle 6 was ignored in both previous editions I figured most players would attack this castle, so I left it exposed to avoid losing troops there."
@@ -625,14 +560,12 @@ So I distributed my remaining 97 soldiers, giving slightly more to the higher-wo
3,3,4,18,18,3,6,11,17,17,I looked at the top deployments from the previous rounds and looked at how they fared against each other. I then chose the best one and manipulated it until it beat all the others.
0,0,0,0,0,25,0,34,41,0,The minimum number of castles needed is 3 which have to add up to 23. 6 is app. 25% of 23 so 25 soldiers 8 is app. 33% of 23 so 34 soldiers and the rest go to 9.
0,3,8,9,13,5,28,30,2,2,
4,4,4,7,5,25,25,25,0,0,"I assume most opponents would direct the greatest resources to the biggest castles, possibly also directing more substantial ones towards those in the middle of the bracket (5 and 6). While I will lose 9 and 10, opponent investments there should enable me to hold 6 ,7 and 8, which would give me a 2-point advantage at the top range. By dedicating some resources lower I think I'm more likely to gain and hold 1-4 even if I lose 5. (I think 7 soldiers are more likely to win 4 than 5, and if I take some of the lower castles I don't care anyway.) "
5,6,7,8,10,12,13,12,13,14,"Summation x+4, then just added random numbers to make it add to 100"
2,2,4,10,2,16,25,3,33,3,"I decided to leave Castle #10 essentially undefended, and instead focused on some of the less-worthy castles, especially #9 and #7, to get a ""winning coalition"" of six castles with around 30 points."
0,0,0,13,0,12,0,0,37,38,23 points are needed to ensure a win - Overwhelming top two castles can get to 19 and then I just need to pick up one more of the other castles to win. Splitting between two helps cover bases if I lose one of the 9/10 and also increases odds i get the one castle to push me over 23 if I win the top two.
2,2,8,2,2,16,2,2,31,33,tried to invest in 4 castles that I felt relatively sure of winning and conceded the rest. High risk appetite!
0,0,0,0,3,16,16,27,27,11,Sacrifice the low scoring to just barely overload the mid-to-high tier castles
0,1,1,1,12,15,18,20,17,15,"3-4 points higher than previous average on higher point castles, at least 1 point per castle."
5,5,5,5,5,15,18,21,20,16,"slightly above the mean of previous rounds, with a little room to spare. It's better to supply low castles with a single high value than try to get all the high castles."
1,2,2,2,3,4,5,25,30,26,"Several troops on each in case someone puts down 0, and tried to have more than 1 since I suspect others will put 1 at each (at least). Thought 10 is a place where people would have very low or high, so I went medium to beat the lows but not waste too much. Trying to really capture 8, 9, and the misses to add up to 23 (winning number)"
1,1,9,9,18,19,20,21,1,1,Have 1 at each castle to win against anyone who doesn’t send at least one troop there. Then I put the rest at the mid tier castles because I just need to win a majority (28). Castles 4-8 are worth 30.
2,2,2,2,6,21,21,21,21,2,"The first 4 are so low value I'm giving them away, and the last one will be so hotly contested it's not worth fighting for. I put two there in case people put 1 - it's basically to take freebies while not costing anything substantial. I wanted to push all my chips in for the upper mid range ones. I went 21 for those as I think people might cap themselves at round numbers (20) for them, so it'd give me a slight edge."
@@ -659,7 +592,6 @@ So I distributed my remaining 97 soldiers, giving slightly more to the higher-wo
1,1,2,4,6,9,13,17,21,26,I made it porportional to the point value squared
1,1,2,3,12,17,3,12,22,27,ez money
1,1,4,4,10,20,20,20,20,0,Avoid wasting resources on a high contention battle (Castle 10). Spread out on high value targets with less contention (Castle 9 through 6).
1,1,2,2,2,22,26,33,5,5,"Placing enough soldiers in the top two castles to beat a minimal scouting group, focus on 6-8 in as they get me most of the points I'll need to win, and then minimal scouts below there just in case any are left empty by my opponent."
0,0,0,15,15,15,25,30,0,0,Play for the middle and push for the top but don’t over commit
0,2,0,0,16,6,19,25,0,32,"Way I figure it, the goal's to get 28 points. Minimum number of castles you can get that with is four. Best way to go about it is to abandon a couple of them completely so you can withdraw troops to ones that help the overall plan, while still targeting another lightly in the event that you lose an opening. Ergo, this."
0,0,0,0,16,19,0,30,35,0,"I'm going all-in for getting the bare minimum points of 28 or more. The fewest castles I need is 4. 10-9-8-7 is an option but lots of people will go after castle 10, so I'm going after 5-6-8-9. Same number of castles, but I'm playing off the beaten path. Also, 5-6-8-9 are all castles that are in fewer winning combinations, so they're more likely to be won by me.
@@ -681,7 +613,6 @@ The actual troop placements are based on the relative difficults I computed for
1,6,11,11,12,13,14,15,16,1,Assume opponent will load up on the most valuable castle so I will concede it and attempt to dominate the middle values.
1,1,3,3,3,14,18,17,20,20,Top heavy is my favorite.
0,1,2,2,2,4,23,23,22,21,
1,1,2,5,20,20,20,20,30,0,"Monte Carlo simulation, I think, with troops being weighted toward the higher-point castles with an inexact strategy picking a random number between 0-100 for the 10th castle and randbetween 0-remaining troops in the 9th and so on until the 1 point castle. simulated this 3000 times, then maximized my point gap between the average results with some buffer troops thrown in. "
4,5,6,7,20,25,30,1,1,1,Capture the low value castles
7,0,0,0,0,0,0,35,32,26,"The bare minimum to win 28 victory points, assuming I win all of my chosen battles. This allows me to maximize my troop deployment to a minimum number of castles. "
10,0,0,0,0,0,0,30,30,30,People are going to overthink it. 1/8/9/10 is enough to win.
@@ -697,13 +628,11 @@ The actual troop placements are based on the relative difficults I computed for
5,0,0,0,0,0,0,32,31,32,The goal is to get 28 points. Concentrated troops at the least amount of castles to achieve that.
1,3,5,10,16,26,20,11,4,4,Why wouldn't you choose this troop deployment?
0,2,3,3,16,20,22,26,4,4,
1,2,3,7,9,17,18,18,19,5,"aim to get 6-9, and maybe grab ten if it is lowly guarded, and then just a little at the bottom ones"
0,0,25,0,25,0,25,25,0,0,"Sacrifices must be made! Castles 1, 2, 4, 6, 9, and 10 are dead to me! Going hyper-aggressive (but not the most aggressive strategy). Best Case: I win! Worst Case: I am a troll!"
0,0,0,0,0,10,15,20,25,30,"Win four of the top five castles, and you win. This particular troop distribution fights harder for the bigger prizes; would win against four of the five top strategies devised last time; and should be able to compete against anyone putting significant effort in winning lower tier castles, as people have been doing."
2,3,4,6,10,13,14,19,15,14,Average of prior deployment data with small adjustments.
8,9,9,10,0,0,0,30,0,34,"Try to win 1,2,3,4,8,10 to get to 28"
0,2,3,1,12,12,12,12,12,34,"Top strategies in round 2 were all-in on 4 specific numbers, particularly 9+10 and a 9-sum pair (4/5, 3/6, 2/7, 1/8). Looking to break that by stealing 10 then getting 3 out of 5-9 range. Loses to top strategies of round 1 (more balanced emphasis on 5-9 range), hopefully the 'meta' doesn't drift back. "
1,6,2,1,14,15,17,21,0,21,"28 is the magic number. My positioning at the top is designed to get value from a variety of opponents. Main winning method: 8,7,6,5,2"
2,2,7,10,13,17,8,10,8,23,"Moneyball style. The goal is to buy points, and our goal is 28 points (more than half of 55). I divided 100 soldiers by 28 points and determined that the ""right"" value of a point is about 3.5 soldiers. I then determined the ""right"" value of each castle. I made a list of all the possible castle combinations to get to 28, and did some math to determine the inefficiencies between ""right"" values and ""actual"" values of the castles in prior exercises (for instance, Castle 10 was worth about 33 soldiers, but averaged 11.5 soldiers). Then I picked one combo that did not emphasize the most emphasized castles in the prior exercises (8,7,9). Then I averaged the ""right"" value for that combination against the average value placed on each castle in the previous two exercises, and went with that. I checked it against the averages and winners of the last one and felt comfortable to submit."
0,4,0,0,22,22,22,30,0,0,
0,1,3,20,3,0,21,24,0,28,"Looked at the past distributions and estimated what it would take to win castles 10, 8, 7, and 4. Saved some leftover men for other random castles. But figured castle 9 wasn't worth it. "
@@ -720,14 +649,12 @@ The actual troop placements are based on the relative difficults I computed for
1,1,3,4,8,13,17,18,27,8,Felt good
1,2,2,18,2,18,22,33,1,1,"I expect that there will be even more of a focus on number 10 this time, so I'm going to ignore that one. My plan is to get to 28 without winning either 9 or 10."
0,0,8,12,13,13,13,13,14,14,
2,3,4,3,17,22,26,26,1,1,"sacrificed 9 and 10, we'll see how many optimize against the last round or play it again."
6,6,6,11,6,16,6,6,16,21,No round numbers. Try to take castles that would be overlooked by others.
0,1,3,5,7,10,13,16,20,25,Based on a fibonacci series with rounding to the nearest integer.
1,1,2,4,10,17,27,32,3,3,
1,1,2,3,10,5,15,32,4,27,I think the key may be to pick up some free points from the lower castles.
0,0,0,0,0,0,25,25,25,25,"Instead of spreading out my troops, I wanted to backend my troops toward the castles with higher amount of individual points."
1,3,5,7,9,11,13,15,17,19,I just distributed troops proportionally to the value of the castle. I very strongly doubt that this will be successful.
4,6,6,2,2,17,17,23,10,15,"I wanted to make sure I got 6/7/8 for 21 points, and if I can clean up a couple more to get the remaining 7 to win, I'll be happy. Last time, it looks like those 3 numbers were more uncontested."
5,6,7,8,9,11,12,13,14,15,"I attempted to give more weight to the more valuable castles, but not neglect the less valuable that could give me the upper-hand."
1,3,6,8,13,14,15,16,1,23,This feels like what Nate Silver's mom would do.
3,2,5,9,11,15,22,20,3,10,Trying to beat the last two averages from the riddles before
@@ -753,13 +680,10 @@ The actual troop placements are based on the relative difficults I computed for
0,2,0,11,11,0,25,24,27,0,You only have to win by a little.
2,6,2,12,2,18,2,28,10,18,"A very non-sophisticated strategy based on simple logic and even numbers. With 55 points up for grabs, I need 28 to win. 10+8+6+4 is my ideal path to 28 in this strategy. So I put lots of troops into those castles. I picked the exact numbers based on multiplying the averages from previous versions of this by ~1.5. I spent what was left by dropping a couple “just in case” 2s in castles 1, 3, 5 and 7, then the remaining 10 in castle 9."
0,0,0,15,15,20,25,25,0,0,Focus more troops on enough points to get more than half of points.
2,2,4,14,1,0,16,16,0,35,
0,4,4,4,8,0,24,26,28,0,"I feel like putting a lot at 10 is risky, because a lot of people will put a lot at 10 and a loss is devastating. I loaded up on castles 7, 8, 9, gave up on castle 6 and 1, and dispersed the rest."
0,3,3,5,10,21,21,21,10,6,"Castle 1 is basically worthless, and as for the rest I just have to beat the most people, not the best people. So I'm assuming most people who do this didn't read and react the previous results and will therefore lose to a similar strategy as before just with minor tweaks."
3,3,3,3,3,17,17,17,17,17,
3,3,3,4,4,5,5,5,34,34,Slanging it
0,0,0,0,1,0,0,33,33,33,"Try to ensure victory at the top 3 values, which are greater than the sum of the rest"
0,6,8,10,11,12,13,14,15,0,I looked at how much more valuable on average each castle is to the others below it and sent troops based on this calculation normalized and rounded for
1,1,1,1,0,0,24,24,24,24,
3,3,9,2,3,14,21,5,17,23,"There are 7 strategies I'm trying to beat, 4 historical and 3 forecasts. The 4 historical strategies are the February Average, the May rematch Average, and the two champions Vince Vatter and Cyrus Hettle. The 3 forecasts are what I call the ""Forecast Average,"" and Copycat 1 and Copycat 2. The Forecast Average is what I expect the average castle distribution to be based on the last two battles: 3,4,8,9,11,11,14,15,12,13. The Copycats are players who are trying to synthesize the strategies of the last two winners. Copycat 1 focuses troops on castles 5, 8 and 9 (distribution: 1,3,5,8,12,2,3,31,33,2). Copycat 2 focuses troops on castles 4, 6, 7, and 10 (distribution: 2,2,6,12,2,17,22,2,3,32).
@@ -776,7 +700,6 @@ My distribution scores very well against the 3 historical averages, which I hope
2,2,2,16,2,2,18,23,30,3,"Trying to win the game 28-27 every time. compete for 9+8+7+4, if we both compete for the same one have just enough to maybe split a weird one (10,6,5)"
4,6,11,4,14,6,21,4,24,6,"Decided to fight heavily for all of the odd numbered castles - competition for 10 is likely to be high based on the last two rounds having 10 be somewhat low! I might pick up some easy points on the even numbers. Rather than trying to come up with a nice pattern, do the unexpected and be odd!"
2,2,2,2,2,12,2,42,12,22,
2,2,2,5,20,26,3,3,31,5,"Figured after the last one more people would go for Castle 10, so decided to pillage Castle 9. Plus 5 and 6 offer good strongholds without losing too many numbers (hopefully). "
1,2,3,4,5,11,16,21,26,11,"Always have at least 1 soldier to pick up free wins. Try to be one above round numbers on the more valuable castles. Assume 10 will be the most contested, so cap out on number 9. Beats a strategy of putting 20 each in the last 5, as well as 25 each in the last 4, or 10 in each."
1,1,1,1,1,15,20,20,20,20,
1,1,12,6,6,23,2,2,25,22,Prior data wanted to win high value targets while getting to 28 in most efficient way possible while still covering possible deficiencies or ignored castles.
@@ -795,9 +718,7 @@ Step 2: Prevent a loss against an archenemy with a normal distribution of forces
Step 3: Place at least 1 in each lesser-targeted castle in case my archenemy doesn't attack it, but put 2 in the lower ones to increase the chance of scooping up extra points to offset a potential loss of a large castle.
Step 4: Bask in glory as I defeat a majority of the would-be warlords in Riddler Nation!
"
0,0,0,17,22,1,6,6,26,26,
0,1,1,1,17,20,2,26,29,3,
6,7,8,9,10,11,12,13,14,15,
1,1,6,10,12,12,15,16,13,14,Assumed a trend based on the first two events. Added one solider more than the anticipated trend value to castles 4 through 10. Put the minimum on Castles 1 and 2 and the remainder on Castle 3. Crosses fingers.
0,0,5,15,5,10,20,20,25,0,I abandoned the first and last castles as not worth fighting over and focused on castles a little before and after the center that other teams might neglect.
1,1,1,1,1,17,18,19,20,21,"Token support on the least valuable castles. Divide the remaining forces on the most valuable 5 castles, weighting the distribution of soldiers to the more valuable castles. "
@@ -808,8 +729,6 @@ Step 4: Bask in glory as I defeat a majority of the would-be warlords in Riddler
5,6,10,3,4,5,4,54,4,5,"Looked at past battles and picked the inflection point of diminishing returns, had like 50 troops left and threw them all at castle 8 which was highest point value with widest distribution"
0,0,0,0,0,100,0,0,0,0,All of the troops at the first castle higher than 5
2,3,4,20,23,13,4,7,0,24,Counter Strategy
4,3,5,9,8,14,15,15,14,14,Balanced towards the top but focused on winnable battles
0,1,17,25,10,9,9,9,6,0,I looked at old answers and fudged a little honestly.
2,4,7,10,12,2,27,28,4,4,"Slightly higher deployment from last time’s in castles 9-10. If people saw the last one and went for 3 soldiers to win it I win, if they didn't see it and behaved the same (average 2-3 soldiers) I still win"
1,2,2,11,11,11,8,18,18,18,Concentrate on the higher values with some randomness mixed in.
4,5,6,5,12,23,14,15,14,2,mystery
@@ -826,16 +745,11 @@ Step 4: Bask in glory as I defeat a majority of the would-be warlords in Riddler
1,4,1,1,1,1,23,1,28,39,"This is my second submisssion, I wanted to try a completely different strategy. Here I aim to win 10, 9, 7 and 2 against many opponents, when that fails, I hope to win enough from the rest as I expect many entries to have several 0's and 1's."
1,4,6,7,12,3,27,33,3,4,"I need 28 points to win. Following the logic from previous iterations, I'm focusing on trying to secure 15 points from castles 7 and 8 while hoping to steal the remaining 13 points from winning 1 or 2 from castles 2-5 and 1 of castles 9 and 10."
0,0,3,7,10,14,18,21,18,9,"Zeroed out castle 1 and 2 since 3 points is small potatoes. Created a constraint that castle 3-10 had to be at least (Round One Median +1). Created 12 opponents, 5 winners from round 1, 5 winners from round 2, 2 opponents of my making. Used excel solver to maximize number of wins out of 12. Essentially creating an optimal solution to beat all 10 named winners with the additional requirement that each castle above castle 2 should be above the median and therefore more than 50% likely to be captured by me in any given game"
3,6,9,11,14,16,19,21,1,1,largely abandon 9 and 10 in order to increase distribution significantly above average for all other castles
2,2,7,10,16,22,29,4,4,4,win everything 7 and below and beat people sending 3 or less to high numbers.
0,1,2,2,15,15,18,19,22,5,Just trying to make sure it added to 100. Silver is Gold.
0,0,8,11,0,22,28,31,0,0,Strongly attacked with the most likely castles to reach 28.
5,8,8,20,13,5,3,18,18,4,"I noticed that there were waves and troughs in the data provided after the first game. Placing a number of soldiers just where a wave ends and trough begins seem to an optimal strategy, intuitively speaking. The first wave nearly always ended at 3, 5 or 8 so I placed corresponding numbers on all the castles. This gave me a leftover of 40 which I dumped on a small number of castles, aiming to catch some of the second wave on those."
0,0,0,0,23,24,25,0,28,0,
1,3,4,13,15,4,6,5,32,22,Based on number 2 last round with minor variations
0,0,9,11,21,18,18,0,0,23,Just kinda throwing some troops like the US Govt throws money at the army
0,5,5,3,23,23,27,11,1,2,"Decided to weigh 7-5 the heaviest, as they are accountable for a good chunk of points. Didn't want to lose 9 or 10 if they were abandoned, so I put a few there (but mostly empty). Then I concentrated some on 8 (expecting that it would be defended less than 5-7 but not as minimally as 9-10). The lower values were kind of chosen randomly."
4,8,8,10,12,12,12,18,20,1,Give up the ten and try to win the high middles
1,1,2,4,6,9,13,17,21,26,"it's a quadratic distribution of soldiers, and I like smooth curves"
0,0,17,0,0,0,29,23,2,29,"All-in on 3,7,8,10"
0,0,2,15,11,6,5,3,27,31,"I tried to place heavier in the 9 and 10 spot to guarantee more points and let the 1 and 2 spots go, as they provide minimal points. I also sacrificed a chicken to Jobu."
@@ -853,7 +767,6 @@ Step 4: Bask in glory as I defeat a majority of the would-be warlords in Riddler
3,4,5,6,10,10,11,13,16,22,"I wanted to use just enough troops on the earlier castles to win them , and wanted to win 9 and 10."
5,0,7,7,7,21,3,24,2,24,"This strategy wins at least 24 points against an average opponent, and has the opportunity to take at least 4 points from castles that must be left largely unguarded. If an opponent takes 6, 8, or 10, then they likely used too many troops to adequately cover the mid-tier castles."
5,0,7,7,7,21,3,24,2,24,"This strategy wins at least 24 points against an average opponent, and has the opportunity to take at least 4 points from castles that must be left largely unguarded. If an opponent takes 6, 8, or 10, then they likely used too many troops to adequately cover the mid-tier castles."
0,0,0,10,15,17,26,30,0,1,
1,3,6,7,9,10,13,15,17,19,"If F is a fraction of the troops, 1F+2F+...+9F+10F should equal 100. F is 100/55, or 1.81818...As there are no fractional people, I wanted to allocate the closest whole-number equivalents to 1F, 2F, etc. to the various castles, to minimize my ‘shortfall fraction’. So because some castles have an extra fractional person, the castles I chose to have a ‘shortfall’ were 1, 2, 4, 5 & 6."
0,0,0,3,3,18,18,18,18,22,
1,1,2,3,5,8,13,21,18,28,"The golden ratio is a beautiful thing. It is everywhere in math, so why shouldn't it solve this problem too?"
@@ -863,7 +776,6 @@ Step 4: Bask in glory as I defeat a majority of the would-be warlords in Riddler
2,9,2,2,1,12,21,16,19,16,trying to divide in a way to get at-least half victory points based on the distribution that might be possible based on the previous two distributions.
3,1,1,1,2,2,2,22,34,32,Seems like it'll do the trick often enough. Not even gonna worry about the meta.
2,2,3,3,5,11,16,16,21,21,I came. I saw. I conquered. I used Google Translations to say something cool in Latin.
5,5,5,5,5,5,5,5,5,50,
1,2,5,13,17,0,26,0,36,0,"I need 28 VPs. So I aimed for an unusual combination of getting them. As long as I get castles 3, 4, 5, 7 and 9, I have my 28 points and have no need to get any others. I will lose only to people who outbid me on one of these five, but those who don't bid 0 on any, or even multiple, castles, will have fewer troops to deploy on those five, so my chances are reasonably good. I expect to lose to those who max out on castles 9 and 10 but to win against a good percentage of other contestants.
I made a late change to go for 3+ points from 1, 2 and 3 combined"
@@ -874,9 +786,6 @@ I made a late change to go for 3+ points from 1, 2 and 3 combined"
2,4,5,7,9,11,13,15,16,18,Based on value of castles.
2,2,7,17,22,22,13,4,4,7,I am inevitable.
4,5,8,10,7,13,10,14,17,12,Mixed strategy
1,4,4,17,19,19,5,4,5,5,"In order to win I have to beat them at a castle that they plan on winning. This means instead of fighting them everywhere for points. I take easy points where they don't plan on winning (I don't think many people are trying to win every castle). Then the rest of my troops only try to play spoilsport. Almost every strategy I can think of is going to use one of castles 4 5 and 6, so I will target those as my 'spoilsport' castles.
I'm obviously vulnerable to people allocating troops evenly or strictly by castle value, but hopefully there will be more people trying to be clever and maximize value per troop."
1,1,2,2,2,10,10,20,50,2,Spread troops to high point value locations but saved on troops sacrificing the highest.
2,4,6,8,10,10,12,14,16,18,
1,2,4,8,12,16,21,31,2,3,Peak at 80 and decline downwards. Don't sacrifice any entirely.
@@ -908,7 +817,6 @@ In this manner, the true key battleground will be Castle 7. If we assume that I
The hope is that the opponent over-commits on the higher value castles while undervaluing the remaining castles. By flipping that thinking on its head, I hope to undermine the opponent's strategy."
3,3,3,7,7,6,6,15,30,20,My goal was to fight for every castle. A sizable investment in castle “9” and “10” was meant to punish any player who got too cheeky while also remaining competitive in the middle values. No castles for free to the opponent.
5,6,7,8,9,10,11,12,13,19,Made it up
3,4,7,8,9,5,21,21,3,3,"Ahahaha, victory is mine!"
2,5,5,2,6,11,30,29,6,4,"Not quite randomly, I looked at a line graph of the averages of top scorers from the first and second iteration. Then I imagined the future iterations as something of a jump-rope moving. While over-caffeinated, this was the decided plan of attack:
Let x1 and x2 be the vectors of troops deployed per castle.
Let y3 = 1/2(x2-x1)
@@ -920,7 +828,6 @@ Magic?"
0,0,8,10,12,14,17,19,20,0,"I guessed that an distribution proportionate to point values will rarely win the 10 and will waste trips on the low-value castles, so I dropped the 10 and the bottom too and then loosely distributed them proportionally from there fight estimating as I wrote on some construction paper with a crayon."
17,11,11,11,12,15,20,1,1,1,"The warlord can win with 1-7. Rather than targeting the high-point castles, target the low-point castles. In case our competitor tries the same strategy, we left one troop on each of 8-10, and loaded up on 1."
0,7,0,0,0,0,25,0,32,36,
1,2,3,5,11,19,20,19,16,5,I tried for a bell curve with the peak between 7-8
1,1,3,5,7,13,16,22,15,17,Value weight plus noise
7,13,7,13,4,16,4,16,2,18,"I was trying to guess the 100,000,000 number and this answer keeps coming up"
6,7,9,12,16,21,26,1,1,1,"Total of 55 VP to be won, and a player who wins the top 4 castles wins the game. Some will push really hard to win the top 4. Others will realize this and try to scoop up the low VP castles cheaply while still competing for some of the top 4. Honestly that's pretty much what I'm doing too, but rather than competing for the top 4, the idea is to scoop up the bottom 7, while tossing a bone to the top 3 castles to hopefully outdo anyone who is using a similar bottom-up strategy.
@@ -928,7 +835,6 @@ Magic?"
The idea is that, while most people will invest a lot into the top castles (because they are valuable and because they expect others to do the same), many will not invest much into the bottom castles. This makes them (hopefully) cheap to obtain, and allows a pretty hefty force to go to castle 7 to (again, hopefully) outdo those who want castle 7, but who value it 4th most."
1,2,2,0,0,4,6,8,34,43,win 10/9 and two average others
5,5,20,5,5,20,5,5,10,20,"Not sure, just playing! "
0,2p,0,0,20,20,20,20,0,0,Try to get to 28 in a way that average person wouldn't do.
0,0,4,15,18,6,4,2,28,23,Random ass guessing
2,5,5,17,19,7,7,6,18,14,"Played around with numbers in excel until I found a combo that would beat all of the top 5 entries from both of the past 2 contests, as well as the mean numbers from both"
0,0,1,18,2,24,3,22,3,27,"go for 4 castles that add up to just over half of points: 10, 8, 6 & 4. put some troops for most other castles in case i get wiped out on my targets by someone who sends few or no troops elsewhere. go all in on castles 6 & 4 (4 & 4.5 troops per point) with less investment in castles 10 & 8 (2.7 & 2.5 troops per point). send 0.33-0.43 troops per point to castles 3, 5, 7 & 9. this troop alignment happens to beat the top 10 previous finishers (5 from first round & 5 from second round). the main weakness of this strategy is if someone sends a ton of troops to castles 10, 9, 8 & 7 however not many players seem to take that strategy. the other weakness is an odd-numbered-focused strategy where the opponent sends a ton of troops to castle 10 or 8, plus a moderate number of troops to castles 9, 7, 5, 3, 2 and/or 1."
@@ -958,12 +864,9 @@ The idea is that, while most people will invest a lot into the top castles (beca
0,1,10,19,2,22,2,4,20,20,"counters some and breaks even with most of the previous top 5s, and counters the counter-strategy by avoiding the hotter zones."
2,3,4,5,9,9,11,19,19,19,Fibbinochi sequence
1,5,5,5,9,16,13,17,21,8,"I went with my gut, I also glanced at the data of the past two matches"
2,3,5,15,20,20,20,20,3,2,I decided to try to capture the middle value castles assuming that others would place more resources into capturing the high value castles. I essentially conceded the 10 point castle to capture the 5-8 point castles.
0,5,0,0,0,0,0,35,30,30,"There is 55 points total. 28 is what you need to win. So win 10,9,8 and 2. Focus on the minimum amount of effort to win. Win by a little or a lot, a win is a win."
2,2,10,12,15,2,3,10,20,34,
1,3,4,13,15,18,1,20,22,3,"Go hard on 4, 5, 6, 8, and 9."
0,0,0,2,12,16,0,33,34,3,"Trying to win 9, 8, 6, and 5, and hoping I can steal some of the others."
0,0,0,1,1,0,1,2,2,3,The mini-me on my left shoulder
0,0,1,16,21,2,25,3,29,3,
1,1,1,1,1,1,40,26,15,13,inverse of the 7 down strat
2,2,2,8,0,19,26,41,0,0,Avoid wasted troops at high value targets and low v; win on aggregate over sim.
@@ -1003,24 +906,19 @@ I do have to punt on one of the bigger numbers, so I choose 7 since I think peop
1,1,3,3,3,4,19,24,20,22,"I would like to say I performed a complex game-theory simulation to optimize the outcome, but I basically eyeballed it to weight toward higher victory points without abandoning any castles; since the two previous contests had both the 7/8 and 9/10 focus strategies winning, I did not exclusively focus on either."
5,6,8,10,1,16,21,31,1,1,"In previous battles the winners took two different approaches. The first round the winners focused on castles 4,5,7,8. In the second the focus was on 4,5,9,10. My idea was to focus on 6/7/8. then capturing as many little castles as I could."
2,4,9,4,4,4,4,4,33,32,"Ensure I could beat both previous winners. This game is transitive, right?! It would be fun to know all the results! Maybe you can share the a google spreadsheet with everyone's answers, but maybe not our names and emails? :)"
5,6,8,12,20,20,12,8,6,5,"Split from the middle, easier to concede the higher and lower"
5,5,5,5,0,0,0,10,30,40,"Intuition and guesswork based on the past data. Most generals had more even distributions and none of the top 10 had any allocations above 40. So if I capture the highest value prizes and a few of the smaller ones that garner less attention, I figure I should be in pretty good shape."
2,3,3,4,5,10,18,22,18,15,I tried to ride the wave from earlier deployments and emphasize the trough in the middle.
6,0,0,0,0,0,0,34,30,30,"A deliberate overkill strategy, designed to get exactly 28 points. If my guess is right then people will back down a bit on the bids on the higher, and still ignore the lower values. In this strategy you have to take the top 3, so the 1 value castle is the best hope to steal a final strategy. It just seemed like an interesting idea."
0,3,0,18,0,17,9,15,5,33,"The winning strategy in round 2 was primarily to take castles 4, 5, 9, and 10. I'm largely trying to disrupt that by using more force at 10 and 4. At the same time I'm trying to take 4, 6, 8, and 10 to get myself to 28."
1,1,2,20,20,2,2,25,4,25,"Faking out most, and winning 27 points against uniform. "
1,2,2,4,4,25,26,26,5,5,The heart wants what the heart wants <3
0,0,0,5,7,10,21,24,33,0,Avoided overcommit on 10. Attempted to stack 9 and upper middle.
1,1,1,6,15,20,25,25,5,1,I put the most troops in castles that were in the middle in points in attempt to win several smaller castles instead of a few larger ones.
4,6,8,9,10,11,12,13,13,14,Trying to get win at several castles with an emphasis towards the high point castles. Weighting for each castle proportional to the square root of the value.
0,0,0,20,0,10,20,30,0,20,just felt intuitively good
1,2,22,1,1,22,1,1,27,22,"It's almost 4 am, this is better than anything"
2,3,4,5,6,7,8,9,10,1,Who can tell?
0,0,0,0,0,0,0,33,33,34,Go big or go home
4,5,6,7,11,27,28,4,4,4,Guess
2,2,2,17,2,18,5,18,32,2,
0,2,7,11,5,16,17,31,4,12,"I like how the last winner put it, “good against the previous result, great against optimized adjustments”. But I’m not sure if I’ve accomplished that"
0,1,1,8,12,1,20,25,30,1,"I just want to make sure I win certain castles (9,8,7,5,4) leaving others with one soldier just in case the other person don't fight those castles"
3,3,6,11,14,2,27,27,2,5,
3,3,4,15,16,15,18,20,3,3,Not really sure
4,0,0,0,0,0,0,33,33,30,"Just need 28 points to win. Figure I can almost always win 1 point with a small number on 1. Then maximize my focus on 8, 9, and 10."
@@ -1045,7 +943,6 @@ Castles 4 and 5 seem to have been highly overvalued in the earlier rounds, so I
0,0,2,30,2,30,2,34,0,0,Three eyed raven told me
0,0,0,10,0,0,0,30,25,35,Just a hunch I had based on previous editions
3,5,1,11,10,15,15,20,17,3,idk it’s 5am
1,2,5,8,9,13,16,19,16,12,I looked at averages from before and thought I might tie or beat most of them where possible.
0,0,0,0,0,19,23,27,31,0,"All focused on the fewest castles needed to win, avoiding the highest and lowest valued."
2,7,2,7,7,19,7,19,7,23,No even numbers. Only choose every second castle for real winning. Take a few to the rest to win against zeros.
2,3,3,7,10,14,18,21,18,4,"I figured I'd look at what strategy riddlers used last time. I looked at both the mean and the median. I started with the median set and increased most of the numbers 1. I also compared this number set to the mean. It won 35 of the 55 points. So, why not go with that? "
@@ -1080,7 +977,6 @@ Going according to the highest points per median soldier allocation battlefield,
If there were any remaining soldiers, I allocated one by one to the battlefield that had the highest points per soldier if adding one more soldier meant I won that battlefield.
"
0,8,8,22,2,20,18,20,2,2,"I realized that you need 28 points to win a match. Winning the bottom seven would give me that. I am willing to concede the top 2 castles if it means winning all 8 bottom castles, other than Castle 5. Essentially, I want to allow my opponents to win Castles 1, 5, 9 and 10, for a total of 25 points. Then I can win Castles 2, 3, 4, 6, 7 and 8, for a winning total of 30 points. I was willing to totally abandon Castle 1, but sent a two-person ""scouting detachment"" to Castles 5, 9 and 10, to ensure that they wouldn't simply be taken unopposed. "
1,3,5,7,11,15,17,19,21,1,"Sacrifice the king, win the rest, and maybe sneak the 10 if someone sacrifices harder. "
0,0,1,2,21,21,22,3,4,26,"Trying a 4-castle deployment, as it's just easier to rely on. Throwing a few around in the larger unattended castles in order to protect against other 4-castle deployments. This mostly beats the recent winners and isn't the obvious 10-8-7-6 that stomps the last round. I could be in trouble if people really try to jump on 10, though."
1,3,5,13,17,2,14,16,17,12,I just took an average of the distributions of the previous two winners
@@ -1089,14 +985,12 @@ If there were any remaining soldiers, I allocated one by one to the battlefield
0,0,0,0,0,20,0,0,40,40,"I wanted to deploy high numbers of troops to the highest value castles to get as close to victory at the beginning as possible. From there, it only takes 6 more points to win the game, so I put all my remaining troops in Castle 6 to have the best chance of taking the points needed to win."
0,1,1,2,18,16,3,25,31,3,"Winning strategies focused on capturing 4 castles that could get you over 28 points so stuck to that. Was hoping 6, 7, and 8 would still be relatively neglected and put my effort toward winning 9."
2,3,5,5,14,14,16,16,14,11,
0,0,1,1,1,4,8,12,36,36,Because I never want to lose a castle sending no men except for castles 1 & 2. I also keep one man in reserves to go act as an assassin just in case I lose because I'm a sore loser.
1,1,8,1,2,2,23,27,3,32,"Hoping to win 10, 8, 7, and 3 for 28 points. Putting small numbers on everything else in hopes I can win some cheap points in case other things go wrong."
2,2,2,2,2,8,13,18,23,28,"2 points on each to hedge, dump the rest at high-value castles"
1,1,1,3,7,16,22,24,3,22,Worked off last time’s results and heavy fortification on number 9
0,2,3,16,2,3,23,24,24,3,I chose 28 points to contend for and 27 to (mostly) cede.
1,2,4,10,19,24,27,4,5,4,This feels nice
10,20,5,6,4,10,10,10,5,20,To keep castles unbalanced.
0,1,3,14,8,1,4,5,32,22,"Ran a genetic algorithm, trained on both previous wars (with double weighting for war2)"
5,5,10,15,20,25,5,5,5,5,"Expecting that the hardest fighting will be for the most valuable castles this should leave the lesser value ones relatively undefended and easier to pick off. However, for those who share my view a small commitment of troops is worthwhile in case others go for an all or nothing strategy and do not think high value targets are worth it. Expecting to win 15 to 25 total victory points remaining consistently around or above average. "
0,0,0,20,0,0,26,26,28,0,"Maximizing distribution to minimum number of castles needed to win, while avoiding expense of castle 10. "
5,5,5,5,5,10,10,15,15,25,If I can commit enough to with with higher value forts then the rest don't matter.
@@ -1126,17 +1020,13 @@ If there were any remaining soldiers, I allocated one by one to the battlefield
1,1,2,10,1,8,8,9,26,34,"First I wanted to beat all 5 of the top 5 from the last time. Then I wanted to beat the build optimized to beat them. Then I wanted to beat the build optimized to beat that. After that I still had 42 troops left, so I started thinking about what I lose to. I lose to builds that are stronger on any of 6,7,8. The way to beat this could be either increase my 6-7-8 numbers or pick up points from elsewhere from that person. I decided that playing for the 9 might be a good idea. The 9 was really expensive last time, but it was enabled to do so by the low 6-7-8 numbers. I'm assuming that this person is beating some or all of my 6-7-8, so they can't shove on the 9 as well. I've fairly arbitrarily decided 26 on the 9. This leaves me 16. First, I'm putting at least 1 on each of the first 5 to punish any 0s. Now I have 11. I might want to put everything on 5, and that would be strong against people who were playing around the previous set where 5 was a huge spike for no reason, but the 5 could easily be a huge spike again for no reason so I don't want to put much into it. The 4 seems like a significantly better spot because it was lower the last time but still part of the spike which means people playing around the last time will avoid it. I'm putting 9 more (10 total) on the 4, leaving me 2 left to place. 1 is going on the 3 to play around 1s and the other is going on the 8 to put it at 9 because I was scared I would lose the 8."
3,3,4,5,3,16,23,7,17,19,"I'm counting on an overreaction to the distribution in 9 and 10 while focusing on the undervalued 7. It seems warlords are maximising the extremes though, so a token force to the lows should capture some value."
1,0,2,15,22,1,2,3,33,21,
0,0,3,10,1,16,28,33,2,3,Forces concentrated on minimum 5 castles to win with small forces on others in case uncontested by opponents
3,4,3,0,15,5,25,31,14,4,"Mainly focusing on winning 7,8,9 and 5, which is enough to win. Small amount of troops in other castles to counter steals."
10,0,0,0,0,0,0,15,25,50,Forces concentrated on minimum four castles to win
51,51,51,51,51,51,51,51,51,51,Kobayashi Maru - hack of rules to win
0,10,0,0,0,0,15,25,50,0,Forces concentrated on alternative 4 castles to win
2,2,2,1,2,2,16,24,24,25,WIn 28 and loose rest
0,0,1,1,15,20,20,1,1,41,"The most direct method of achieving a majority while (hopefully) limiting exposure to defeat by fielding more men along my prescribed victory path than does the opposition.
No backup plan, no reserves. When in doubt, attack. "
0,0,0,0,18,22,22,33,0,5,Give up 5 castles expecting to split points on some of them. Maybe get a cheeky 10 against similar strategies.
0,3,3,6,9,16,16,16,23,24,"weighted from higher point values to lower point values, not overlooking valuable stretches"
1,1,1,1,1,1,1,1,46,46,"I'm predicting that most of your audience is pretty smart, and will have worked out that you only need 1, 8, 9 and 10 to win, and will have placed 25 soldiers on each of those castles. This strategy is designed specifically to beat that."
0,0,0,0,19,23,0,27,31,0,"Go all-in on 4 castles that give just enough points to win (28), ceding the other 27 points’ worth. Stack a few more troops on the high value castles just because."
1,1,1,3,3,27,28,30,3,3,"Weighted on 6,7,8 which would get 21 out of needed 28 points to win, and cover just enough on the others to prevent easy steals"
@@ -1148,20 +1038,16 @@ The troop deployment also forfeits castles 1, 2 and 3 to reinforce higher value
1,3,5,7,9,11,13,15,17,19,Assigned soldiers proportional to castle value
1,3,4,6,15,21,3,19,8,20,"Castle 6, despite good value, has been ignored in the past two games. Castle 10 needs to be contested, but not with too many troops. Similarly, castle 8 should be one that there is a large play for. I expect many players to overcommit to castle 9 and waste a lot of troops for something I can easily overcome with castles 6, 8, and 5."
2,2,2,15,20,20,20,15,2,2,
0,1,1,12,10,19,1,21,1,32,curious about this.
1,5,6,9,5,4,10,20,0,40,"I've done these things before, and I know that people stack the second-highest value. I decided to go a more conservative approach and split a lot of things, stacking on those where less soldiers would be and retreat where others would stack."
0,1,1,2,2,20,11,24,11,28,It's a bifurcated attack on the previous two seasons.
1,5,5,5,5,5,5,5,32,32,Put a lot on high value targets + pick up the forgotten points. We'll see how it goes.
1,3,5,7,9,11,13,15,17,19,Gave more to more valuable castles without writing any off
1,1,1,1,23,6,11,11,23,22,"First, leave nothing undefended. Next, beat an naive even distribution (10 everywhere) and a distribution that concedes the first 5 and doubles up on the rest. Bonus that it beats most of the previous winners and the top 10 from 10 million random strategies I ran on the computer."
1,5,1,1,1,1,30,1,31,30,"My ideal war is pretty obvious :P
I didn't come up with this through a strategy or anything fancy. To misquote _Macbeth_, all hail Zach who shall be king hereafter!"
1,1,1,1,1,10,15,10,34,26,"Looking at the last two top deployments and data breakdowns, the top deployments were throwing the bank at 9 and slightly less for 10. My strategy is top-heavy; it is very dependent on winning the top end and all but sacrificing the lower end (one soldier per castle for the bottom five will claim undefended territories and nothing else).
The focus was on beating the winning strategies from the last cycle. 34 for castle 9 and 26 for castle 10 beats the top four cleanly, for a cost of 60 soldiers. Castle 7 gets some value play, too, so 15 goes there, and 10 each for castles 6 and 8. This leaves five soldiers to pick off anything undefended; our strategy is to win all or nearly all of the top 5, and then anything below is gravy. Weaknesses are if they can claim the 6-8 and not sacrifice the bottom to do so; a tie or better on one of those three and winning 9 and 10 should bring victory."
0,0,0,4,4,10,17,28,32,5,"The additional deployment scheme was won with emphasis on castles 7 and 8 .. and in the reprise (second) simulation, the winning submission emphasized Castle #9 and #10. By putting 0 soldiers in Castle #1, 2 and 3, I am going to concentrate my forces in Castles #6 - #9 with just putting enough soldiers in Castle #10 to avoid giving it away cheaply. In addition, I am putting 4 soldiers each in Castles #4 and #5 as a way to score a few ""cheap"" points against people who concentrate almost exclusively in Castles #6 - 10."
1,2,2,2,11,15,17,22,15,13,COC
11,11,11,12,14,15,16,0,0,0,I went for 28 out of 55 points by selecting the lowest values that add to 28.
3,7,10,14,18,22,26,0,0,0,"I aimed to win 28 points (minimum for a simple majority out of 55), and targeted the lowest value castles to reach a 28-point total while avoiding committing troops to the high-value targets. My goal was to pay just over 3 troops per point. "
0,7,1,0,0,1,28,1,33,29,I took one of the better performing solutions from last simulation that seemed to work well against the other top solutions and tweaked it slightly.
1,1,0,0,0,15,20,31,30,2,"I figured most people would favor Castle 10, so I instead heavily reinforced Castles 8 and 9. I also left several troops in Castles 6 and 7. If I can win the middle numbers, I will be in good shape. "
@@ -1178,15 +1064,10 @@ The focus was on beating the winning strategies from the last cycle. 34 for cas
0,0,0,20,20,20,20,20,0,0,Why not?
0,0,0,0,10,12,15,18,21,24,Started proportionally and then let go of the lesser castles
0,0,12,1,1,23,3,3,33,24,Used a genetic algorithm (the same as last competition) to explore distributions that would be good against the second round distributions and the first and second round distributions combined. Then used the same algorithm to optimize against *those* and the first and second round distributions simultaneously.
0,7,7,10,0,0,25,26,27,0,"I need at least 28 points to win. I expect a lot of people will spend heavily on 10, so I skipped it and focuses on 9, 8, and 7. Then I spent enough with the lower numbers to make up the remaining 4 points in a few ways."
2- z,4- z,4- z,7- 15,12- 20,15,20,22,7,7,
1,2,1,12,22,4,8,10,23,17,I used an excel sheet and found a strategy by trial and error and some calculations that would best every previous winning line up and that would also beat the average line up.
1,2,1,12,22,4,8,10,23,17,I used an excel sheet and found a strategy by trial and error and some calculations that would best every previous winning line up and that would also beat the average line up.
3,2,5,6,4,12,12,22,22,22,
3,6,7,10,10,18,16,14,1,15,"General ramping-up from low to high, leaving out one high to improve the chances on the others"
3,2,5,5,10,20,20,20,10,5,"Best to at least contest the small ones, 10 is gonna be over deployed y a lot of people. Capturing the soft gooey middle should rack up enough points to win a fair number."
1,1,1,1,6,14,20,25,35,1,Putting my forces towards hopefully overlooked castles.
2,3,4,3,3,3,35,3,43,3,"Guarantee 9 and 7 (in most cases), with a good enough chance of picking up the remaining 12 somewhere else"
1,1,1,1,1,1,1,1,1,91,
3,4,5,4,4,4,31,4,37,4,"Try to guarantee 9 and 7 and pick up 12+ elsewhere
@@ -1248,7 +1129,6 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
0,0,2,3,12,15,18,11,5,34,28 to win. Win 10. Win any 3 of 5-8.
2,4,5,7,9,11,13,15,16,18,"I chose a simple strategy: based on the total points available, determine the number of points per soldier, and deploy the appropriate number of soldiers to each castle assuming they would win that number of points. While this strategy does not account for the slight differences in over and undervaluing deployment if one is rounding up or rounding down (since only whole numbers of soldiers can be deployed), it should (in theory) help to appropriate weight the value of all castles and penalize opponents who skew their distribution of soldiers too heavily in any direction."
3,3,3,3,3,17,17,17,17,17,This strategy is to spread a wide net. Which clearly hasn't worked so far. But lets try it
2,2,3,6,11,3,26,18,26,4,Why all the pearls? Why all the hair? Why anything?
2,2,2,10,10,20,2,2,25,25,"Basically, I assume people will see what happened last time (lots of troops in 4,5,9, and 9) and avoid those this time. So I put troops there."
2,2,3,3,14,18,25,25,2,6,"Target middle value castles (5, 6, 7, 8) with larger forces while deploying a midsized force to castle 10."
1,2,2,3,4,6,9,14,22,37,fibonacci is awesome so fibonacci +1 must be better
@@ -1280,7 +1160,6 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
0,10,0,0,0,0,0,30,30,30,Make or break: a massive push to reach the target point value to win (i.e. 28 points)
0,0,0,0,0,40,60,0,0,0,Want to overwhelm the squishy undervalued middle with enough troops to fend off anyone who doesn't just flood one of the two castles. Pin the rest on luck and the fog of war.
1,2,2,2,2,16,22,23,27,3,Ancient warlord secret
2,5,5,10,15,18,21,22,0,0,
0,1,11,2,3,24,6,8,37,8,"The big lesson from round 2 was that it's really effective to invest heavily in only four castles, totalling 28 points. Not only did all the top deployments from round 2 follow that strategy, but deployments optimized against the first two rounds' results (and deployments optimized against optimized deployments!) follow it also, sometimes even more strongly. That has left me perfectly torn between two opposite approaches - take the obvious lesson, invest heavily in 4 castles and try to win that way (which would mean a deployment like 0-0-11-0-0-23-1-2-36-27); or assume that everybody will try 4-castle approaches now, and optimize against them while still scoring decently against other plans. I've changed my mind about a dozen times, and finally decided to do the latter. I'm tackling the 4-castlers head-on in castles 3, 6 and 9 (a 4-castle plan needs to go through at least one of those), and putting more than just a token presence in castles 7, 8 and 10 because simulations. The problem is that unlike the 4-castle approach, which is essentially dumb-plan-proof, my approach loses to simple deployments like 1-3-5-7-9-11-13-15-17-19 or even the dreaded ""put ten guys in every castle and pray""; and because my presence in castle 3 isn't that great I'm somewhat vulnerable to a 10-8-7-3 plan too. But the advantage is that fewer people will likely try this approach than the 4-castle one; even if the 4-castle approach turned out to be the winning approach in general, there's no guarantee that I personally would win; whereas if this is the basic winning approach, my chances of winning or placing high should be good. Essentially, I'm gambling that not too many people will submit really simple and obvious deployments."
2,3,3,12,13,2,3,29,31,2,Similar to winning results in prior battles
0,0,0,0,0,0,10,20,30,40,
@@ -1288,10 +1167,8 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
0,8,10,0,4,23,26,0,0,29,"Winning castles 2, 3, 6, 7, and 10 are enough to win a majority of point, so i spent most of my soldiers there, with an extra 4 in castle 5 who could win some points here and there"
7,8,10,10,15,15,15,0,20,0,"I ceded two of the bigger castles knowing my opponent would load them up, and targeted the mid range castles"
0,0,2,14,15,5,5,5,34,20,"I assumed that most people would choose a strategy from one of the top performers from the last time we ran this competition. I started my “strategy bank” with the top three performers from last time. Then, my process was to move a single soldier from one castle to another for each strategy, store this as a new strategy in the “strategy bank”, play each strategy against the others, and keep the top 2% performing strategies as the seed for the next generation of strategies. I coded this in Matlab. After 5 generations, the top strategy I got was [0 0 2 14 15 5 5 5 34 20]."
3,5,7,12,17,23,31,2,4,4,
0,0,2,2,17,18,27,3,4,27,Hold strong on 10+7+6+5. If I don't win one of these distribute enough to hopefully get lucky on one or two other castles. This strategy has better than 75% win percentage against previous rounds and beats 8 of the 10 top 5 competitors in the previous two battles.
0,0,8,0,3,0,31,9,9,40,"Noticing that in both prior rounds people have hammered the middle numbers or the top numbers, but not both, I wanted an allocation that would win outright at one of those values (31 on 7, 40 on 10) while also winning whichever of 8 or 9 opponents leave under-defended, and winning enough lower-hanging points to get to magic number 28."
0,0,12,0,0,0,25,25,0,33,"//Spam troops at only locations that add up to 28. Sacrifice castle 9 because it was too hot in the previous round, take castles 10, 8, 7, and 3. "
2,2,2,8,2,2,20,26,34,2,"4, 7, 8, 9 and sneak a couple of others."
3,3,3,3,3,3,3,26,26,27,Trying to maximize value at the bottom side poaching empty castles while still having a shot against most who split their forces to 25 or less.
0,0,0,0,0,6,16,21,26,31,
@@ -1303,7 +1180,6 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
2,5,5,2,2,16,2,2,32,32,
3,2,5,18,9,18,6,15,6,18,Trying to get to 27 against various previous methods.
0,0,0,0,0,10,20,30,40,0,"Most people will try locking in 10, I'd rather let them spend their points since 9 is almost equal. Further it allows me to hit a few more relatively high value targets further down"
3,3,4,12,14,16,18,20,18,2,"Concede 10, try to win on castles 4-9 "
1,4,5,11,12,0,15,12,19,21,Not really sure
4,4,4,18,23,0,13,0,34,0,I concentrated on winning more of the lower value castles.
0,0,1,15,1,1,26,26,30,0,I just tried to ensure I had 28 points and didn't want to invest in 10 or 1/2
@@ -1312,13 +1188,11 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
1,1,1,1,1,14,17,19,21,24,My foggy early morning math says that I’ll need to win 28 points in battle...I’m giving minimal protection to low-value castles and increasing value to the rest...
2,3,10,13,16,19,3,3,4,27,"Good against last round, great against the schemers"
0,0,0,3,0,22,23,24,25,3,
0,16,0,16,16,16,17,17,0,0,
1,1,10,3,3,18,3,3,29,29,Focused on winning these 4 battles to get to 28 as 3&6 have been under focused in past battles.
0,1,1,1,2,2,2,5,41,45,"Focus almost entirely on the big castles, but spread some soldiers out for easy pickups."
2,3,5,7,11,3,15,18,27,9,
1,1,1,6,1,19,19,26,1,25,Counter
0,9,0,0,2,1,29,1,31,27,"Used a genetic algorithm which slowly replaced the original entries with the newly generated ones, hopefully optimising against everyone optimising for the previous round. "
3,5,8,10,1,14,18,20,18,2,Gut.
1,1,1,17,10,21,5,5,35,4,Noticing that winning strategies go big on 2 high value castles and 2 low midvalue castles. Decided to go all in on 1 high value castle - and try 3 midlevel castles that would be split evenly lower for anyone throwing points at a secondary high value castle. And raised the lower bar up to 4 for castles >3 points as easy gimmes in case people copy last winning strategy.
0,0,0,5,5,15,15,15,20,25,Random
0,0,0,5,5,15,15,15,20,25,Random
@@ -1330,7 +1204,6 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
0,2,6,4,8,5,20,12,23,20,
0,5,7,9,11,21,0,21,0,26,"2, 3, 4 instead of 9, and then and 3 of 5,6,8, and 10"
0,0,3,0,0,14,14,5,33,31,"I tried to come up with a troop arrangement that would outscore the top five deployments (averaged out) and the top deployments from the previous rounds. It was mostly a matter of trial-and-error. And I didn't quite succeed in my goal (my deployment beats the ""average"" 36-19 and the second round winner 43.5-11.5, but loses to the first round winner 25-30). But I feel good about my choices of castles to attack with strength (9, 10) and about my decision to emphasize attacking castles 6 and 7 at the expense of castles 4 and 5. I am a little bit uneasy about my decision to make only a modest 5-troop deployment to castle 8 as there may be a rush by others to scoop up those points this round. But I think the decision to abandon castles 1 and 2 in favor of a token 3-troop deployment to castle 3 is sensible. "
1,2,3,5,1,11,20,26,0,32,Because it'll win?
1,1,3,10,20,20,20,10,10,5,"I tried to put troops in the middle where points would be high, but not so high that everyone would attack there first"
0,1,1,1,1,4,9,14,25,44,Guessing
0,0,0,5,4,5,24,5,30,27,"Winning the first few castles is essentially meaningless, so any significant troops sent there are wasted, even as a blocking action. Beyond that point, it's a matter of trying to strike a balance with remaining troops between attacking in force, and defending against small raids. There seems to be a consistent trend in the previous battles to focus most troops on Castle 8, so that seems to be the best place to not fight too hard over, in order to preserve sufficient troops to win other battles instead."
@@ -1344,9 +1217,7 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
2,4,5,7,9,11,13,15,16,18,"I calculated that there are 55 point in total, and for each castle, I assigned a number of soldiers proportional to the percentage of total points. I rounded up or down with fractions. I am pretty sure this would beat most people, since it is human nature to greedily focus on the large point values and overlook the small ones. "
0,0,0,0,8,2,25,30,35,0,
0,0,0,15,15,0,0,0,35,35,We go all in on the minimum value to win.
2,2,2,17,18,18,18,20,2,2,All in on 4-8 for a total of 30 points.
2,1,1,17,0,31,0,33,4,11,"I'd like to rescind my previous submission! I've now looked at the previous two metas. I'm trying to anticipate the next 28-set and stake out a slightly different 28-set, with the guess that 10 will skew low again. "
1,0,0,16,22,1,2,3,33,23,Based it off the last winner
0,1,1,16,21,3,2,1,32,23,better than Vince hahaha
0,2,4,14,15,5,5,5,33,17,better than Winder
0,0,0,15,18,1,1,1,32,32,better than Derek
@@ -1360,7 +1231,6 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
0,1,9,0,0,19,6,0,35,30,I went with my gut
2,2,11,1,2,16,3,3,30,30,"Last round fight was for 4&5, so I went after 6&3 (Plus 9&10 to get to 28)"
1,1,2,2,6,6,14,20,22,26,"I didn't think about it too much. I guess I tried going one above round numbers (1,5,20,25) to beat people dividing troops with that type of organization."
0,4,7,7,7,7,7,7,7,37,7 is my lucky number
1,5,1,12,2,18,3,24,4,30,People like odd numbers - so contest the even ones.
4,0,9,5,1,18,1,33,3,26,Attempted optimization against both of the previous two rounds.
0,2,2,16,22,16,16,22,2,2,"I'm hoping to pick up on points in the middle, also I picked slightly above nice round numbers (e.g. 16 instead of 15) hoping to win some castles against people who chose the round numbers"
@@ -1368,7 +1238,6 @@ Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq"
2,4,8,10,3,13,14,15,6,25,"2-3 soldiers per point, with castles 5 and 9 adjusted according to the fact that they were so heavily garrisoned last time. These bids will win against others who neglect these castles for that reason, and will not be too costly of a loss against those who distribute soldiers more proportionately."
11,15,6,20,9,1,9,16,12,1,"Wrote a Python program to randomize troop deployment; as I'm submitting this I realize that the program was built upon failed assumptions, but that will be even more hilarious if it places in the top-5."
5,5,10,10,10,10,10,10,10,20,"even spreading of troops....except 10 is prioritized highly, at the expense of lesser castles 1 and 2"
1,1,1,1,1,1,1,26,33,33,"Looking at the last two rounds and how different the average distributions were, I figured there were a few strategies everyone else could employ: they could copy the winning strategy from the last round, copy the strategy from the first round, optimize against these two strategies, optimize against those optimizing against the last two strategies, or ignore everyone else and go with their gut. As I don’t think there is any way to predict how many people will employ each strategy, and there is no way to optimize against all of them, so I went with the least logical solution and went with my gut. I decided to put all my eggs in one basket. I just needed to win castles 8, 9, and 10 to win, so I focused all my troops on those three, taking from the least valuable of them to send a lone scout to capture any undefended castles should my opponent load up even more than I do on any of the big three. This strategy beats the average distribution of the last two rounds."
6,3,0,0,0,0,1,32,32,26,"Loading up on the high value castles is in some ways the most obvious strategy. However, it is possible that folks will overthink, in which case this might do well."
2,3,5,0,0,0,15,25,0,50,Arbitrary
1,4,0,0,20,20,21,21,7,6,"Middle of the road approach targeting 5-8 heavily, ignoring 3 and 4 which have low point to troop value across most top scorers and the averages."
@@ -1390,8 +1259,6 @@ I recommend, after the main contest's round robin, you try scoring it a differen
3,6,9,12,15,0,0,0,26,29,minimize cost/point
4,7,9,15,21,0,0,0,27,17,minimize cost/point based on previous responses
4,6,9,16,21,0,0,0,27,17,minimize cost
1,1,1,0,2,21,27,5,34,7,"The most successful strategies have been to concentrate enough soldiers in some castles to virtually assure victory there, and spread enough around in others to maybe 1/4th of the time win those.
This particular setup folows that, and also defeats most of the top scores from both rounds 1 and 2, as well as as the vast majority of entries from round 1."
0,1,1,0,3,22,27,5,34,7,my earlier entry only had a total of 99 troops. Bad math!
6,10,13,6,8,16,16,9,7,9,I can't do number theory logic so I just simulated a ton of games in Matlab.
3,0,0,0,0,0,0,30,33,34,I'm trying to get the majority of available points with the fewest castles.
@@ -1431,7 +1298,6 @@ Most pick-4 strategies (where you try to perfectly distribute on 4 castles to hi
0,0,2,5,17,5,17,17,33,4,I want to win a number of castles. I tried to adjust for the adjustments people would make when comparing the two previous winners.
4,8,12,15,19,22,4,5,5,6,"From the previous round of this game, two peaks are observed: those at the low quantities from those who barely defend and those at the high quantities from those who value the castle. If I can stay just ahead of those barely defending, then I distribute the remaining troops as possible to attack the well-defended."
3,3,3,17,17,17,17,17,3,3,total guess
2,0,1,2,10,14,1,15,31,23,
5,3,4,2,5,18,20,19,21,3,"I wanted to avoid any single troops beating me. My goal is to win 6, 7,8, 9 and from there win 2 castles from my opponent undercommitting. "
0,0,0,14,21,1,0,1,33,30,"This combo won 100 simulation rounds in a row using randomized, previous champs, and tweaks of previous round winners."
6,1,1,1,1,1,1,28,30,30,"I ran some quick analysis and was aiming for 28 points, the minimum for victory with the existing point structure. Given those constraints there are 40 solution combinations. I further narrowed it down based on which involved the fewest castles. Of the 40 solutions, 9 required focusing on 4 castles. From here on it becomes judgment calls.
@@ -1439,7 +1305,6 @@ The last warlords competition saw 4 of the top 5 winners with the combination 10
On choosing the amounts, the first warlords page provided some very useful information on the underlying statistics of the distribution. I noticed this was missing from the next time, so I made some inferences. We see the skewed distribution for just about all 10 castles, so the median should nearly always be lower than the mean – and in this case significantly so. So choosing the amounts for castles 8,9, and 10 I based off the mean (and previous winners for an approximate upper range) to establish a point where my guess would be safely in the 90%ile or higher for each.
For the remainder of castles, I feel leaving them empty is unwise – as most of the time my selections for 1,8,9, and 10 should all win against normal opponent selections – for castles 2 through 7 I was debating leaving anywhere from 1 to 3 to defend. I landed on 1 in the interest of increasing defense for my primary 4, but so that in the fringe case that somebody defeats one of my castles I have a chance to gain points back if they leave something undefended.
"
4,4,4,2,2,2,2,12,6,2,"This is exactly the same tactical problem as in the game subterfuge. It is all about figuring out where the cheap wins are. Of course this depends on your enemies tactics. I go for cheap wins on 1,2,3. I’ll send some troops to 4,5,6,7,10 just in case the enemy does not send any or only 1. Castle 8 is for my left overs. Castle 9 is based on an enemy wanting to win castle ten and deploying half his troops there leaving him less than 50 for 9. Hopefully I win 1,2,3,8,9 and a lucky other one. "
0,0,4,17,21,2,4,5,32,15,evolutionary ai found a better solution
0,1,0,15,18,2,3,5,33,23,"This is my *second solution*. Please delete if that's not allowed. Strategy is the same as the first solution: used a genetic algorithm (the same as last competition) to explore distributions that would be good against the first and second round distributions. Then used the same algorithm to optimize against *those* and the first and second round distributions simultaneously. However in selecting *this* solution, I constrained the final search to make sure to pick a distribution that tied my first solution."
0,0,8,0,13,4,6,5,36,28,"Similar to last time's champion, optimised against first and second submissions and solutions optimised against them with more weighting given to the latter."
@@ -1468,17 +1333,14 @@ The King took their heads and he sent them to hell.
6,9,12,16,19,22,4,4,4,4,"This is a joke entry, but I may not have the time to create a serious entry, so this is what you get."
10,0,0,0,0,0,0,30,30,30,Adds up to 28
0,4,5,5,5,7,8,11,20,35,"I wanted no Castle to contain more than 40 troops. The higher the point value of the Castle, the more troops deployed. An even distribution would have yielded 10 troops per castle, so I had 3.5X that amount for my highest-point Castle, and 2X that amount for my 2nd highest-point Castle. One more than that amount for my third-best Castle."
4,1,7,2,3,19,3,31,3,28,Modified earlier answer based on skim of prior data. Seeking to optimize vs. all previous submissions.
2,2,3,5,8,10,10,15,20,25,Put more troops on castles worth more points
5,0,1,10,9,12,5,0,18,40,"I ran a program that simulated a thousand rounds of battles with 20,000 participants and made random updates to each strategy after each round based on how well the players performed on the previous round. This was the winner of the last round."
0,2,3,3,13,13,21,20,0,25,I consulted Mars the God of War and he suggested this.
1,3,6,11,21,26,31,0,0,0,"Assumed people would dump heaps of soliders into 9 and 10, so didn't waste troops there. 55 points total, so I need over half. And then I guessed :-)"
0,0,0,15,20,20,20,25,0,0,Figuring the enemy would over commit to the larger value castles.
1,1,2,2,2,14,20,25,30,3,I chose the deployment that would win.
0,4,5,2,12,19,2,2,24,30,"To win you need 28 victory points which gives about 3.5 troops per point (which suggests it is not worth sending more than 3.5 troops per castle point). Finally the last two rounds showed a the field adopting the previous strategy and the winners planing to win against it. Assuming that people are still seeking patterns and have detected the shift and will now have the default as the shift, whilst still keeping some value on the high value castles. Also from examining the averages the 7,8 castles are over valued compared to the 9,10's suggesting a strategy strong on these will do well. Also this means that if both of these are won only an additional nine points need to be picked up elsewhere.
Finally the minimum should always be 2 as it beats both zero and the cheap guess which beats 0. Except for one because I believe that 2 soliders will have a more effective return elsewhere"
0,0,0,4,0,6,0,34,0,36,Gematria
0,2,2,4,7,15,15,25,3,27,The best defense is a good offense.
0,1,11,3,2,22,2,2,29,28,Win enough castles to get to 28. Put enough in non target castles to pickup if unmatched.
1,2,4,7,13,12,15,3,22,21,In consulted my 9 month old and this is what he suggested after simulation with his toys.
@@ -1518,17 +1380,14 @@ I also made sure that my solution beats most typical solutions (i.e. even splits
1,1,11,14,18,22,1,1,1,30,"Targeted 28 pts via Castles 10, 6, 5, 4, 3"
2,2,5,5,5,5,20,24,6,26,"Decided to abandon Castle 9 with the aim to win the battles for Castles 7, 8 and 10. With a possible 55 points on the board, winning a guaranteed 25 and hoping to steal one more castle of at least 3 points should give me the win in most matchups"
0,0,11,11,1,20,22,34,1,0,"Trying to win the lowest number of castles that reach 28 points, with maximum force at higher numbered castles where more enemy attacks can be expected. We hope to take away castle 8 from anyone who is focusing on the top castles, and win some cheaply. "
1,1,5,6,7,5,5,31,5,32,"In Game 1, winning players chose 6,7,8. In Game 2, they shifted to 9 and 10. I'm expecting this time they will shift again, especially leaving the highest castles of the first two rounds vulnerable. "
0,0,0,0,0,0,10,20,30,40,"Higher value=more soldiers, keep it simple"
6,8,11,14,17,20,6,6,6,6,A slightly altered version of my 'joke' entry. Definitely no 'evolved' entry coming like in previous battles.
1,1,13,1,1,23,2,3,26,29,"Thought the 10,9,5,4 strategy might be overused because of success last time so went with 10,9,6,3"
1,1,1,9,22,24,24,6,6,6,"I tried to guess what would beat the people who tried to guess how to beat the last winning strategy. 1 up the people who tried to 1 up the low number of soldiers for the high valued towers. Assume I win one one of those which means I can lose towers 1, 2, 3 and sometimes 4 depending on which high value tower I won. "
1,2,3,2,22,4,3,3,34,25,"Dominate the last winner, then dominate that."
2,2,2,2,2,20,24,24,20,2,I wanted to beat anyone trying to be crafty sending just one person to each castle while beating anyone who didn't commit to the higher valued castles. I gave up on castle 10 thinking some players will just send all of them to 10 in some circumstances.
0,4,1,3,19,10,12,7,12,32,"I ran a genetic algorithm starting from the best solutions from Riddler Nation Battle Royale round 2, and testing against both round 1 and 2 deployments. The one I submitted is just the deployment with the most wins after a bunch of iterations."
1,1,2,16,21,3,2,1,32,21,simulations
1,1,1,1,1,20,25,30,1,19,Trying to pick the gaps in previously winning deployments.
0,0,5,5,5,10,15,15,15,31,
0,0,0,2,20,18,2,24,32,2,"Since the previous contest winners all focused on a group of castles totalling 28 points, I somewhat randomly chose 5, 6, 8, 9 and put 3 troops per point value in each of these. That left me 16 troops. I decided to minimally defend castle 4, 7, and 10 with two troops each and then reinforced two of my targeted castles with five more troops each. "
2,3,5,4,11,13,16,6,6,34,I went with a strategy designed to beat the best strategies from the first two rounds and the average of the previous games. I didn't want to think harder than that.
10,1,1,1,1,1,1,28,28,28,
@@ -1548,17 +1407,6 @@ I also made sure that my solution beats most typical solutions (i.e. even splits
Then looking at the previous answers it looked like you could do fairly well against a good mix of opponents by fighting particularly hard for 9 and 10 and fairly hard for 6, 7, and 8. The 7 and 8 aren't 15 and the 9 and 10 aren't 25 because I figured a lot of people might use those nice round numbers."
0,8,6,8,13,1,19,11,2,32,"Ran a genetic algorithm simulation and this was the winning strategy. The best strategy depends on the other strategies entered, so it is within the space of possible, winners, but probably won't win."
0.1,5.1,0.1,0.1,17.1,22.1,25.1,1.1,6.1,23.1,"A few guiding observations:

-The champion sets of the other two had about an 80% win rate. That seems like a good target for this time.
-The champion set from the second iteration would have done well on the first. It makes sense to make something that would have done well in the others.
-The champion set from the first iteration would have gotten obliterated in the second. It's a good idea not to repeat either of the champions.
-The top sets from the first iteration prioritized 8, 7, 5 and at least one of 6 and 4.
-The top sets from the second iteration prioritized 10, 9, 5, and 4.
-That one person had fractional troops in the second iteration. That seems good and reduces the need to consider draws. Also, that allows one to overshoot a target by a smaller degree, freeing up backups for less-guarded castles.
I found the 80th percentile number for each castle from each iteration. I then took the higher of these 80th percentilers of the two iterations and created the set (4, 6, 9, 12, 16, 21, 25, 31, 29, 23). I then treated that as a single entry and found roughly the cheapest way to beat it to 28 points--targeting 10, 7, 6, and 5. I was able to cover these with 85.4 troops. Of course, if I target only those, I have to win every single one of them, or I lose. For that reason, I chose to post a small contingency in 9 and 2 (which will cover me in the case that I lose either 10 or both 6 and 5... 2 had a significantly lower barrier than 3/4, and 9 was somehow softer than 8). I then gave 0.1 troops to 1, 3 and 4 to ensure I outright win any undefended castles. Castle 8 seemed weird to do just 0.1 for, so I threw 1.1 there. Then, adding one more troop to 6 and 7 seemed to have a very good ROI for the other two iterations, so I went ahead and did that.
Final stray observations: I wish I had marked my other two entries in such a way that I could identify them easily. I feel like this one will stand out in the data a lot better (though I suspect a few others will utilize decimal troops as well)."
1,1,1,0,0,20,20,22,35,0,
6,1,2,2,1,3,6,24,34,21,"Previous battle victories seemed to be all-or-nothing attempts to get 28 pts from the fewest castles to maximize troop strengths. That's fine. If four castles is what it takes, that's what it takes. My goal in this round is to make Castle 1 mean something! Assuming you're a real warlord, going in order, you want to get that first victory to make your troops follow you. Besides that thought, I used no formulas or special computations. I just looked at what went before and decided this looked reasonable enough."
1,3,5,7,9,11,13,15,17,19,Each castle has just under twice their point value in troops.
@@ -1568,7 +1416,6 @@ Final stray observations: I wish I had marked my other two entries in such a way
0,1,2,3,16,19,22,5,6,26,"Try to win castle 10. Put one more than 25 there, thinking that some people will go for the even number. Add 5, 6 and 7 as a strategy to get 28 with 10. Try to capture the other numbers a fair fraction of the time when nobody targets them, but don't overspend on low numbers."
0,0,0,10,10,25,25,15,10,5,Because the middle will be ignored
3,0,6,8,15,22,4,3,31,8,a computer told me to
3,5,7,5,8,9,10,13,20,21,Decided to add more troops the higher it got because of how much more each castle was worth
0,3,3,12,12,17,12,17,12,12,"Looking at the data from the first two iterations, castles 6 and 8 seemed most likely to be winnable. I focused on 12s and 17s as I assume others like to throw in a lot of 11s and 16s to get 1 army over those who put in 10s and 15s."
5,0,0,12,0,13,0,30,35,5,Trying to secure a baseline of 17 and steal either 10 or 7+3 as well as the first castle
0,0,3,5,11,13,21,22,14,11,"Kind of a guess, really"
@@ -1656,11 +1503,9 @@ At least one of these strategies will do well depending on the market. And the m
But really I built a simulation and tested out a variety of strategies against a computer to see what I liked best. It really comes down to if I use the least used strategy that provides the most wins. Plus a little bit of razzle dazzle.
Cheers."
3,3,7,11,14,16,19,22,3,3,"Didn't want to put less than three in any castle, to prevent seceding it to someone who played 2 to beat a 1. Went for the midrange and lower castles to bolster points. 2. 75 men per point after eliminating 10, 9, 1 and 2."
5,2,5,7,22,23,22,2,2,10,
0,3,3,8,5,19,19,20,20,3,"Created two sets of the 1000 top results out of 1000 random arrays compared against themselves. Then compared the top performing array sets. The above was the best performing solution. Performed with SAS, using SQL and the datastep. Run time was about 20m."
3,3,3,3,3,3,3,26,26,27,"The top 3 castles are worth the same as the other 7, so I focused troops there and equally disbursed troops in the other 7 castles to pick up any that they didn't attack with much force."
1,1,1,1,1,1,23,70,1,1,Maybe the worst idea I thought of is the best.
3,5,1,9,17,13,15,19,11,7,"Odd numbers between 1 and 19, centered on Castle 8 and distributed around it in descending order."
0,1,2,16,21,2,3,1,32,22,"I built myself a fancy excel spreadsheet of all of the previous submissions, and then attempted to optimize against those."
2,2,3,5,5,8,10,15,20,30,"Guessing, I guess..."
@@ -1671,19 +1516,6 @@ p.p.s. Also happy to share my python code for this."
1,2,4,10,21,12,26,16,4,4,"Contest everything, but don't commit heavy to the point-heavy (castles 9 & 10) obvious grab strategies that people are likely to employ (similar to the first round of the contest, but countered in round two with a lot of people choosing a 4,5,9,10 strategy). Deployment had to defeat/tie some of the default, non-strategic assignments (e.g., 10 everywhere, 25s in each 7-10, % assignment based on value). Castles 5 (main counter to round two strategies), 7 (main counter to round one strategies), and 8 (some round one strategies) can break a lot of opponent strategies so contesting them is where my main investment took place. It is a bit of a gamble to pick up stray points in low commit castles when my other investments aren't high enough to offset opponent high commits."
2,4,6,9,0,3,3,21,24,28,I chose something that held up well against different scenarios like previous winners and averages.
3,3,7,4,4,24,5,34,8,8,I spent way too long on this and I still hate my answer.
5,5,5,5,5,6,6,6,6,6,to test whether multiple submissions are allowed
5,5,5,5,5,6,6,6,6,6,to test whether multiple submissions are allowed
5,5,5,5,5,6,6,6,6,6,to test whether multiple submissions are allowed
5,5,5,5,5,6,6,6,6,6,to find whether multiple submissions are allowed
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is a good counter over and over
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is a good counter over and over
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is a good counter over and over
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is a good counter over and over
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is a good counter over and over
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is the perfect counter over and over
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is the perfect counter over and over
5,5,5,5,5,6,6,6,6,6,to test whether someone could potentially submit a deployment to which his deployment is the perfect counter over and over
0,3,1,14,7,7,17,22,23,9,A nice guess.
1,1,1,6,6,12,16,21,31,5,Top heavy while giving up ten for most battles.
2,1,1,1,1,13,22,34,24,1,I wanted to have really high on either 8 or 9 for people wanting to win by going after the top 3. Then leave some to go after some castles that might have no troops.
2,3,10,10,10,5,20,30,5,5,Eh?
@@ -1691,8 +1523,6 @@ p.p.s. Also happy to share my python code for this."
1,2,8,16,16,5,14,15,18,5,bi modal distribution seems optimal from previous battle royales
1,4,1,8,1,13,15,17,19,21,"Adjust forces to prizes, sacrifice 2 castles to be slightly better elswhere"
0,0,0,18,18,2,2,2,34,24,This strategy beat the previous top-5.
2,3,5,4,8,8,12,16,5,32,Random Number Calculator.
1,3,4,8,10,12,13,15,17,18,
0,1,2,16,21,2,3,1,32,22,I used the data from the previous two competitions and this was the highest win rate configuration I could find.
0,0,3,3,16,6,16,21,4,31,"I know this is really late, but here is a serious entry. The code used to generate this is at https://pastebin.com/ieFeGQzN"
1,0,0,0,0,0,10,27,29,33,"My focus was on getting 28 total victory points out of a possible 55, so I concentrated on 8, 9, 10, and winning 1 extra point on the ""1"" castle."
1,0,0,0,0,0,10,27,29,33,"My focus was on getting 28 total victory points out of a possible 55, so I concentrated on 8, 9, 10, and winning 1 extra point on the ""1"" castle."
1 Castle 1 Castle 2 Castle 3 Castle 4 Castle 5 Castle 6 Castle 7 Castle 8 Castle 9 Castle 10 Why did you choose your troop deployment?
11 2 1 5 20 4 20 4 20 4 20
12 1 4 12 14 7 16 18 20 3 5 I focused on a combination that would get me to 28 points, but still tried to have above average on the castles that others might try to put 1-3 troops at.
13 1 2 1 3 5 20 21 33 7 7
3 6 11 13 5 18 22 11 6 4
14 4 0 0 0 0 0 0 32 32 32 You only need 28 to win
15 1 1 6 10 14 15 23 24 3 3 I'm reverting to something closer to the winning strategy of this question's first instance. I'm sending few troops to the highest and lowest valued castles, instead focusing my parties on the middle-values.
16 1 1 1 2 1 15 21 26 31 1 Goal is to maximize odds of winning 28 or more, and winning 6 through 9 seemed to have the easiest path of getting there. Skipping 5 and leaving 2 at 4 is because 4+6+7+8+9 is enough to win, happy to leave 5 behind to win 6-9.
20 3 5 7 9 11 2 16 18 15 14 I have optimised this strategy to beat the average deployment from the last iteration of the game, by sacrificing castle 6,which was not well contested last time, so I expect it to be hotly contested this time round.
21 1 1 1 1 23 23 24 24 1 1 Trying to capture the mid-high castles and sacrifice the others
22 3 3 3 3 3 10 15 20 30 10 Just guessing based on the previous two events. 678 heavy vs 459,10 heavy, sort of a mix.
2 2 2 2 12 20 20 20 20 20 I spread my troops on the five highest value castles, hoping that I can beat out some of them, and sent two to the lower value ones so I can beat someone who sends the minimum.
23 1 2 2 8 10 15 17 19 23 3 I tried to look for a mix between the successful armies in 1 and 2. I targeted 4-9 because they total more than half the points, and dropping 1-2 of these castles wouldn't stop my victory.
4 6 7 4 4 4 30 32 4 4 mostly random TBH, just gut feeling
24 2 2 3 14 2 16 2 4 32 23 Intuition.
25 2 3 4 5 7 9 26 33 6 5 It just felt *right*
26 4 4 4 4 16 4 16 28 16 4 To mess with the averages
27 6 6 7 0 0 0 21 25 0 35 Castles 1-3 and 6-8 were the most ignored by the top 5 warlords in the last round. 4-5 and 9-10 were most popular. I figured if I can almost guarantee getting 10 by placing 35 soldiers, ignore 9 where most others will send a significant amount, capture 7-8 which look to be ignored by most, and capture 1-3 which will be ignored for low point value, I could total 31 points which is more than enough to win a majority of the battles. Maybe a simpleminded strategy but this is based purely off the results of the last round and it could be an obvious one.
3 5 6 10 13 18 28 7 6 5 1 thru 7 are worth 28 points while 8-10 are worth 27. So sacrifice those for volume ;)
28 2 6 9 9 12 2 28 27 2 3 Just did a pretty similar strategy to Cyrus.
29 1 1 1 1 1 5 5 10 25 50 I figured if I can guarantee a split or victory of high level castles, that can override the lower level ones--this is not very scientific. Also, the form doesn't allow us to send 0 soldiers to a given castle.
30 2 4 5 8 10 11 12 14 16 18 Impossible to say.
1 3 6 8 10 12 14 16 18 20 Linear
31 1 1 1 1 1 1 91 1 1 1 Banking on winning ALL the battles at Castle 7
32 1 1 1 2 14 15 2 28 32 4 Winning 5, 6, 8, and 9 gives me just over half of the available points, so I went hard for those four.
4 5 7 9 11 13 14 16 13 11 Used the last answer and increased deployment for the first 5 by 1 and decreased the last 5 by 1 to account for evolution.
33 1 3 5 7 9 11 13 15 17 19 Linear
34 4 4 4 5 5 16 5 5 21 31
35 1 6 6 11 11 16 16 16 11 6 Figure 5x would be a popular number to distribute, so 5x+1 along a skewed curve based on intuition.
51 4 4 4 4 4 24 24 24 4 4 I figured at least 4 in each would pick off the people who sent out tiny forces, but still let me sink in a few in more strategic spots.
52 1 5 8 12 13 1 26 30 2 2 I copied the first winner one minor arbitrary change.
53 2 4 6 7 9 11 13 14 16 18 Weighted distribuation
1 1 1 1 1 17 17 20 40 2 My line of thinking is that most other warlords would work to capture Castle 10 with the majority of their troops, so I avoid it completely and work with my forces to conquer the second-strongest castles. If however, my opponent ignores castle 10 as I did, and goes after the lesser castles, I'd designate two soldier in the off chance they could conquer the castle alone. If I conquer Castles 6-9, I'd win the war even if I lose all the others.
3 6 9 14 18 22 28 0 0 0 Ignore the top ones, focus on minimum needed for majority of points
54 1 3 1 6 1 9 1 14 2 18 7 22 10 28 20 0 35 0 22 0 I went top heavy and ignored the low point castles due to their inefficiency as the are 1.8 digits Soldiers per point. Ignore the top ones, focus on minimum needed for majority of points
55 1 2 1 0 1 0 1 0 2 0 7 0 10 32 20 32 35 33 22 The top 3 castles score 27 points in total, almost 50% of the point total. Assuming I can win all 3 and pick up a single unguarded low point castle, i will prevail. I went top heavy and ignored the low point castles due to their inefficiency as the are 1.8 digits Soldiers per point.
56 1 1 2 5 0 10 0 1 0 15 0 16 0 17 32 1 32 26 33 The top 3 castles score 27 points in total, almost 50% of the point total. Assuming I can win all 3 and pick up a single unguarded low point castle, i will prevail.
57 2 4 5 7 9 11 13 15 16 18 I took the ratio of the points for each castle against the total points possible (10/55) and multiplied it by 100 to determine the number of soldiers for each castle.
1 4 9 10 1 13 16 17 14 15 I assumed the number of soldiers necessary based a trend from the previous two events. I then added one soldier to castles 6 through 10 and subtracted one soldier from castles 1-5. I then decided to sacrifice castles 1 and 5 and minimize their defenses and put their soldiers on the other 8 castles.
58 4 1 0 4 1 9 1 10 1 0 13 0 16 31 17 31 14 31 15 My goal is to acquire 28 points. This is on permutations of castle attacks that makes it likely I assumed the number of soldiers necessary based a trend from the previous two events. I then added one soldier to castles 6 through 10 and subtracted one soldier from castles 1-5. I then decided to sacrifice castles 1 and 5 and minimize their defenses and put their soldiers on the other 8 castles.
59 15 4 1 0 1 1 1 1 0 30 0 30 31 25 31 24 31 First, we have to find the minimum number of points to needed to win (28). Then we have look at the minimum amount of castles needed to secure that, which is 4. Holding the top 3 pts Castles will only get to 27 pts; however, holding point 7 will get 34 pts, but that an extra six points not needed. So, having strong defenders on the top 3 castles, of which in previous games few went above 30 to hold, and then holding castle 1 strongly, will give the best opportunity to hold the least castles with the least wasted points to win. But if one is lost, all is lost. :) My goal is to acquire 28 points. This is on permutations of castle attacks that makes it likely
60 4 0 0 0 0 0 0 32 32 32 I do have to win all 4 of my engagements, which doesn't leave any margin for error. I'm confident in castle 1, and 2/3 for 8-10. So I just have to get a little lucky that opponents spread their forces out too much.
2 2 9 11 16 10 30 5 8 7 Based on last year's deployments I observed that very few soldiers were deployed to the 9 and 10 castles so I send a force to that could take both of those. I sent a token force to the 1 and 2 castle as they are not worth that much. For the remainder I tried to get above last year's average except for castle 8 which I can afford to lose if I take either 9 or 10. However I may just be fighting the last war and be destroyed.
3 3 1 1 1 1 10 35 44 1 focus on castle 8 and 9 with the assumption that castle 10 is likely going to be taken and castle 1 and 2 will have 1 soldier brought to them
3 8 10 11 16 22 2 23 2 3 Designed to lose 10, 9, 7 which would counteract the strategy of only winning the bottom 7 (since I'll steal 8, in exchange for their 7), and the strategy of winning the top numbers (I'm sacrificing 9, 10, while investing a lot in 8, 6, and lower, which adds up to more points than 7, 9, 10).
61 1 2 1 2 1 9 2 11 7 16 18 10 20 30 22 5 23 8 5 7 Seemed pretty good I guess Based on last year's deployments I observed that very few soldiers were deployed to the 9 and 10 castles so I send a force to that could take both of those. I sent a token force to the 1 and 2 castle as they are not worth that much. For the remainder I tried to get above last year's average except for castle 8 which I can afford to lose if I take either 9 or 10. However I may just be fighting the last war and be destroyed.
62 1 3 0 3 0 1 20 1 20 1 0 1 0 10 0 35 35 44 24 1 Magic focus on castle 8 and 9 with the assumption that castle 10 is likely going to be taken and castle 1 and 2 will have 1 soldier brought to them
63 4 3 8 8 10 8 11 12 16 32 22 17 2 4 23 3 2 4 3 Get 7 through 5 and then either 10 or 4 through 1. Designed to lose 10, 9, 7 which would counteract the strategy of only winning the bottom 7 (since I'll steal 8, in exchange for their 7), and the strategy of winning the top numbers (I'm sacrificing 9, 10, while investing a lot in 8, 6, and lower, which adds up to more points than 7, 9, 10).
81 1 1 2 4 3 8 6 10 9 13 14 16 19 17 16 12 16 seems plausible It slightly beat something that slightly beat May's average.
82 3 4 6 4 6 4 11 5 11 1 17 27 23 30 26 2 3 3 cluster forces around valuable castles most likely to be fought over (7 and 8), choose one middle but less valuable castle (6) to offer almost no defense of, give 11% of forces to next level valuable castles (4 and 5) assuming most will give 10% to those castles. Also assumes most will attempt to cluster forces proportionately to win larger castles in some ratio of all forces in the 10, 9, 8, 7 castles, keeping more than 25% in castles 8 and 7.
83 1 1 7 4 1 8 18 10 20 13 2 16 23 19 25 16 2 12 Go big on some, steal the rest with some 1>0s and hope for some luck! seems plausible
2 2 5 5 10 15 20 25 5 6
84 2 3 4 6 5 6 7 11 9 11 11 1 12 27 15 30 16 2 19 3 Direct mapping. Soldiers per castle = (points per castle / total points) * total soldiers, with rounding, and leftover soldier goes to castle 10. Trying to win by playing simpler than people expect. :) cluster forces around valuable castles most likely to be fought over (7 and 8), choose one middle but less valuable castle (6) to offer almost no defense of, give 11% of forces to next level valuable castles (4 and 5) assuming most will give 10% to those castles. Also assumes most will attempt to cluster forces proportionately to win larger castles in some ratio of all forces in the 10, 9, 8, 7 castles, keeping more than 25% in castles 8 and 7.
85 1 3 1 5 7 7 1 9 18 11 20 13 2 15 23 17 25 19 2 Trying to be competitive at every single castle, without wasting too many soldiers. Go big on some, steal the rest with some 1>0s and hope for some luck!
86 1 2 1 4 1 5 1 7 14 9 20 11 30 12 30 15 2 16 2 19 Direct mapping. Soldiers per castle = (points per castle / total points) * total soldiers, with rounding, and leftover soldier goes to castle 10. Trying to win by playing simpler than people expect. :)
2 7 2 2 13 18 23 29 2 2 I wanted to get 28/55 points by committing to castles 8,7,6,5 and 2. I deployed these troops to help obtain 8 most frequently and 2 the least. I deployed 2 troops on each other castle to not allow for my enemies to get an easy 1-0 victory on any castle. If I can win one or two of those, that would be great
87 15 1 15 3 7 5 2 7 26 9 2 11 2 13 3 15 10 17 18 19 Last time winners focused on the middle. I'm focusing on the edges Trying to be competitive at every single castle, without wasting too many soldiers.
88 1 2 1 7 1 2 1 2 1 13 5 18 10 23 15 29 25 2 40 2 I wanted to get 28/55 points by committing to castles 8,7,6,5 and 2. I deployed these troops to help obtain 8 most frequently and 2 the least. I deployed 2 troops on each other castle to not allow for my enemies to get an easy 1-0 victory on any castle. If I can win one or two of those, that would be great
1 6 14 19 1 15 21 21 1 1 I focused on the 3,4,6,7,8 field, that have good reward, but aren't tied. Put down at least one in the others to surprise my enemies who left castles unattended. By giving my enemy 10,9,5,2,1, I win out by 1. I am weak to attacks on the higher values, as a 7,8,9 30 split with a dump on 10 will destroy my attempt. As long as the enemy doesn't consolidate, then I shall claim victory.
89 1 15 2 15 3 7 5 2 7 26 15 2 30 2 33 3 2 10 2 18 Get to as close to 28 without wasting troops Last time winners focused on the middle. I'm focusing on the edges
90 2 1 2 1 3 1 3 1 20 1 20 5 20 10 20 15 5 25 5 40 the plan is to win castles 5,6,7,8 and then hopefully pick up one more somewhere else.
91 1 5 6 0 14 7 19 8 1 21 15 0 21 28 21 30 1 0 1 optimize higher castles but never go in increments of five (leads to more ties which are inefficient). use 0 on castles that have a higher chance of being contested I focused on the 3,4,6,7,8 field, that have good reward, but aren't tied. Put down at least one in the others to surprise my enemies who left castles unattended. By giving my enemy 10,9,5,2,1, I win out by 1. I am weak to attacks on the higher values, as a 7,8,9 30 split with a dump on 10 will destroy my attempt. As long as the enemy doesn't consolidate, then I shall claim victory.
103 5 1 5 1 5 1 3 1 3 1 19 20 1 2 1 27 34 30 39 Based on the last two games, those with less troops were overwhelmed. I figure most people will leave 9 and 10 relatively open, and 1-5 will be given 4, to take out the 3's from round 2. Let's see what happens! Ties are wins
104 2 1 2 1 2 1 2 2 4 19 5 19 36 20 36 24 12 28 2 7 and 8 seem like a sweet spot for points vs competition, and I want to put in enough to beat most people who came to the same conclusion. At the same time, I want to make sure I don't get beaten by tiny troop commitments to the other castles. I figured 9 would be a nice bonus to sometimes get.
105 3 5 3 5 14 5 4 3 18 3 15 19 3 1 15 2 4 27 21 30 Randomish Based on the last two games, those with less troops were overwhelmed. I figure most people will leave 9 and 10 relatively open, and 1-5 will be given 4, to take out the 3's from round 2. Let's see what happens!
1 2 2 16 19 3 3 3 26 27 Im fighting the ghosts of wars past
106 2 3 3 1 14 5 4 16 18 28 15 6 3 9 15 18 4 12 21 Troop deployments to low point castles are just enough to tie up enemy troops while focusing on the mid to upper range castles that are worth the most. Don't over dedicate to 10 as people are drawn to the easy number. Randomish
1 1 1 1 1 6 15 18 20 25 random
107 1 2 2 3 3 1 4 5 4 16 16 28 18 6 24 9 27 18 2 12 Highly valuing castles 6-9, if one wins those 4 they win. Hoping to win many battles by having the opposing army massively overspend to win castle 10 while my force wins 6-9. Troop deployments to low point castles are just enough to tie up enemy troops while focusing on the mid to upper range castles that are worth the most. Don't over dedicate to 10 as people are drawn to the easy number.
1 9 20 29 15 10 2 8 5 1 Distribute to all, try to find a place where numbers will be thin.
108 1 1 9 2 20 2 29 26 15 10 15 2 15 8 26 5 2 1 The total point possibility is 55, so you need 28 to win. From there, troop (resource) distribution is a mix of math (what are the best combinations that can lead to 28?) and human behavior speculation (metagaming). Castle 10 is a trap and a good way to get your opponent to waste resources, since they are working with incomplete information, so I threw only 2 troops there (to minimize my investment while hedging against other players who choose 0 or 1). Castles 1-7 add up to 28, so a popular strategy may be to aggressively claim them. The 26 in Castle 5 is designed to disrupt that, as players who go for this strategy may emphasize their investments in Castles 6 and 7, and will be afraid to over-invest in 5 without hedging earlier castles accordingly. Meanwhile, there are enough troops in castles 6-9 to yield likely wins, while hedges in the lower castles may secure additional value. Distribute to all, try to find a place where numbers will be thin.
1 0 0 0 0 13 17 20 23 27 Win big (I only want 0 troops at castle 1 but it won't let me. Hoping I dont get disqualified.)
1 1 1 1 1 23 23 24 24 1
109 2 1 2 1 2 11 2 16 26 16 10 26 15 16 15 5 26 4 2 It seemed to me that the chance of winning castles 9-10 is relatively low, since many warlords will send more troops there. I focused more strength on the mid-range, castles 5-8. chose mostly uneven numbers (rather than rounding at 5, etc) in hopes of beating warlords who divided by 5s or 10s. And I sent at least some troops to every castle, since this guarantees a win against a warlord who sends 0 to any of them-- making that number greater than 1 for each castle, since many players will send a minimal force to those castles. The total point possibility is 55, so you need 28 to win. From there, troop (resource) distribution is a mix of math (what are the best combinations that can lead to 28?) and human behavior speculation (metagaming). Castle 10 is a trap and a good way to get your opponent to waste resources, since they are working with incomplete information, so I threw only 2 troops there (to minimize my investment while hedging against other players who choose 0 or 1). Castles 1-7 add up to 28, so a popular strategy may be to aggressively claim them. The 26 in Castle 5 is designed to disrupt that, as players who go for this strategy may emphasize their investments in Castles 6 and 7, and will be afraid to over-invest in 5 without hedging earlier castles accordingly. Meanwhile, there are enough troops in castles 6-9 to yield likely wins, while hedges in the lower castles may secure additional value.
110 2 1 3 1 4 1 4 1 21 1 21 23 21 23 22 24 1 24 1 I sacrificed 9 and 10 hoping that my enemy would focus a lot of soldiers on them and instead tried to capture a lot of of the mid value castles.
4 1 5 10 25 0 0 0 30 25 Trying to pick up 5, 9 and 10. Get enough value in the early battles to pick up over half the points.
111 1 2 0 2 0 2 0 11 0 16 0 16 0 26 0 16 99 5 0 4 Just Cause It seemed to me that the chance of winning castles 9-10 is relatively low, since many warlords will send more troops there. I focused more strength on the mid-range, castles 5-8. chose mostly uneven numbers (rather than rounding at 5, etc) in hopes of beating warlords who divided by 5s or 10s. And I sent at least some troops to every castle, since this guarantees a win against a warlord who sends 0 to any of them-- making that number greater than 1 for each castle, since many players will send a minimal force to those castles.
112 3 2 6 3 9 4 11 4 13 21 14 21 18 21 22 2 1 2 1 55 total points and 100 troops means just fewer than 2 troops per point. Assuming opponent uses same math, I will overemphasize the lesser valued castles and hope she goes big. I sacrificed 9 and 10 hoping that my enemy would focus a lot of soldiers on them and instead tried to capture a lot of of the mid value castles.
113 1 4 1 1 5 6 10 7 25 20 0 27 0 35 0 1 30 1 25 I wanted to win the middle castles Trying to pick up 5, 9 and 10. Get enough value in the early battles to pick up over half the points.
124 1 1 0 1 0 1 0 10 0 10 0 2 0 20 99 20 0 34 0 Try to create as many options to get to 28 as possible. Goal is to win 2 out of the top 3 then pickup enough of the rest to get to 28+ You need to get points, and probably the only way to do that is to win a house outright. I am guessing that someone will do 100 for 10 and 9, so guessing 8 will be the one where people don't apply 100.
125 2 2 2 2 10 11 1 11 1 2 25 22 25 44 30 2 I was looking for four castles that would add up to 28 points, the minimum required to win. I found I could not do this without castle 9. I chose to leave out castle 7 because 5 and 6 should be easier to get. I sent token forces to 1, 2, 3, 4, 7, and 10 to force my opponent to keep those covered. That left me 88 troops. I sent half of those to castle 9, which I assumed would be contested heavily. Half of what was left was sent to castle 8. The remaining troops were split between 5 and 6. Maximize the troops that could take 28 points, and the others are 2 to cleanup places where my opponent sent only 1.
126 2 1 2 1 4 1 7 1 9 10 11 10 14 2 15 20 17 20 19 34 Added up all the VPs to be had (55) took 100 and divided it by 55 (1.8). This is how many soldiers each VP is worth. I then multiplied the castle number by 1.8, rounded and skewed it towards the high end a bit for people who employed the same strategy. Try to create as many options to get to 28 as possible. Goal is to win 2 out of the top 3 then pickup enough of the rest to get to 28+
1 0 9 15 0 20 25 30 0 0
127 1 2 0 2 0 2 4 2 11 14 11 21 2 26 22 24 44 0 2 I started with zero at Castle 10, and a large chunk (25) at 8 and 9. I then gave 5 fewer troops to each Castle going down until I ran out. Then I went back and added in a bit of noise. Then I noticed it required >0 for Castle 1, so I put that in. I was looking for four castles that would add up to 28 points, the minimum required to win. I found I could not do this without castle 9. I chose to leave out castle 7 because 5 and 6 should be easier to get. I sent token forces to 1, 2, 3, 4, 7, and 10 to force my opponent to keep those covered. That left me 88 troops. I sent half of those to castle 9, which I assumed would be contested heavily. Half of what was left was sent to castle 8. The remaining troops were split between 5 and 6.
128 1 2 1 2 1 4 21 7 1 9 1 11 22 14 24 15 26 17 2 19 I figured a lot of people would go 10 on each, and this would consistently beat those ones. I also guessed a lot of people would put two on each of the lower ones to beat out the one you are forced to put there, so I made sure to take that into account. The second question for me was the people who went a bunch in top half and left one each to the lower ones so I knew I would need to adjust the numbers to favor something would also win against someone who went 1-1-1-1-1-19-19-19-19-19 because that seemed like it would be like the second most common formidable strategy. The last thing I considered was that because you need 28 points to win and the easiest way to there seems to be 9+8+7+6 the easiest way to get there. I ignore the ten because other people will dump a bunch of points there and either way I will need to get four numbers total as 10+9+8 only gets you to 27. This strategy pretty cleanly beats both those strategies. To beat this you would need to foresee it probably and get 9 at least. I think if you went for a 10-9-8 strategy and just low balled a bunch of other numbers hoping to get one you might beat me but you will lose to everyone playing 10 on everything so I think this is the most stable that I can come up with. Added up all the VPs to be had (55) took 100 and divided it by 55 (1.8). This is how many soldiers each VP is worth. I then multiplied the castle number by 1.8, rounded and skewed it towards the high end a bit for people who employed the same strategy.
129 1 3 0 1 9 7 15 4 0 12 20 32 25 3 30 34 0 3 0 Lots of folk went for 7-8 or 9-10 previously. I figure few will go for 7-9. With those in the bag, I need another 12 points. I'm hoping for 2-4-6, but also spreading out my options to get lucky against a poorly defended 8, 10, and 5.
130 1 0 1 1 6 21 22 1 12 1 8 22 14 24 6 26 30 2 I chose a strategy that could beat each of the top 5 from the last two times, could beat an even distribution, could beat a focused attack at the top, and could beat a (10,0,0,0,0,0,0,30,30,30) strategy. The first strategy I found was (1,2,2,18,1,6,2,33,11,24). Then, I used random sampling to see if I could find strategies that would beat my strategy. Out of a sample of 200, I found 84. I compared these 84 against the original 13 strategies, and found 1 that beat all of them. This strategy was (0,1,1,6,22,12,8,14,6,30). However, your entry form won't let me put 0 for castle 1, so I switched castle 1 and 2. This seems to work just fine as well. I figured a lot of people would go 10 on each, and this would consistently beat those ones. I also guessed a lot of people would put two on each of the lower ones to beat out the one you are forced to put there, so I made sure to take that into account. The second question for me was the people who went a bunch in top half and left one each to the lower ones so I knew I would need to adjust the numbers to favor something would also win against someone who went 1-1-1-1-1-19-19-19-19-19 because that seemed like it would be like the second most common formidable strategy. The last thing I considered was that because you need 28 points to win and the easiest way to there seems to be 9+8+7+6 the easiest way to get there. I ignore the ten because other people will dump a bunch of points there and either way I will need to get four numbers total as 10+9+8 only gets you to 27. This strategy pretty cleanly beats both those strategies. To beat this you would need to foresee it probably and get 9 at least. I think if you went for a 10-9-8 strategy and just low balled a bunch of other numbers hoping to get one you might beat me but you will lose to everyone playing 10 on everything so I think this is the most stable that I can come up with.
2 2 2 5 12 2 5 28 32 10
131 1 1 3 12 1 1 7 1 4 20 12 1 32 1 3 34 28 3 Anticipating another adjustment after the second round. Min/maxing numbers to reach the 28 point threshold. Lots of folk went for 7-8 or 9-10 previously. I figure few will go for 7-9. With those in the bag, I need another 12 points. I'm hoping for 2-4-6, but also spreading out my options to get lucky against a poorly defended 8, 10, and 5.
132 3 1 4 0 4 1 11 6 12 22 16 12 20 8 21 14 4 6 5 30 Try to pick up a couple with my 3-5 at the ends and then win 4 of the middle ones where the strength is. I chose a strategy that could beat each of the top 5 from the last two times, could beat an even distribution, could beat a focused attack at the top, and could beat a (10,0,0,0,0,0,0,30,30,30) strategy. The first strategy I found was (1,2,2,18,1,6,2,33,11,24). Then, I used random sampling to see if I could find strategies that would beat my strategy. Out of a sample of 200, I found 84. I compared these 84 against the original 13 strategies, and found 1 that beat all of them. This strategy was (0,1,1,6,22,12,8,14,6,30). However, your entry form won't let me put 0 for castle 1, so I switched castle 1 and 2. This seems to work just fine as well.
133 2 3 2 0 2 5 7 12 12 2 16 5 18 28 18 32 19 10 Idk let's see if I win
149 3 2 1 2 1 2 1 7 1 7 1 27 2 27 26 2 27 10 37 14 Get 28 points with the fewest number of castles possible (10, 9, 8 & 1). Try to defend those with as many soldiers as possible and leave 1 at the other castles in case any are left undefended. Paired scouts to 1/2/3 - not worth more troops, but good to snipe or deny a 1-troop snipe. Common practice in last games has been to focus on 4 castles, with a small number spread to others. This strategy is designed to narrowly defeat any small force at any castle, while focusing on castles 6 & 7 (usually ignored, but form a good base to combine with other towers) and increasing numbers of troops to castles 9 & 10. Castle 8 is almost ignored, anticipating others will focus efforts there.
150 1 1 4 1 4 1 10 23 12 23 14 23 16 23 18 2 20 2 Trying to capture all of the middles and maybe steal the top 2
151 3 5 1 7 1 2 1 2 1 15 1 18 2 20 26 0 27 28 37 The Name of this game should be 55. Why? Well for a similar reason why your website is called 538. 55 is the number of total points a player could win in this game, but 28 is the number of points a player needs to win, like 270 in an election. If a player can get to 28 points then he automatically wins. (Said player can win with less if there are ties). Instead of viewing the board as 55 points I can win, I view it as 28 points I need to win. That being said, each point is worth 3.57 of my soldiers (100/28). I am making an assumption, that most people will undervalue lower point tiers. Putting 3, 5, and 7 soldiers on tiers 1, 2, and 3 respectively, 15% of my soldiers, but gains 21% of the points needed. A major victory for my army. 4 and 5 are tricky. They are needed to win if you go the 10,9,5,4 strategy (last season's winners did). But they were overcommitted to those areas. Being wary of losing them due to people overcommitting on them, I left them at 2. Every soldier needs someone to guard his back. Pick up the easy win vs those who bid 0 or 1, but don't lose out on those playing the 10,9,5,4 strategy. Probably a minor loss for my army. 6,7,8 are much easier. They deserve 21, 25, and 28 soldiers respectively (using 3.57x *point value). But they are also VERY underappreciated by both past winners, and the average submission. Capitalizing on this, I can gain these points by using a decent amount of soldiers, but near the amount they deserve. Another major victory for my army. I can count on wins by using only 15, 18, and 20. This leaves me with 9 and 10. And 28 troops. If history tells us anything, its that people like castle 9 more than they like castle 10. This is an either or situation, you won't win both unless you overcommit. I place all 28 in castle 10. Get 28 points with the fewest number of castles possible (10, 9, 8 & 1). Try to defend those with as many soldiers as possible and leave 1 at the other castles in case any are left undefended.
2 2 5 13 16 1 7 16 33 5 I looked at the distributions of the two previous wars and picked out some forts that have a potential to be left unguarded and put a couple more troops in there, while approximately splitting the difference between the two sets of winners, hoping that others might have the same approach, allowing myself to have a couple more in those key forts mentioned above.
152 1 1 1 4 1 4 1 10 3 12 33 14 20 16 20 18 19 20 To achieve over 50% of the available points, you must either win either the lowest 7 or highest 4, or otherwise mix and match point values up to 28 points. I have chosen to fight hard for the 4 highest values, in hopes that most spread their troops more conservatively. Because Castle 7 is included in both of these combinations, it is likely to be highly contested, so I have placed a third of my troops there. 1 troop was distributed to all castles in the lower 6 to snag extra points in case of similar strategies, or to those which chose not to contest certain castles. This strategy only works if I am able to win all 4 top castles, so this beats the winning Feb 2017 strategy of aiming low, but not the Jun 2017 strategy of splitting between 9/10 and 4/5. That makes this strategy considerably more risky and dependent on what the general trends are among the other participants this time.
153 1 3 1 5 1 7 2 8 2 10 15 20 18 25 20 30 0 2 28 The Art of War The Name of this game should be 55. Why? Well for a similar reason why your website is called 538. 55 is the number of total points a player could win in this game, but 28 is the number of points a player needs to win, like 270 in an election. If a player can get to 28 points then he automatically wins. (Said player can win with less if there are ties). Instead of viewing the board as 55 points I can win, I view it as 28 points I need to win. That being said, each point is worth 3.57 of my soldiers (100/28). I am making an assumption, that most people will undervalue lower point tiers. Putting 3, 5, and 7 soldiers on tiers 1, 2, and 3 respectively, 15% of my soldiers, but gains 21% of the points needed. A major victory for my army. 4 and 5 are tricky. They are needed to win if you go the 10,9,5,4 strategy (last season's winners did). But they were overcommitted to those areas. Being wary of losing them due to people overcommitting on them, I left them at 2. Every soldier needs someone to guard his back. Pick up the easy win vs those who bid 0 or 1, but don't lose out on those playing the 10,9,5,4 strategy. Probably a minor loss for my army. 6,7,8 are much easier. They deserve 21, 25, and 28 soldiers respectively (using 3.57x *point value). But they are also VERY underappreciated by both past winners, and the average submission. Capitalizing on this, I can gain these points by using a decent amount of soldiers, but near the amount they deserve. Another major victory for my army. I can count on wins by using only 15, 18, and 20. This leaves me with 9 and 10. And 28 troops. If history tells us anything, its that people like castle 9 more than they like castle 10. This is an either or situation, you won't win both unless you overcommit. I place all 28 in castle 10.
154 1 2 4 2 12 5 20 13 24 16 32 1 1 7 1 16 1 33 1 5 Guess Wildly I looked at the distributions of the two previous wars and picked out some forts that have a potential to be left unguarded and put a couple more troops in there, while approximately splitting the difference between the two sets of winners, hoping that others might have the same approach, allowing myself to have a couple more in those key forts mentioned above.
171 1 1 3 1 3 1 4 1 4 1 7 19 8 22 13 25 20 28 37 Proportionally allocated to the top four based on point values Roughly exponential increase for each next castle
172 1 1 2 8 12 10 3 16 18 16 4 22 24 5 1 30 1 Go strong to get to the 28 point win count from castles 10, 8, 6, and 4, and scatter other forces to avoid losing other high value castles to just 1 or 2 soldiers. Given that strategy, allocate soldiers in proportion to the castles' value. Specifically, targeted castles get 3x their value in numbers of soldiers while the remaining castles get half, rounded up. Given 100 soldiers, the specific numbers just sort of shook out that way. Round 1 winners went strong for upper-middle and low numbers to get to 28 -- something like 8,7,5,4,3,1. In response, round 2 winners went strong specifically for 10, 9, 5, and 4. I'm countering those while still focusing on my primary strategy: try hard to get my primary targets to get to 28 points, while giving myself a chance on the other castles if I happen to lose one or two of my primary targets. Running against the previous 10 finalists I'd finish 9-1, and the one loss is 28-27, so mine may be a popular winning strategy as a counter to those, just as the leaders in previous iterations of the game used similar strategies to each other. ------ I wonder if you could provide the average score for the previous winners, and other people who might have had a higher average result, but won fewer duels.
173 2 1 17 1 9 1 19 1 17 1 3 1 4 19 16 22 15 25 1 28 Random numbers between 1 and 19 Proportionally allocated to the top four based on point values
1 1 1 2 3 26 30 30 3 3 Highest value avoiding copy cats and those who will put everything on 10 and 9
174 1 1 2 2 12 2 3 16 18 16 4 30 24 3 5 27 30 Not too sure. Go strong to get to the 28 point win count from castles 10, 8, 6, and 4, and scatter other forces to avoid losing other high value castles to just 1 or 2 soldiers. Given that strategy, allocate soldiers in proportion to the castles' value. Specifically, targeted castles get 3x their value in numbers of soldiers while the remaining castles get half, rounded up. Given 100 soldiers, the specific numbers just sort of shook out that way. Round 1 winners went strong for upper-middle and low numbers to get to 28 -- something like 8,7,5,4,3,1. In response, round 2 winners went strong specifically for 10, 9, 5, and 4. I'm countering those while still focusing on my primary strategy: try hard to get my primary targets to get to 28 points, while giving myself a chance on the other castles if I happen to lose one or two of my primary targets. Running against the previous 10 finalists I'd finish 9-1, and the one loss is 28-27, so mine may be a popular winning strategy as a counter to those, just as the leaders in previous iterations of the game used similar strategies to each other. ------ I wonder if you could provide the average score for the previous winners, and other people who might have had a higher average result, but won fewer duels.
175 1 0 1 0 1 2 21 3 22 26 3 30 24 30 27 3 0 3 Key is to get to 28. Wanted to stack as few castles as possible to increase probability of winning those. Left 7, 4, and 3 as contingency plans in case someone was doing the same. Highest value avoiding copy cats and those who will put everything on 10 and 9
176 3 1 5 1 4 2 4 2 12 2 12 16 26 16 26 30 4 3 4 27 Overvalue the undervalued Not too sure.
205 1 1 1 1 1 12 1 12 9 24 20 1 30 46 35 I dunno I want castle 10 baby!!!!!!!!!
206 1 1 0 1 0 5 0 10 0 20 9 25 10 30 10 3 35 4 35 Shooting for mid numbers (adds up to more than the extremes put together). Still put a few in the top numbers in case of a steal. For the goal of winning 28 points, I plan to take castle 9 and 10. Then win any two among castle 7-9. I'm avoiding castle 4 - - 5 as they seemed to be hotly contested in prior matches
207 1 0 1 0 14 9 22 14 2 20 2 25 24 30 33 0 2 0 Why did you force at least 1 unit to go to castle 1? Just give up on the biggest ones, probably a waste
1 5 5 5 20 20 20 20 0 0
208 1 1 1 4 1 12 1 20 1 2 4 2 20 6 20 30 50 22 Randomly, kind of based off the previous renditions.
209 3 1 3 0 3 0 3 0 12 0 12 0 3 0 29 22 29 37 3 40 I choose to concentrate on towers 8 and 9, hopefully winning them almost all the time. I should also win towers 5 and 6 much of the time making 28 points for a victory. If I miss one or both of 5 and 6, I hope to make it up with scouting forces of 3 soldiers which may be more than most scouts.
210 1 1 1 4 1 5 1 9 1 12 9 12 20 18 30 12 35 26 I want castle 10 baby!!!!!!!!! Seemed like a good idea at the time
212 0.00001 1 0 1 0 1 0 7 5 10 5 12 5 14 15 16 30 18 40 20 the previous winners clearly picked a lane, some highs and mids, or some mids only, my lane is to go top heavy. As long as I can claim two top tier and two lower tier, I can win. More troops for higher value castles, but not ignoring lower value ones
213 1 1 4 0 4 9 13 14 9 20 10 25 10 30 23 0 19 0 7 Just give up on the biggest ones, probably a waste I am no game theorist, but I figure a decent concentration on the higher and middle numbers couldn't hurt.
214 1 0 1 14 1 0 19 0 5 18 5 0 6 0 35 33 28 34 :) Going big on castles 10, 9, 6, 3. It is designed to "just barely" win against what I figure is an average deployment. It matches up well with the top castles of Round Two but struggles against some of the top castles from Round One. As you might be able to guess, I don't expect people to go back to the Round One strategy.
1 1 4 12 20 2 2 6 30 22 Randomly, kind of based off the previous renditions.
1 0 0 0 0 0 0 22 37 40
1 1 4 5 9 12 12 18 12 26 Seemed like a good idea at the time
1 0 0 12 14 13 0 0 31 29 I expect eight and seven to be hotly contested, so I left them open along with three and two giving the opponent 20 points out of the gate. One required a value greater than zero, so I gave it one. With an average of three, I will likely lose one and the opponent will have 21 points. I plan to take four and five which were hotly contested in the last round and may be less so in this round. Six will be a toss-up. Nine and ten must be taken. If I can take four, five, nine, and ten, I will have 28 points and the opponent would have 27.
1 1 1 7 10 12 14 16 18 20 More troops for higher value castles, but not ignoring lower value ones
1 4 4 13 9 10 10 23 19 7 I am no game theorist, but I figure a decent concentration on the higher and middle numbers couldn't hurt.
1 0 14 0 0 18 0 0 33 34 Going big on castles 10, 9, 6, 3. It is designed to "just barely" win against what I figure is an average deployment. It matches up well with the top castles of Round Two but struggles against some of the top castles from Round One. As you might be able to guess, I don't expect people to go back to the Round One strategy.
3 5 7 9 11 13 15 17 19 1 Prioritizing high-end targets while keeping out of Castle 10 battle - marginal gain on that castle is not worth the battle
1 1 1 15 17 19 21 23 1 1
1 0 0 12 0 12 25 25 25 0 In order to assign the maximum number of soldiers to selected castles, from all castle combinations that sum up to 28 with just 4 castles, I choose to ignore castle 10 and concentrate forces to 9,8,7 (25 on each) then I just need one of 4,5 or 6 so I had to share the rest 25 soldiers to those 3 castles. To increase chances I placed 12 soldiers to 4 and 6 and the last remaining to castle 1( that was unintentional, since I had to place at least on soldier to castle 1)
215 2 3 5 4 7 3 9 7 11 11 13 11 15 26 17 4 19 27 1 Gut feeling Prioritizing high-end targets while keeping out of Castle 10 battle - marginal gain on that castle is not worth the battle
216 1 1 4 1 13 15 13 17 18 19 22 21 22 23 3 1 3 1
1 1 13 2 2 14 2 3 31 31 Trying to win 10+9+6+3=28 points
217 1 1 0 2 0 12 16 0 3 12 2 25 2 25 28 25 33 0 idk, put all my eggs in castle 9 and 10 and hope the rest works itself out In order to assign the maximum number of soldiers to selected castles, from all castle combinations that sum up to 28 with just 4 castles, I choose to ignore castle 10 and concentrate forces to 9,8,7 (25 on each) then I just need one of 4,5 or 6 so I had to share the rest 25 soldiers to those 3 castles. To increase chances I placed 12 soldiers to 4 and 6 and the last remaining to castle 1( that was unintentional, since I had to place at least on soldier to castle 1)
218 2 2 5 2 4 30 3 30 7 2 11 2 11 2 26 15 4 13 27 Gut feeling
219 31 1 31 1 31 4 1 13 1 13 1 18 1 22 1 22 1 3 1 3 Trying to get the top three castles and then hopefully catch one other castle my opponent didn't put any troops at
221 3 1 6 1 9 2 12 15 16 16 3 15 2 12 2 9 28 3 33 I think the middle castles will be where the war is won idk, put all my eggs in castle 9 and 10 and hope the rest works itself out
222 1 2 2 5 2 6 30 16 30 9 2 4 2 17 2 36 15 4 13 Chose a deployment that defeats all previous top 5 deployments.
223 1 31 1 31 2 31 9 1 15 1 8 1 18 1 21 1 0 1 25 1 Mean of previous winners, then equalization of ROI on all but Castle 9 because I don't like the location of that property . Trying to get the top three castles and then hopefully catch one other castle my opponent didn't put any troops at
3 5 7 7 8 10 10 10 20 20 Used the previous results, and tried to pick the opposite strategies
2 2 3 4 8 11 12 28 29 1 Have at least 1 at every castle, aim for capturing castles 6 - 9, much higher value than the lower value counts, and hopefully less contested than castle 10
224 1 2 3 5 9 7 10 9 11 11 12 13 15 14 17 15 19 11 I reinforced the higher value castles with 1 army from each less-valued castle in the hopes that I could both win some high-value battles against warlords trying to win a greater number of low-value castles and some (more?) low-value battles against top-heavy warlords. random assignment
225 1 3 1 6 1 9 15 12 22 15 2 16 6 15 6 12 34 9 13 3 I hand-tuned to win against the previous 5 top warlords as well as the averages in the last two competitions. I think the middle castles will be where the war is won
226 4 1 4 2 4 5 4 6 4 16 22 9 13 4 22 17 21 36 2 4 In hic signo vinces Chose a deployment that defeats all previous top 5 deployments.
228 2 3 4 5 6 7 7 8 15 10 23 10 35 10 0 20 0 20 Idk, could work Used the previous results, and tried to pick the opposite strategies
229 1 2 5 2 10 3 1 4 1 8 19 11 2 12 23 28 34 29 4 1 28 by way of 2,3,6,8,9 instead of 4,5,9,10 or 1(2),3,4,5,7,8. Mixed strategy which emphasizes 3 and 6 over 4 and 5 and splits the first two rounds emphasis on 7,8 and 9,10 by focusing on 8,9 Have at least 1 at every castle, aim for capturing castles 6 - 9, much higher value than the lower value counts, and hopefully less contested than castle 10
230 1 2 3 4 5 6 7 8 9 11 14 13 16 15 18 17 20 19 True percentages, rounded down and subtracted 1 for less valuable castles 2-5, and rounded up and added 1 for more valuable castles 6-10 I reinforced the higher value castles with 1 army from each less-valued castle in the hopes that I could both win some high-value battles against warlords trying to win a greater number of low-value castles and some (more?) low-value battles against top-heavy warlords.
1 0 0 16 18 1 1 20 21 22
1 1 1 1 4 12 20 28 20 12 fun
231 1 4 1 4 1 4 14 4 21 4 2 22 2 13 25 22 28 21 5 2 Weighted heavily to certain castles in the aim to almost always win those points In hic signo vinces
232 1 2 0 2 1 3 1 12 25 18 1 16 1 30 1 8 35 5 34 4 Copy the same strategy as last time, but more extreme (thinking people are going to go back to strategy 1) I need 28 points of castles to win. I started by thinking I would sacrifice 8, 9, and 10 because IF I could win the rest, I'd hit my 28. Recognizing that putting more troops in the remaining high value castles left the low valued castles relatively weak I decided to further reduce the troop deployment at the low end to slightly increase deployment in the 8pt castle. This is an interesting game because I need to decide which bucket of castles I want to commit to while leaving a token force at the rest. There's a subtle rock paper scissors element to this this game but with an extra depth of how sharp are your scissors, how heavy the rock, and how thick the paper. I'd like to know how viewing past battle strategies of winners affects this outcome. If the previous results weren't published, would this third round have a distribution of troops similar to the first round?
233 1 2 4 1 6 1 7 1 8 1 15 1 23 30 35 32 0 28 0 going for the top 3 and hoping to get lucky and get one other Idk, could work
234 1 1 5 1 10 1 1 1 19 1 2 31 23 31 34 31 4 28 by way of 2,3,6,8,9 instead of 4,5,9,10 or 1(2),3,4,5,7,8. Mixed strategy which emphasizes 3 and 6 over 4 and 5 and splits the first two rounds emphasis on 7,8 and 9,10 by focusing on 8,9
235 1 1 2 1 4 8 6 10 8 14 11 17 14 19 16 16 18 13 20 I guessed how people would react to the last round, and reacted to that True percentages, rounded down and subtracted 1 for less valuable castles 2-5, and rounded up and added 1 for more valuable castles 6-10
236 2 1 2 0 2 0 3 16 3 18 11 1 31 1 36 20 6 21 4 22 Trying to capture the sweet spot of being 1 more than multiples of 5, or just 1 or 2. I bet this game play very differently with prime numbers of troops and castles, that are not easy to divide.
1 1 11 1 1 1 1 21 32 30 I want to beat troop allocation based on castle % worth. And also equal split. The base naive case. While at the same time I want to have an edge against some of the winners in Feb and June meta. I win against 40% of Feb winners and 20% of June winners. The meta unlikely to repeat. My max overpay is +16. Median overpay is -2. It’s a more concentrated strategy. June had a more displaced strategy. Feb is more concentrated. Meta will swing back towards concentration.
237 1 1 3 1 3 1 1 4 22 12 1 20 8 28 27 20 33 12 I was bored in class, troops weren't going to deploy themselves fun
238 3 1 4 1 7 1 1 14 19 21 1 2 27 2 1 25 36 28 1 5 I needed to contest every castle in the event someone did not place any troops there and I could get it for "free". Then I figured out there are 55 total points available, so I needed to get 28 to win. If you divide the points available of each castle by the 55 total, you can get a % of points for each. If you then multiply by 100 you get what each castle is "worth" in manpower. I figured if I roughly double the "expected worth" in manpower, I will win the castle more often than not. I then picked a combination of castles to focus on that if I won them, would give me 28 pts. I wanted to avoid #10 because I expect there will be a lot of fighting for that one, so I concentrated on 9, 7 and 5, to give me a good base of 21 pts. I then focused on the bottom 3 castles because I expect them to be lightly guarded. If I happen to "steal" a castle from someone since they put no one there, even better. Weighted heavily to certain castles in the aim to almost always win those points
239 1 0 1 2 1 12 25 21 1 27 1 32 1 2 35 2 34 never gonna win 9 & 10, don't want 1-4, split the rest leaning higher for higher values Copy the same strategy as last time, but more extreme (thinking people are going to go back to strategy 1)
240 1 1 4 1 2 1 3 1 5 1 8 1 14 30 25 32 40 28 loosely based off fibionnaci sequence going for the top 3 and hoping to get lucky and get one other
1 2 3 4 15 15 15 15 15 15 balanced chance for the higher scoring castles, and can still get points for those who neglect the lower scoring castles
241 1 0 1 9 1 0 1 0 1 20 1 20 1 20 31 0 31 30 31 You must win at least 28 points. Since the given strategy seems to be to avoid large commitments on 10, and attack 4,5, and 9, I chose to deploy my troops to 10, 8, 7, and 6 in large numbers, concentrating the rest on 3 to offset losing 1 and two. Its a high risk strategy, because losing just one of the higher values will result in a loss.
1 2 2 2 4 4 1 28 28 28 I'm punting 7 towers. Looking over past results, I'm choosing towers that were punted most often - I put enough into lower towers in case someone went on a one tower strategy.
242 2 1 2 1 2 1 8 9 10 10 14 12 17 22 19 31 16 2 13 Wag I guessed how people would react to the last round, and reacted to that
243 1 2 1 2 1 2 13 3 15 3 19 11 22 31 24 36 2 6 2 4 Castles 1-3 not worth winning Castles 4-8 are enough to win Two troops at Castles 9 and 10, in case they are undefended. Trying to capture the sweet spot of being 1 more than multiples of 5, or just 1 or 2. I bet this game play very differently with prime numbers of troops and castles, that are not easy to divide.
244 2 1 3 1 5 11 8 1 2 1 22 1 23 1 4 21 27 32 4 30 Well, I didn't use *actual* game theory, that's for sure! I want to beat troop allocation based on castle % worth. And also equal split. The base naive case. While at the same time I want to have an edge against some of the winners in Feb and June meta. I win against 40% of Feb winners and 20% of June winners. The meta unlikely to repeat. My max overpay is +16. Median overpay is -2. It’s a more concentrated strategy. June had a more displaced strategy. Feb is more concentrated. Meta will swing back towards concentration.
262 1 2 4 2 6 2 9 3 12 18 14 18 16 26 17 26 19 2 I want this to be fun, not work, so I avoided any serious algorithm and went with my gut. Seems like you should send at least 1 to every castle, and given the linearly-increasing value of each castle, it makes sense to send numbers that follow that pattern. THEN YOU GET TRICKY and spice it up with a few extras taken from the lower valued castles and given to the mid-range castles, because I figure there's other lazy nerds like me who'll do the same thing as I did in paragraph 1, and I WANT TO BEAT THEM AND HEAR THE LAMENTATIONS OF THEIR ADVISORS. Thus, castles 6-8 got one extra soldier, who will provide The Edge To VICTORYYYYY!!!!!!!!!!! Avoid 10 as the most likely to be contested. Put 2 as a mininum to beat anyone just throwing 1's in. Focusing on 6, 7, 8 & 9 as together they defeat 1, 2, 3, 4, 5 & 10.
263 3 1 3 4 3 5 3 5 3 5 20 10 20 10 21 20 21 20 3 20
264 5 1 5 1 5 2 5 15 5 2 5 2 10 17 20 27 20 31 20 2 1)Focus on 4 castles that give 28 (just over 50%) and sacrifice biggest prize castle 2) don’t give away any castles for free 3) anticipate opponent strategy to send at least 1 to all castles and send 2 to hedge in case one of key 4 is lost 4) calibrate weights to beat simple backloading
1 1 2 1 20 5 2 1 32 35 I suspect folks will counter the previous round(s) strategies, so I want to zig while they zag and capture the big prizes.
265 1 3 1 1 6 19 6 19 8 17 22 17 13 18 15 3 24 4 2 idk tbh I'm not even going to pretend I can guess what everyone else is doing, so I kind of focused on getting 6 and 9, but might have enough from 7, 8 and the lower end if people overcommit there.
266 2 7 10 8 10 9 2 10 20 11 2 12 2 13 24 14 2 16 26 0 This was all a fluke. Sac the queen!
267 1 1 3 1 5 16 7 19 10 2 12 2 0 2 19 21 23 20 Slight tweak on EV 1, 3, 5 etc. deployment
289 1 1 2 7 3 9 17 1 14 1 4 30 3 48 2 1 21 1 33 I wanted to assure myself of winning 20 points and invested heavily in those castles unlikely to be the principle investments of others. I picked a strategy similar to the previous champion, but modified to be able to beat the previous champion.
290 2 10 4 1 6 1 8 1 10 1 12 1 14 1 18 39 25 20 1 25 By giving up castle 10 entirely I can distribute more troops elsewhere, with at least 2 soldier per point for castles 1-9. I did leave one soldier on castle 10 as a counter play for anyone who sends noone for similar reasons
291 2 1 2 2 5 6 5 16 7 20 20 22 20 5 20 5 0 Looked at the two previous, split the difference, was too lazy to tweak deployments. Sacrificed Castle 10 in hopes of winning slightly-lesser castles
10 10 10 10 10 10 10 10 10 10 To beat me, you have to place 11 soldiers at 6 castles. You can't. I win!
292 1 2 1 2 1 7 18 9 1 2 1 15 18 17 26 20 32 21 1 5 Getting to 28 points I will probably lose 5 & 10 (15 points) and win 6, 7, 8, & 9 (30 points) against most value-based opponents. I left castle 10 with enough resources to hopefully win that castle against similar counter-value-based strategies.
1 3 7 17 17 18 22 5 6 4 I kept enough in the top three to catch any that decided to sluff those, then loaded up on 4-7. 10 is just not SO much more than 6 or 7 that it justifies a huge commitment.
293 1 2 2 2 5 2 5 2 5 20 21 20 26 20 32 20 1 10 My strategy is to invest heavily in castles 7-9 to get to 24 and then try to secure the other 4 points by divesting my remaining points and hope to capture enough. Essentially, splitting the difference between the first two rounds by having even numbers across castles 6-9, a fair number on 10, and token troops on 1-5.
294 3 1 8 1 11 7 21 9 3 1 4 1 3 30 4 48 22 1 21 1 I focused on getting to 28-half of all points and other than a few scouts, focused on winning the fights that would just barely allow me to make it I wanted to assure myself of winning 20 points and invested heavily in those castles unlikely to be the principle investments of others.
295 3 2 0 4 7 6 10 8 20 10 0 12 30 14 30 18 0 25 0 1 I targeted 6 castles that would get me 28 points. If I go 6/6 on those ones that I bet big on then I win (doesn’t really feel like a good strategy, but I wanted to see how it would play out) By giving up castle 10 entirely I can distribute more troops elsewhere, with at least 2 soldier per point for castles 1-9. I did leave one soldier on castle 10 as a counter play for anyone who sends noone for similar reasons
296 5 2 6 2 8 2 5 6 10 16 2 20 2 20 15 22 23 5 24 5 How do you know which risks in war are the right ones? You wait to see if you win. Looked at the two previous, split the difference, was too lazy to tweak deployments.
1 0 1 7 1 20 3 27 14 26
297 1 10 1 10 1 10 1 10 1 10 10 15 10 20 10 20 10 30 10 The first 4 castles are only worth as much as 10 combined, so I'm willing to give up the smaller ones for a higher point castle. Then just lower the troops accordingly, weighted towards the higher points. To beat me, you have to place 11 soldiers at 6 castles. You can't. I win!
298 5 1 4 1 12 1 12 18 14 1 20 1 3 18 3 26 5 32 22 1 DAVE ALWAYS WINS Getting to 28 points
299 8 1 0 3 0 7 0 17 0 17 0 18 0 22 31 5 31 6 30 4 I am just trying to get to the minimum amount of points to win: 28. I found the combination with the least amount of castles I possibly need to win and dumped all my points into these 4, forgoing the rest completely as they are not important in my winning strategy. Also, based on the previous 2 games, I decided to put the least in castle 1 in order to stack 8, 9, and 10 to the fullest possible. I kept enough in the top three to catch any that decided to sluff those, then loaded up on 4-7. 10 is just not SO much more than 6 or 7 that it justifies a huge commitment.
315 2 1 2 8 2 9 3 15 5 3 21 3 21 5 2 6 21 28 21 22 I couldn't put a 0 in some of the columns (the webpage rules wouldn't allow me). So knowing that, I put heavy focus on winning 4/5 top levels and put slightly more than minimum on the lower ones (hoping to pickup a couple scraps). Intuitive distribution, then found local maximum
316 2 1 5 1 5 1 1 23 1 1 18 1 21 25 26 35 29 2 1 My goal was to win 8 and 9. With that I only need 11 more points to secure victory. I sacked 6 and 7 given that they were low in the last one and more people are likely to focus on those. That leaves me with needing to win 5 and 3 and then either 1 and 2 or 4. I sacked 4 given that it was high in both prior events. All castles should have at least 1 soldier just in case someone sends 0. Castle 10 will be the hardest to capture so put the minimum. Castle 6-9 will need to be captured to win if castle 10 is sacrificed. Proportionally distribute remaining soldiers to castles 6-9 favoring the higher scoring castles slightly.
317 5 1 7 3 8 5 10 7 15 9 25 13 30 16 0 18 0 15 0 13 Willing to concede three castles with most points in hopes of winning all others (28 of 55 possible points). Assigning most soldiers to those with most points among the group that I was aiming to win. I took last round's averages and shaved the lower half to give more juice to the top castles.
1 1 2 4 6 8 10 20 40 8 Thought it looked cool
318 0 1 0 1 0 1 14 10 17 13 20 17 23 25 26 30 0 1 0 1 Ignored 9&10 and chose the fewest castles past that to give me more than 28 points and weighed troops by value
319 2 1 4 1 5 1 7 1 9 10 11 15 12 20 14 25 16 25 20 1 guess Giving up on the 10
320 1 1 2 1 2 1 2 3 3 7 4 1 8 21 18 1 59 63 f(1)=1.218, f(x)= f(x-1)^1.4. Rounded result, mostly.
322 1 6 4 1 7 1 9 1 11 1 13 38 16 39 18 1 20 1 1 11 most people will load up heavy on the castles worth more points, i went for an even distribution slightly skewed towards the higher value castles. Based on the numbers 1-9 percentage of 45. IE 9 was 20%. I just took one off the lowest value castle in case someone did the same thing and put it on the 10. Castles 6 and 7 seemed undervalued so I focused troops there and put a middling 11 on castle 10 in case a significant number based their strategies on the previous battle.
323 2 1 2 1 2 10 3 12 5 2 21 19 21 25 2 25 21 3 21 The idea was to win 7,8, and 9 as well as one of 4 and 5. That gives me either 28 or 29 which wins. The others are to make sure i dont lose to a 1 or 2 I couldn't put a 0 in some of the columns (the webpage rules wouldn't allow me). So knowing that, I put heavy focus on winning 4/5 top levels and put slightly more than minimum on the lower ones (hoping to pickup a couple scraps).
324 7 2 8 5 8 5 1 1 23 18 1 18 1 1 25 37 35 1 2 Win Castle #9 and the other castels that seem overlooked. My goal was to win 8 and 9. With that I only need 11 more points to secure victory. I sacked 6 and 7 given that they were low in the last one and more people are likely to focus on those. That leaves me with needing to win 5 and 3 and then either 1 and 2 or 4. I sacked 4 given that it was high in both prior events.
1 1 1 1 1 23 5 33 30 4 Because it's the best
325 0 5 1 7 1 8 20 10 22 15 4 25 5 30 6 0 10 0 31 0 Before looking at the historical data, I settled on a 10-9-5-4 distribution, with individual soldiers heading to remaining castles so as not to completely cede any points. Once I looked at the last match, I saw that this had been a popular choice for the leaders, confirming its soundness. My draft distribution lost against those leaders, though, due to weakness in the 8-7-6 range. I also noticed that the bulk of forces were being sent against castle 9, producing uncertainty around the success of even a healthy amount of force there. To adjust, I reduced allocation to castle 9, redistributing those troops across castles 9-8-7-6, but left my highest concentrations at 10, 5, and 4. I ultimately ceded castle 1, because I assessed the value of an additional soldier to win a 4+ castle as higher than avoiding the 1 point loss (and most likely, the Battle for Castle One will be a quiet 0-0 match, yielding a free .5 point anyway). Willing to concede three castles with most points in hopes of winning all others (28 of 55 possible points). Assigning most soldiers to those with most points among the group that I was aiming to win.
326 12 1 12 1 12 2 12 4 12 6 14 8 26 10 0 20 0 40 0 8 I figure the bulk will put their points in to the top 4 if i can win everything else i should be good to go Thought it looked cool
327 1 0 2 0 2 0 12 14 15 17 16 20 4 23 26 18 0 4 0 I punted on Castle 10 assuming that a large number of people would simply deploy troops largely in direct proportion to the number of points, but still put more that 0-2 in the hopes of catching some that decided to punt entirely. I grouped the bulk of my troops around the 5-9 castles as I assume most would do, but hope to have just a few more quite often. To do this, I picked another one to punt on (Castle 7) guessing that that is a sweet spot in terms of points I can lose and where I think others will load up. My strategy is going to require me to win almost all the castles to which I committed significant troops (which is somewhat risky—but I think really the only way to go) or to steal a lot from the castles I committed few (but not zero) troops to. That seems like an unlikely path to victory but a decent hedge against someone that stacks all of their troops on Castles 7-10. I am quite worried about a 25-25-25-25 or a 27–26-24-23 deployment, so I decided to put 26 in Castle 8 which should give me a victory over all of those. Also a little worried about those deployments along with 1 troop at other castles, so decided to go with 2s mostly on the punts. Ignored 9&10 and chose the fewest castles past that to give me more than 28 points and weighed troops by value
328 5 2 7 4 8 5 10 7 15 9 20 11 26 12 3 14 3 16 3 20 Try to win 1-7, and sneak a few victories over 8-10. guess
1 6 1 13 1 21 24 1 31 1 I chose 5 castles (9,7,6,4,2) to try and win 28 points most often and sorted my troops according to point values per castles. Then I took 1 troop from each castle and allotted to other 5 castles (just in case opponent sent 0 or 1 troops to those castles also).
329 0 1 0 1 0 2 0 2 5 2 20 3 20 4 20 8 20 18 15 59 f(1)=1.218, f(x)= f(x-1)^1.4. Rounded result, mostly.
330 1 0 1 0 2 0 7 13 3 15 12 18 7 26 22 28 8 0 37 0 The crux of the 4 castle strat is taking castle 10. So if I get it, then have even deployment in the other castles, I'll beat everyone who tries it hinging on 10. If the majority of people hinge the 4 castle strat on 9, I'm screwed. Distributed my troops evenly through 4-8 which will give me 30 points each time banking on that I have more troop in those stations giving the other opponent 10-9-3-2-.
331 2 1 2 4 2 7 2 9 10 11 12 13 14 16 16 18 18 20 20 1 The larger number castles are important to win but not that life changing to put 20+ troops. If you sell out for the three largest castles and end up splitting and losing the rest you will not win. most people will load up heavy on the castles worth more points, i went for an even distribution slightly skewed towards the higher value castles. Based on the numbers 1-9 percentage of 45. IE 9 was 20%. I just took one off the lowest value castle in case someone did the same thing and put it on the 10.
384 1 1 2 1 1 10 1 20 11 30 12 35 31 1 35 1 5 IDRK I earn enough victory points from castles 6, 7, 8 and 9 so I focused on them. I put at least an army in each castle to prevent free wins. I only sent a few armies to castle 10 because I felt others would devout a lot of troops there. I didn't want to waste mine in a large battle there but I put some in case others have my same strategy of avoiding a large battle at castle 10. I also put a great deal in castles 8 and 9. I wanted to nearly guarantee victories at those castles.
385 0 3 0 7 8 2 19 13 17 2 12 19 4 22 4 25 4 3 32 4 Trying to win 10, 6, 5, 4, 3. Probably not a strategy to win the whole thing but should be good enough to be in top 50%. I wanted to aim for what I hoped was a less conventional 1-2-4-6-7-8 win, with enough scouts at the others to swing a few battles.
386 1 2 0 4 19 4 1 1 2 21 24 0 26 23 3 0 31 34 3 Gotta take >half the points baby
0 0 1 19 0 19 1 25 1 34
387 0 1 11 0 0 19 0 1 16 1 19 21 22 0 31 23 0 1 34 There are 55 points on offer. But you only need to win half plus 1 (.5 actually) My strategy was to secure the minimum points for victory by winning the 5 Castles. 8,7,6,5 and 2. Hopefully avoiding the high value castes will allow me to put more troops on lower values and win the war. Throwing 1 soldier to castle 10 in the event my opponent is thinking the same way.
388 5 3 7 3 9 3 3 8 11 5 11 27 16 31 21 2 26 3 You’ll never know
10 11 10 10 11 11 11 11 10 5 Pretty much evenly distribute my forces winning any castle left undefended, while sending one extra guy to 5 castles that accumulate enough points to win on their own. Sacrifice Castle 10 as I don't need it to win and hope others will focus on it
389 1 0 2 0 2 8 11 19 15 17 1 12 3 4 31 4 31 4 2 32 tried a hybrid model between the winning strategies of round 1 and round 2 Trying to win 10, 6, 5, 4, 3. Probably not a strategy to win the whole thing but should be good enough to be in top 50%.
390 6 1 6 0 5 19 15 1 20 1 20 21 28 0 0 23 0 0 34 Seed the top scoring castles and focus heavy on winning the middle ones. The castles worth few pointe I assumed few people would go for
391 1 0 1 0 2 1 3 19 5 0 8 19 13 1 21 25 34 1 12 34 Starting with Castle 1, it is the first 9 terms of the Fibonacci Sequence (1,1,2,3,5,8,13,21,34). ΣF9=88, 100-88=12 troops remain for Castle 10. I don't think I'm likely to win, but isn't it more important to be beautiful?? https://www.youtube.com/watch?v=93lrosBEW-Q
400 0 2 2 0 2 16 15 3 8 19 8 3 28 0 33 33 1 24 1 Did not overthink it.. the strategy likely relies too heavily on taking castle #10 with a modest deployment 1. In order to win one only needs to get 28 points. 2. Most players will send most of their troops to the top two or three castles, with minor amounts sent to castles at the bottom end of the scale. Most players will probably ignore castles 5 and 6. 3. Occupying castles 4-8 will win the game for a player. 4. Player should make only a minor attempt to capture castles 9 and 10, and should throw the lion's share of their forces against castles 7 and 8. They should also send a small force to each of the low scoring castles, as insurance in case of failure. 5. Player should send at least one soldier to each castle, just in case the enemy ignores them. 6. Player should send two or three soldiers to castles 1-3, to prevent a single enemy spy from capturing them.
401 4 8 5 12 5 13 6 13 7 13 9 14 11 0 16 27 27 0 10 0 Reverse variant of Benford's law. Law typically only covers numbers 1-9, so I gave castle 10 the average weight of 10 soldiers, then reversed the probabilities of the Benford's law digits putting 9 highest and 1 lowest, and divided by the new total weight of 110. Probably suboptimal, but who knows. I hope to allow my opponent to take the top two and the 7th castle while preserving those forces to have enough to counter what I expect to be a smaller amount dedicated to castles 1-6 and 8, thereby getting a majority of points and castles.
402 0 1 0 3 0 5 16 7 1 9 1 11 25 13 28 15 28 17 1 19 I figure everyone else is goint to overthink it, so I just went with a basic strategy. Since every castly is worth progressively more, I decided to put progressively more troops in each castle
0 0 6 7 23 24 25 7 7 4 go for the middling castles while not totally abandoning the higher ups, hopefully will win a number of battles while just winning 4 castles, but hopefully will get 5 & hopes it be the right 5. willing to concede 3 points...
403 0 1 6 9 0 12 0 6 0 5 0 26 0 5 33 5 33 7 28 24 I wanted to win 28 point by attacking as few castles as possible. By focusing as many troops as possible on castles 8, 9 and 10 and choosing a low value castle that people typically don’t commit many resources to, I hoped to win the majority of bouts.
404 0 1 1 3 3 4 17 15 21 15 17 16 14 16 16 26 5 2 6 2 I devised a strategy to beat all ten presented in previous iterations, then I added that strategy and devised the way to beat all ten plus that solution. I repeated several times adding improved solutions to my list to beat. Two basic "coalitions" can get to 27 points. The first is 8+9+10 (or mods of 9+10 lower numbers). The second is 8+7+6+(7--either 5+2, 3+4, 4+2+1, 5+3, 5+4). Because the winners all took the first last time, I'm focusing on the second. I give extra protection to 8 because it is most likely to be challenged by an 8+9+10 strategy. I need to win all of 8, 7, 6 and at least one of 5, 4, with 3,2,1 insuring against the loss of either 5 or 4. The oddity of my approach is that it would lose to the past winning strategy, but I expect that the _reason_ that strategy won is that most people attacked the 8 rather than devote so many resources to the 4 and 5, and that people will shift toward 8,7,6 and away from 4 and 5 this time. I keep a few guys on 9 and 10 as insurance against similar strategies that are more purist.
1 2 3 16 23 2 4 6 23 20
405 1 0 1 2 1 0 1 16 1 3 8 19 14 3 19 0 26 33 28 24 nearly abandoning the first 5. then load up 6-10. Winning 4 of those 5 guarantees a win. probably won't win Did not overthink it.. the strategy likely relies too heavily on taking castle #10 with a modest deployment
406 0 4 1 5 1 5 17 6 20 7 20 9 20 11 20 16 1 27 0 10 Dominant the middle/paint like in basketball Reverse variant of Benford's law. Law typically only covers numbers 1-9, so I gave castle 10 the average weight of 10 soldiers, then reversed the probabilities of the Benford's law digits putting 9 highest and 1 lowest, and divided by the new total weight of 110. Probably suboptimal, but who knows.
407 1 0 1 0 1 0 13 16 5 1 11 1 20 25 20 28 20 28 8 1 I saw the most potential value in the 7-9 range so I wanted to focus there, while guaranteeing the exploration of any opponent who sent 0 to a castle.
419 0 1 2 2 17 3 20 15 17 15 14 15 16 15 6 18 7 15 Beat previous submitted solution (plus all others considered...but with smaller margins on many others).
420 1 2 7 2 1 8 1 2 13 2 17 18 22 2 36 2 1 31 1 31 At least 1 soldier at every castle to take easy points from undefended castles, but mainly focusing on castles 8,7,6,5, and 2 which yield enough points on their own to win a battle with half the points + .5 Bc 2 > 1 and 10+9+6+3=28
421 2 1 4 1 5 1 7 1 9 17 11 12 13 22 15 23 16 21 18 1 On average, you can deploy 1.8 troops per castle point. This strategy sends troops to each castle based on their values. Winning big on castles 7, 8, 9, and loosing most of the rest on the assumption people will increasingly ignore 7, 8, 9 based on past data
2 9 3 10 3 18 3 22 3 27 straight up guess
422 10 5 10 7 10 9 13 13 1 12 16 15 16 20 17 1 15 1 Trying the maximize the chance of at least winning 28 points.
423 1 2 10 1 13 11 13 8 13 2 15 17 2 24 27 5 3 3 27 Think I need to send somebody to every castle, but potentially concede 10,9,7,1; hopefully sweep remainder. Trying to maximize a few different areas (victory points) while not giving many easy wins to others.
424 0 0 2 0 2 20 4 20 4 0 7 0 7 8 7 26 35 27 32 I tried to defend the minimum amount of castles needed to hold a majority of the hit points (assuming I understood the directions which, you know, 50/50), while another castle was defended with a small amount of troops to diminish attacking forces. Try to obtain 9 and 10 over all others, and for those who can beat me in one or both; punish them by taking other castles they hopefully skimp on.
434 2 1 2 1 2 1 2 1 2 1 2 1 20 32 20 31 20 27 30 Win the big castles, grab a couple other points somewhere. No strategy, just tried to weight the higher points castles higher
435 2 3 4 3 7 8 9 3 17 21 19 5 30 26 4 10 4 10 4 11 With the power of my brain. I wanted to defeat the previous champions. The first round winners won by going heavy in 4,5,9,10. The 2nd round they went heavy in some combination that didn't include 9,10. I went for go for 7, 5 and 3. With average values in 8,9,10 in hoping to get one or two of these.
436 0 0 2 15 1 2 1 2 19 2 22 23 25 25 28 2 1 29 1 This strategy should beat proportional strategies and rotations of proportional strategies, and I think that these will be the most common type. This will probably lose to some similar strategies (very concentrated on a few highest numbers and some low numbers), but by betting 2 on some of the middle numbers we'll hopefully beat more similar strategies than we lose to. We'll get crushed by strategies that beat us on 10 and 9 and also win a lot of low numbers, but I think these strategies will be least common. Stating the obvious first- there are 55 possible points, meaning you need 28 points to guarantee a victory. I feel like Castles 9 and 10 are overrated since Castle 10 is worth the same as Castles 8+2, 7+3, etc. My strategy was to win castles 5, 6, 7 and 8 for a total of 26 points. If accomplished, I only need to win ONE castle out of castles 2, 3, 4, 9 and 10 to guarantee a victory. I dedicated the vast majority of my soldiers (94) to get castles 5-8 while the rest only got 1 or 2 soldiers each. I actually put 2 soldiers on Castle 2 since it has the lowest value, I feel like putting a 2 there gives me the best chance of getting it. Putting 1 soldier each at 9 and 10 may seem silly but I still may get points against some other similar strategies. Even winning half of those castle 9 or 10 points would put me over the top. Anyway I have an English degree so the pressure is on you, math people! I wish you good fortune in the wars to come.
5 5 0 0 0 0 0 20 30 40 Castles 3-7 are pretty lame
437 2 2 6 2 5 1 15 1 18 1 2 1 12 32 3 31 35 27 Based on the last couple of series I tried to take advantage of what people were conceding without overspending. The most valued castles (9&7) I largely abandoned in favor of 10, 8 and 6. If I win those three and a couple low point castles I can secure a win. Win the big castles, grab a couple other points somewhere.
438 1 2 1 4 3 7 1 9 10 17 10 19 18 30 24 4 31 4 1 4 I believe that most individuals will go for the 10 point castle, and i will concede it, in order to focus on the next-highest value targets. With the assumption that I can win most but not all of the castles of high value below 10 points, I then distributed 3 soldiers to the 3 point castle in order to try to add to my value with an easier to acquire target. I also added 1 soldier to the remaining castles in order to take it from individuals who simply leave it alone. With the power of my brain.
439 7 0 9 0 11 15 13 2 15 2 16 2 1 23 26 25 1 2 1 29 I used one soldier for the 7, 9, and 10 castle. If someone chose not to attack a given castle, it is worth my deployment of at least one soldier there. But then, I figured that castles 10, 9, and 8 would see the highest deployments. My goal is to get to 28 points... so even if I lose castles 7, 9, and 10, I can still win by winning every other castle (with one VP to spare). I have a lot of excess soldiers to win all of these. I chose to fight hard for castle #8, figuring there was a decent "bang for your buck" return on that castle. So I distributed my remaining 97 soldiers, giving slightly more to the higher-worth castles, and prayed! This strategy should beat proportional strategies and rotations of proportional strategies, and I think that these will be the most common type. This will probably lose to some similar strategies (very concentrated on a few highest numbers and some low numbers), but by betting 2 on some of the middle numbers we'll hopefully beat more similar strategies than we lose to. We'll get crushed by strategies that beat us on 10 and 9 and also win a lot of low numbers, but I think these strategies will be least common.
443 26 7 11 9 11 11 13 11 15 12 16 15 1 1 26 1 1 It's sort of a counter-intuitive strategy that ignores average return per troop deployed in favor of attacking three strategies I think will be most common. Ironically, castle #1 is the pivot for many strategies that I think will be most common, so it's more important than the return of 1 would indicate. I think a lot of people are going to try to reach 28 troops by taking 10,9,8 and 1. This makes sense intuitively, because you're defending the fewest number of tiles, but it would mean glossing over 7-2, and I doubt many of those people would put more than a quarter of their troops on castle 1. I'm also trying to maintain enough troops on 7-2 to beat anyone who just assigns 10 troops per castle. If a player is taking a rational approach and assigns troops in such a way as to average out the expected return for each troop deployed, it would look something like 2,3,5,6,9,11,14,15,17,18 with .5-.67 expected return per troop and a slight preference on sending leftovers to the higher number castles. I would still get them by sweeping 1-7. I've also defended against even more extreme players like me by leaving 1 troop going to 10, 9, and 8 to get a quick score if they get too cute by leaving those blocks totally undefended, and I'll almost certainly still take #1 for the win hahaha. My strategy is most vulnerable to a more moderated version of my strategy where less resources are attributed to castle 1 and distributed over the mid range, but I would expect them to lose a high percentage of games to people pursuing the 10,9,8,1 strategy. Overall, I think my strategy will be successful. I used one soldier for the 7, 9, and 10 castle. If someone chose not to attack a given castle, it is worth my deployment of at least one soldier there. But then, I figured that castles 10, 9, and 8 would see the highest deployments. My goal is to get to 28 points... so even if I lose castles 7, 9, and 10, I can still win by winning every other castle (with one VP to spare). I have a lot of excess soldiers to win all of these. I chose to fight hard for castle #8, figuring there was a decent "bang for your buck" return on that castle. So I distributed my remaining 97 soldiers, giving slightly more to the higher-worth castles, and prayed!
444 0 1 0 1 0 1 11 1 0 1 0 15 26 17 31 19 32 21 0 23 I went for the less "psychologically significant" castles which would still give me a significant advantage. I sent 11 troops to 4 as an additional bonus in case someone is close to me in the upper ranges, or sweeps all the castles I didn't send any troops to - and since 11 just barely beats the simple strategy of sending 10 troops to each castle. I sent 26 to 7 because 26 is one more than 25 (another round number I expect people to use a lot), and similarly I sent 31 (rather than 30) to #8. Hope this works! Calculated relative worth of each castle and deployed troops accordingly, then removed all but 1 troop from lower half of castles (to get more points from enemies who chose 0) and distributed them evenly over the high value castles, because I have no clue which ones will be highly sought after this round.
445 0 0 3 3 5 3 4 3 10 18 17 18 0 3 0 26 29 26 32 Focus on castles 5-6 and 9-10 I assumed everyone would group-think back to the round before the last one (focusing on 7 and 8). Given that, I mostly copied the strategies of the last round , assuming that everyone else is "too smart" to try it.
6 0 0 0 0 0 0 32 31 31 If I win the 10, 9, 8 and 1, I have 28 which is just enough to win.
446 5 1 5 1 10 1 15 1 15 6 15 0 15 0 10 30 5 0 5 60 Compete everywhere, but not too hard for the low and high value castles Many players won't choose lower point castles, so it could be potentially easy to get several low-point castles and gain as many points as the largest castle.
447 1 26 1 11 1 11 1 11 1 11 10 12 14 15 19 1 25 1 27 1 55 possible points, first 5 only get you 15. Just in case the other warlord did not use any on the first 5 I will win with one on each. For castles 6-10 I dispersed the rest of the troops with the number getting bigger as the castle’s value got bigger It's sort of a counter-intuitive strategy that ignores average return per troop deployed in favor of attacking three strategies I think will be most common. Ironically, castle #1 is the pivot for many strategies that I think will be most common, so it's more important than the return of 1 would indicate. I think a lot of people are going to try to reach 28 troops by taking 10,9,8 and 1. This makes sense intuitively, because you're defending the fewest number of tiles, but it would mean glossing over 7-2, and I doubt many of those people would put more than a quarter of their troops on castle 1. I'm also trying to maintain enough troops on 7-2 to beat anyone who just assigns 10 troops per castle. If a player is taking a rational approach and assigns troops in such a way as to average out the expected return for each troop deployed, it would look something like 2,3,5,6,9,11,14,15,17,18 with .5-.67 expected return per troop and a slight preference on sending leftovers to the higher number castles. I would still get them by sweeping 1-7. I've also defended against even more extreme players like me by leaving 1 troop going to 10, 9, and 8 to get a quick score if they get too cute by leaving those blocks totally undefended, and I'll almost certainly still take #1 for the win hahaha. My strategy is most vulnerable to a more moderated version of my strategy where less resources are attributed to castle 1 and distributed over the mid range, but I would expect them to lose a high percentage of games to people pursuing the 10,9,8,1 strategy. Overall, I think my strategy will be successful.
448 1 0 2 0 2 0 2 11 18 0 17 0 16 26 15 31 14 32 13 0 I went for the less "psychologically significant" castles which would still give me a significant advantage. I sent 11 troops to 4 as an additional bonus in case someone is close to me in the upper ranges, or sweeps all the castles I didn't send any troops to - and since 11 just barely beats the simple strategy of sending 10 troops to each castle. I sent 26 to 7 because 26 is one more than 25 (another round number I expect people to use a lot), and similarly I sent 31 (rather than 30) to #8. Hope this works!
452 1 1 1 15 1 1 18 10 1 14 26 19 2 25 34 27 Trying to secure 28 points via castles 10, 8, 6, and 4. If other responses rely heavily on similar castles...hopefully a few stragglers in each castle provide a fighting chance. This loses to strategies that sell out for castles 6 or 8 pretty dramatically but I think those will be few and far between. 55 possible points, first 5 only get you 15. Just in case the other warlord did not use any on the first 5 I will win with one on each. For castles 6-10 I dispersed the rest of the troops with the number getting bigger as the castle’s value got bigger
453 0 1 0 2 4 2 13 2 16 18 8 17 14 16 14 15 17 14 14 13 Took the average of the previous two winners and made a team that could beat that.
454 0 2 0 2 0 2 0 15 20 15 50 15 30 15 0 2 0 2 0 30 6 seems like a good number. And I didn't want to send any lone soldiers off to die. I expect to win Castle 6 around 1/3 of the time, so hey, that's like 2 points. I'm feeling positive about it. Basic bell-curve distribution, with a good amount on 10 to potentially tie at best with someone who puts a lot at 10.
0 2 8 2 2 14 2 2 34 34 Never send just 1 so that you win vs any solo scouts, focus on 9 and 10 to try and insure 19 out of 28 required points, aim for over average on 3 and 6 to try and secure the 8 additional points needed for a win while hoping that victories over singles allow for any shortfall, sacrifice the 1 pt castle as winning it fails to make up for a split anywhere else that will determine the game.
455 2 1 3 19 3 1 15 19 18 1 23 19 24 1 1 19 1 10 19 If you win the even numbered castles, you win.
456 0 2 0 4 0 5 1 7 18 9 21 11 0 13 22 15 36 16 2 18 Gave castles weighted amount based on their value
457 1 2 1 3 1 10 15 25 1 4 18 5 1 5 26 10 2 35 34 Trying to secure 28 points via castles 10, 8, 6, and 4. If other responses rely heavily on similar castles...hopefully a few stragglers in each castle provide a fighting chance. This loses to strategies that sell out for castles 6 or 8 pretty dramatically but I think those will be few and far between.
472 2 3 2 0 4 0 8 0 16 0 32 0 16 0 14 32 2 33 2 32 I need 28 points to win, so I'm fighting hard for those 28 points.
473 5 0 5 0 5 0 6 0 12 11 12 11 16 11 9 21 12 21 18 25 Hoping other warlords don't put very many in the early castles Guarantee 10 and then assume no one else would expend more than 20 on any particular castle. Guarantee 9 and 8 on this rule and then spread the rest out descending.
474 2 0 1 0 0 12 0 0 0 22 0 28 0 33 34 36 32 4-castle all-in no scouts. Relative value. My min allocation has to be > 10 to beat naive even split. My overpayment vs avg cost... I must win castle 9. The other castles I will overpay relative to my overpayment on castle 9. Castle 3 +7, castle 6 +11, castle 9 +18, castle 10 +14. You really have to beat my contested castles. Weakness is castle 3, but I’m at +7 and castle 6, +11. Beats all past winners.
1 1 2 15 19 0 11 14 17 20 I tried to plan a balanced attack of the high-value castles (7-10) and the low-value castles (4-5) with increasing troops in each category. Since castle 6 was ignored in both previous editions I figured most players would attack this castle, so I left it exposed to avoid losing troops there.
475 0 10 0 10 0 10 5 10 10 20 10 20 15 5 20 5 22 5 18 5 Maximize points from ties My strategy is people don't expect you to send troops to the small stuff, so they don't send troops there. The most troops are sent to the big ones, so your best chance of getting points is in the middle.
476 1 2 3 4 5 9 7 17 9 22 10 16 13 5 15 7 17 5 20 13 Roughly their percentage value of 55 total available points. I took the top 5 winners from the last 2 times, along with the averages for each castle from the last 2 times, then maximized the number of points scored if my distribution faced each of these 12 opponents.
477 0 1 3 4 6 5 8 1 10 8 12 15 14 18 16 22 15 24 15 Looks good to me! I split the difference between the average soldiers per castle from the previous iteration vs. roughly proportional #s of soldiers per castle value.
493 5 2 5 2 5 4 5 10 5 2 15 16 18 25 21 3 20 33 16 3 slightly above the mean of previous rounds, with a little room to spare. It's better to supply low castles with a single high value than try to get all the high castles. I decided to leave Castle #10 essentially undefended, and instead focused on some of the less-worthy castles, especially #9 and #7, to get a "winning coalition" of six castles with around 30 points.
494 1 0 2 0 2 0 2 13 3 0 4 12 5 0 25 0 30 37 26 38 Several troops on each in case someone puts down 0, and tried to have more than 1 since I suspect others will put 1 at each (at least). Thought 10 is a place where people would have very low or high, so I went medium to beat the lows but not waste too much. Trying to really capture 8, 9, and the misses to add up to 23 (winning number) 23 points are needed to ensure a win - Overwhelming top two castles can get to 19 and then I just need to pick up one more of the other castles to win. Splitting between two helps cover bases if I lose one of the 9/10 and also increases odds i get the one castle to push me over 23 if I win the top two.
495 1 2 1 2 9 8 9 2 18 2 19 16 20 2 21 2 1 31 1 33 Have 1 at each castle to win against anyone who doesn’t send at least one troop there. Then I put the rest at the mid tier castles because I just need to win a majority (28). Castles 4-8 are worth 30. tried to invest in 4 castles that I felt relatively sure of winning and conceded the rest. High risk appetite!
2 2 2 2 6 21 21 21 21 2 The first 4 are so low value I'm giving them away, and the last one will be so hotly contested it's not worth fighting for. I put two there in case people put 1 - it's basically to take freebies while not costing anything substantial. I wanted to push all my chips in for the upper mid range ones. I went 21 for those as I think people might cap themselves at round numbers (20) for them, so it'd give me a slight edge.
496 1 0 1 0 16 0 2 0 2 3 21 16 2 16 2 27 26 27 27 11 It's based on previous player's strategies. Focus on getting just enough points to win, while trying to pick up a few extra points on unguarded castles. Sacrifice the low scoring to just barely overload the mid-to-high tier castles
3 3 3 1 1 15 3 22 27 22 This combination had a good performance in tests against the data from past competitions
497 1 0 3 1 4 1 7 1 13 12 20 15 24 18 28 20 0 17 0 15 I figured most people would choose increasing sequences, which means a lower numbers on 1-8 and more on 9 and 10. So if I put all my solders on 1-8 and beat them, maybe I'd have a better chance! :) 3-4 points higher than previous average on higher point castles, at least 1 point per castle.
2 2 10 2 30 36 3 3 6 6 Trying to beat more people so i assumed that people either put a lot of soldiers in the higher castles or none at all(1-5 soldiers "just in case")
498 2 1 4 2 7 2 9 2 12 3 2 4 27 5 31 25 3 30 3 26 Built to beat Cyrus Several troops on each in case someone puts down 0, and tried to have more than 1 since I suspect others will put 1 at each (at least). Thought 10 is a place where people would have very low or high, so I went medium to beat the lows but not waste too much. Trying to really capture 8, 9, and the misses to add up to 23 (winning number)
499 1 1 1 9 1 9 5 18 15 19 20 25 21 30 1 1 I'm assuming that most people will try to take Castle 10 - so I'm giving that castle up (with a single soldier in the event that I battle someone with a similar strategy who puts 0 in there). From there, I gave preference to the remaining castles based on higher point values. Have 1 at each castle to win against anyone who doesn’t send at least one troop there. Then I put the rest at the mid tier castles because I just need to win a majority (28). Castles 4-8 are worth 30.
500 0 2 0 2 9 2 22 2 22 6 6 21 27 21 2 21 6 21 6 2 I chose to give up 1 and 2 completely, focus on 4,5, 7 while putting enough points into the rest to hopefully stall non advances. The first 4 are so low value I'm giving them away, and the last one will be so hotly contested it's not worth fighting for. I put two there in case people put 1 - it's basically to take freebies while not costing anything substantial. I wanted to push all my chips in for the upper mid range ones. I went 21 for those as I think people might cap themselves at round numbers (20) for them, so it'd give me a slight edge.
501 2 1 4 1 5 16 7 2 9 2 11 21 13 2 15 2 16 26 18 27 There are 55 victory points up for grabs, so I found the value of each castle (castle #10 was worth 18.1% of the points; #9 was 16.3%, etc.). From there, I placed troops with those percentages as the base (18% at castle #10, 16% at castle #9). However, I would choose to round up the number of troops if the decimal would have rounded to 1 decimal point (ex: castle #6 is worth 10.9%, so I placed 11 troops). So basically just expected value. It's based on previous player's strategies. Focus on getting just enough points to win, while trying to pick up a few extra points on unguarded castles.
502 0 3 1 3 2 3 8 1 10 1 18 15 27 3 27 22 4 27 3 22 11% 1st 4, 55% middle 3, 1/3 top 3 This combination had a good performance in tests against the data from past competitions
5 5 5 10 10 5 11 30 11 8 I felt like Castle 8 had the best view, so I really wanted to take that one.
503 1 1 3 1 4 1 7 17 13 19 20 19 24 19 28 21 0 1 0 Prioritizing middle enough to win, safeguard others with 1 point I figured most people would choose increasing sequences, which means a lower numbers on 1-8 and more on 9 and 10. So if I put all my solders on 1-8 and beat them, maybe I'd have a better chance! :)
504 7 2 1 2 1 10 1 2 0 30 0 36 0 3 27 3 28 6 35 6 There are 55 available points among the castles, which means I need 28 to win. My strategy is to sell out for the top 3 castles, which gives me 27 if I win them all, then hope to take the smallest castle to push me over the edge. In addition I have a single scout sent to the next three smallest castles to try and steal one of those as well. Castles 5, 6, and 7 I will concede in favor of castles 8, 9, and 10. Trying to beat more people so i assumed that people either put a lot of soldiers in the higher castles or none at all(1-5 soldiers "just in case")
505 0 2 9 4 0 7 0 9 0 12 0 2 0 27 32 31 32 3 27 3 Built to beat Cyrus
546 0 1 0 1 0 2 0 2 15 17 20 17 2 17 2 4 27 1 34 38 Focusing resources where they could be useful, deliberately avoiding a couple of high-value targets to win the war Maximize towers to get to 28 points
547 5 0 0 0 0 20 0 0 0 32 0 31 40 32 40 The goal is to get 28 points. Concentrated troops at the least amount of castles to achieve that. 23 points to win. Overload the highest rated castles and sacrifice everything else
548 1 0 3 4 5 6 10 8 16 11 26 14 20 22 11 23 4 12 4 0 Why wouldn't you choose this troop deployment? I'll never tell.
0 2 3 3 16 20 22 26 4 4
549 1 3 2 5 3 6 7 8 9 0 17 12 18 14 18 15 19 17 5 20 aim to get 6-9, and maybe grab ten if it is lowly guarded, and then just a little at the bottom ones Scale investment to reward, but then abandon castle 5 and use the extra soldiers to try to beat other warlords scaling investment to reward
550 0 0 4 25 6 0 9 25 12 0 15 25 18 25 0 0 18 0 18 Sacrifices must be made! Castles 1, 2, 4, 6, 9, and 10 are dead to me! Going hyper-aggressive (but not the most aggressive strategy). Best Case: I win! Worst Case: I am a troll! Previously I had anticipated 10 to be the central battleground and abandoned it, the past two rounds the central battleground has ended up being 8 instead. I've abandoned contesting 8, focusing on the surrounding high number figures, and tapering off from there. 1 is also abandoned as low reward.
551 0 0 0 0 0 10 15 15 17 20 0 25 33 30 35 Win four of the top five castles, and you win. This particular troop distribution fights harder for the bigger prizes; would win against four of the five top strategies devised last time; and should be able to compete against anyone putting significant effort in winning lower tier castles, as people have been doing.
560 1 0 3 2 0 3 4 1 15 12 0 12 21 12 16 12 9 12 31 34 I generated it randomly. I multiplied the value of each castle by a random real number selected from a Poisson distribution with rate=2, rounded down to the nearest integer, then gave any remaining soldiers to castle 10. I generated a few allotments this way, picked one that looked nice, and checked it against the top five from the past two iterations. I had a decent record against past winners so I went for it! Top strategies in round 2 were all-in on 4 specific numbers, particularly 9+10 and a 9-sum pair (4/5, 3/6, 2/7, 1/8). Looking to break that by stealing 10 then getting 3 out of 5-9 range. Loses to top strategies of round 1 (more balanced emphasis on 5-9 range), hopefully the 'meta' doesn't drift back.
561 1 2 0 2 4 7 0 10 3 13 20 17 27 8 6 10 34 8 5 23 I picked something that would defeat the top 3 in both prior battles. I added one army in #1 to catch those with zero in #1, for a 9+7+6+5+1=28 win. I put five in #10 to catch those who put two to four in it. I think my most-likely wins will be 9+8+7+6, 10+9+7+6, 10+9+7+3, 10+8+7+6, 9+7+6+5+3, 9+7+6+5+1, 8+7+6+5+3. I will lose to anyone who is heavier in 10+8+5+4+2 or 10+8+5+4+1. Moneyball style. The goal is to buy points, and our goal is 28 points (more than half of 55). I divided 100 soldiers by 28 points and determined that the "right" value of a point is about 3.5 soldiers. I then determined the "right" value of each castle. I made a list of all the possible castle combinations to get to 28, and did some math to determine the inefficiencies between "right" values and "actual" values of the castles in prior exercises (for instance, Castle 10 was worth about 33 soldiers, but averaged 11.5 soldiers). Then I picked one combo that did not emphasize the most emphasized castles in the prior exercises (8,7,9). Then I averaged the "right" value for that combination against the average value placed on each castle in the previous two exercises, and went with that. I checked it against the averages and winners of the last one and felt comfortable to submit.
562 1 0 4 9 0 7 0 3 22 9 22 7 22 25 30 20 0 15 0 Heavy on 8s and 9s thinking others would overrate 10.
1 2 4 7 19 11 24 17 3 12 I chose it for the win!
563 1 0 2 1 6 3 1 20 1 3 18 0 3 21 2 24 33 0 33 28 To maximize winnings. Looked at the past distributions and estimated what it would take to win castles 10, 8, 7, and 4. Saved some leftover men for other random castles. But figured castle 9 wasn't worth it.
564 1 0 1 0 4 0 12 0 20 17 20 21 20 0 20 26 1 36 1 0 I assumed most opponents would go for castle 9 or 10 so I tried to leverage 5-8, with a 12 also likely taking 4. I added 1's to other castles just in case an opponent deployed a zero on X castle strategy also. I think a lot of people will be fighting for #10 and #1 because 10 is worth the most points and #1 is the tiebreaker if you went 10,9,8,1 or 7,6,5,4,3,2,1. I considered going for 10,9,8, 2 to avoid fighting over the #1 and because I could win even with a tie on #2, and then realized I could avoid #10 as well. In summary, I'm avoiding fighting over what I expect to be hotly contested #10 and #1 in favor of #6 and #5 while maintaining the concentration of my troops by only needing to capture 4 castles to win. As far as specific troop distribution goes, I made sure I had at least three times the castle number and dumped a bunch extra on #9, which I think will receive a heavy designation from anyone pursuing a variant of the 10,9,8,1 strategy. I did not assign any troop numbers that end in 0 or 5, they are too popular.
565 2 1 0 3 6 0 0 4 2 15 0 23 21 36 16 0 9 31 I think people are going for 9. Trynna lock down 8 and 10 and hope 7&3 are strong enough. I generated it randomly. I multiplied the value of each castle by a random real number selected from a Poisson distribution with rate=2, rounded down to the nearest integer, then gave any remaining soldiers to castle 10. I generated a few allotments this way, picked one that looked nice, and checked it against the top five from the past two iterations. I had a decent record against past winners so I went for it!
566 2 1 2 0 2 4 2 0 2 3 11 20 21 27 31 6 11 34 16 5 I think a major underlooked part of the strategy is that many people will default to round numbers. Going one over the natural human instinct for round numbers should have a high return all over the board. Additionally, the previous two winning strategies had low numbers on the high-value castles, presumably because competition is fierce up there. But eventually enough people will switch resources away from those castles to make them profitable conquests again. I'm hoping third time's the charm! I picked something that would defeat the top 3 in both prior battles. I added one army in #1 to catch those with zero in #1, for a 9+7+6+5+1=28 win. I put five in #10 to catch those who put two to four in it. I think my most-likely wins will be 9+8+7+6, 10+9+7+6, 10+9+7+3, 10+8+7+6, 9+7+6+5+3, 9+7+6+5+1, 8+7+6+5+3. I will lose to anyone who is heavier in 10+8+5+4+2 or 10+8+5+4+1.
567 0 1 3 4 6 9 8 7 9 3 11 9 12 7 14 25 17 20 20 15 Using a base-10 logarithmic scale to determine base troop deployment for each castle (base troop deployment = log(castle#) * 10). Deduct each base number of troops deployed at each castle from 10, and send those troops to each castle in reverse order. E.g. spare troops from #1 go to #10, spares from #2 to #9, and so on until spares from #10 go to #1. I end up not sending any to #1 because log(1) = 0 and log(10) = 1. Heavy on 8s and 9s thinking others would overrate 10.
568 1 1 2 3 4 4 7 8 19 13 11 17 24 18 17 27 3 8 12 Felt good I chose it for the win!
1 2 2 18 2 18 22 33 1 1 I expect that there will be even more of a focus on number 10 this time, so I'm going to ignore that one. My plan is to get to 28 without winning either 9 or 10.
569 0 1 0 2 8 6 12 1 13 1 13 18 13 3 13 2 14 33 14 33 To maximize winnings.
570 2 1 3 1 4 3 12 17 20 22 20 26 20 26 20 1 1 sacrificed 9 and 10, we'll see how many optimize against the last round or play it again. I assumed most opponents would go for castle 9 or 10 so I tried to leverage 5-8, with a 12 also likely taking 4. I added 1's to other castles just in case an opponent deployed a zero on X castle strategy also.
571 6 2 6 0 6 11 0 6 2 16 0 6 23 6 36 16 0 21 31 No round numbers. Try to take castles that would be overlooked by others. I think people are going for 9. Trynna lock down 8 and 10 and hope 7&3 are strong enough.
592 1 1 1 10 9 12 16 9 21 18 22 2 23 2 5 20 1 25 I am deploying to win points, not the most castles. If most are deploying troops to the larger point totals, they can win those in a blowout, while I put together a strong contingent of mid tier wins to get to 28 total points. However, I avoid conceding any castle outright.
593 0 1 3 1 5 1 6 1 15 19 5 19 6 2 10 20 24 34 26 2 Basically a half-baked revision of the winner of the last time (trying not to duplicate exactly or respond too directly) I do whatever your mom tells me to do.
594 1 3 2 3 2 6 5 13 7 6 20 18 20 9 20 11 20 14 3 17 I generated some random troop deployments, had them all battle each other, and this was the best one.
0 1 1 16 21 2 2 3 32 22 I created a giant spreadsheet that I filled with placements from the previous rounds (with winners on the list twice because they rock). Then I built formulas to calculate my win percentage against them and played with my placements. After lots of testing, I chose a modified Vince Vatter (Round 2 champ who) that performed slightly worse that his Round 2 victory in my experiments. I did this because I figured people would note that leaving 0 or 1 soldier in a castle was a bad move and would start leaving 2 or 3. Basically, I did some math then took a guess as to how the masses would behave. My goal is over 80% victory!
595 1 4 1 0 1 0 1 5 6 17 10 17 24 17 23 20 27 20 I didn't put much into the lower troops, but went bigger into high troops. Tried to eek out a win at Castle 1, but other than that I went low.
596 1 3 1 3 1 1 2 2 3 5 6 11 5 24 20 26 12 28 45 Take the highest values, easy points for people abandoning low values Made a non linear shot for two big numbers and hope to get a couple of lower castles.
597 1 2 1 11 1 2 9 14 16 16 21 17 22 31 23 3 5 3 1 Go for the middle I am deploying to win points, not the most castles. If most are deploying troops to the larger point totals, they can win those in a blowout, while I put together a strong contingent of mid tier wins to get to 28 total points. However, I avoid conceding any castle outright.
613 0 3 0 3 8 9 4 2 4 3 21 14 16 21 22 5 4 17 21 23 Rd2 winners saw 2 trends v. 1: Entrants mimicked 1 and therefore 2 winners were differented from 1 winners in placement and throw-away towers were defended with 3-4 v. 1-2 solders to win. I picked a strategy that is different from 1-2 and increases throw-away defense slightly. There are 7 strategies I'm trying to beat, 4 historical and 3 forecasts. The 4 historical strategies are the February Average, the May rematch Average, and the two champions Vince Vatter and Cyrus Hettle. The 3 forecasts are what I call the "Forecast Average," and Copycat 1 and Copycat 2. The Forecast Average is what I expect the average castle distribution to be based on the last two battles: 3,4,8,9,11,11,14,15,12,13. The Copycats are players who are trying to synthesize the strategies of the last two winners. Copycat 1 focuses troops on castles 5, 8 and 9 (distribution: 1,3,5,8,12,2,3,31,33,2). Copycat 2 focuses troops on castles 4, 6, 7, and 10 (distribution: 2,2,6,12,2,17,22,2,3,32). My distribution scores very well against the 3 historical averages, which I hope will represent the majority of players and get my win rate above 50%. And hopefully it narrowly defeats most of the elite players who are trying to copy previous champions, putting me in the upper echelon.
614 2 0 5 4 8 5 10 6 15 16 5 15 30 18 23 8 5 17 0 Rd2 winners saw 2 trends v. 1: Entrants mimicked 1 and therefore 2 winners were differented from 1 winners in placement and throw-away towers were defended with 3-4 v. 1-2 solders to win. I picked a strategy that is different from 1-2 and increases throw-away defense slightly. Putting more troops into the medium level castles
615 1 3 1 6 1 0 13 14 16 0 19 22 22 25 25 30 1 0 1 0 4-5-6-7-8 is enough to win. I figured you need 28 points to win and winning 1-7 will get you there exactly. That means you can reallocate all your points from 8-10 to 1-7 and stand a good chance of winning. Other people might do that too though, so I did some other stuff on a whim to mix it up.
4 4 4 14 14 14 4 4 34 4
616 2 0 1 0 10 8 12 4 14 4 3 21 13 16 4 22 37 4 4 21 Defensive strategy, hope opponent went all in on 9. Rd2 winners saw 2 trends v. 1: Entrants mimicked 1 and therefore 2 winners were differented from 1 winners in placement and throw-away towers were defended with 3-4 v. 1-2 solders to win. I picked a strategy that is different from 1-2 and increases throw-away defense slightly.
617 9 2 9 5 9 8 9 5 9 6 9 16 9 15 9 18 9 8 19 17 Rd2 winners saw 2 trends v. 1: Entrants mimicked 1 and therefore 2 winners were differented from 1 winners in placement and throw-away towers were defended with 3-4 v. 1-2 solders to win. I picked a strategy that is different from 1-2 and increases throw-away defense slightly.
618 0 1 0 1 1 10 13 11 16 12 19 1 22 1 25 32 1 32 1 Fight for the top two, plus the center 4-5-6-7-8 is enough to win.
628 1 3 1 7 12 9 6 12 6 8 23 24 2 30 2 3 25 3 22 Prior data wanted to win high value targets while getting to 28 in most efficient way possible while still covering possible deficiencies or ignored castles.
629 1 2 2 3 3 4 4 6 10 7 15 11 15 12 15 14 4 16 31 25 Last time it seems the top teams underrepresented castles 5-8. Zig when they zag and whatnot. Trying to adhere to the 2 troops for 1 vp but with some skew to capture 10 based on last time around.
630 0 0 7 0 8 3 11 10 0 21 0 29 23 22 25 11 26 4 Created a slightly skewed normal distribution centered on 7 then mapped 100 soldiers across that distribution!
4 7 10 14 17 22 26 0 0 0 Distributed proportionally-ish on the buckets (hopefully) most likely to get to 28
631 5 1 0 3 0 7 0 9 0 12 0 8 0 24 30 30 3 35 3 28 points is a win, so that's all I'm going for. The Castle 1 victory is essential!
632 2 1 2 2 3 2 4 2 10 22 15 22 15 22 15 22 4 2 31 Give me all those 1 troop castles. They are mine. Last time it seems the top teams underrepresented castles 5-8. Zig when they zag and whatnot.
633 3 0 5 0 11 7 18 8 2 11 19 0 19 0 17 23 2 25 4 26 Already submitted but I think I typoed to have my totals over 100?
634 3 4 4 7 4 10 4 14 4 17 25 22 25 26 26 0 2 0 3 0 Distributed proportionally-ish on the buckets (hopefully) most likely to get to 28
635 2 5 2 0 2 0 11 0 2 0 21 0 1 0 28 30 1 30 30 35 Step 1: Secure enough points (28) for the win with as few castles as necessary (4) to allow for largest deployments. Attempt mainly even numbered castles - partially a gut feeling, partially so that a lost castle can be compensated with a few small ones more easily. Step 2: Prevent a loss against an archenemy with a normal distribution of forces (10 at each castle) by using at least 11 at my primary targets. Step 3: Place at least 1 in each lesser-targeted castle in case my archenemy doesn't attack it, but put 2 in the lower ones to increase the chance of scooping up extra points to offset a potential loss of a large castle. Step 4: Bask in glory as I defeat a majority of the would-be warlords in Riddler Nation! 28 points is a win, so that's all I'm going for. The Castle 1 victory is essential!
0 0 0 17 22 1 6 6 26 26
636 0 2 1 2 1 2 1 2 17 2 20 22 2 22 26 22 29 22 3 2 Give me all those 1 troop castles. They are mine.
637 6 3 7 5 8 11 9 18 10 2 11 19 12 19 13 17 14 2 15 4 Already submitted but I think I typoed to have my totals over 100?
638 1 3 1 4 6 4 10 4 12 4 12 25 15 25 16 26 13 2 14 3 Assumed a trend based on the first two events. Added one solider more than the anticipated trend value to castles 4 through 10. Put the minimum on Castles 1 and 2 and the remainder on Castle 3. Crosses fingers.
649 0 1 0 17 0 25 0 10 0 9 100 9 0 9 0 6 0 0 I looked at old answers and fudged a little honestly. All of the troops at the first castle higher than 5
650 2 4 3 7 4 10 20 12 23 2 13 27 4 28 7 4 0 4 24 Slightly higher deployment from last time’s in castles 9-10. If people saw the last one and went for 3 soldiers to win it I win, if they didn't see it and behaved the same (average 2-3 soldiers) I still win Counter Strategy
651 1 2 2 4 2 7 11 10 11 12 11 2 8 27 18 28 18 4 18 4 Concentrate on the higher values with some randomness mixed in. Slightly higher deployment from last time’s in castles 9-10. If people saw the last one and went for 3 soldiers to win it I win, if they didn't see it and behaved the same (average 2-3 soldiers) I still win
4 5 6 5 12 23 14 15 14 2 mystery
652 2 1 2 2 2 11 2 11 2 11 10 8 25 18 50 18 3 18 I gave at least two to all the castles so I can try to bank some smaller points and I think if my opponent tries the same he'll probably only throw one out there. Then, I targeted Castle 9 with Castle 8 as a back up, in case they throw all of their points at 10. Then I stagger the rest I guess Concentrate on the higher values with some randomness mixed in.
653 1 4 7 5 1 6 1 5 14 12 18 23 21 14 33 15 2 14 2 Similar strategy to previous winners, adjusted numbers slightly for some variation mystery
654 2 3 2 5 2 6 2 7 2 15 2 14 10 15 25 16 50 17 3 Tried to win castle 6, plus 2 of 7, 8, 9, 10 assuming that most contestants will go for 2 of 7, 8, 9, 10. Then scatter enough on 1-5 to pick up some points there. I gave at least two to all the castles so I can try to bank some smaller points and I think if my opponent tries the same he'll probably only throw one out there. Then, I targeted Castle 9 with Castle 8 as a back up, in case they throw all of their points at 10. Then I stagger the rest I guess
655 1 2 7 2 1 2 1 11 14 2 18 21 26 33 31 2 2 Tried to win 7/8/9 in most cases, then need only 4 pts left for victory. 2 gaps help defeat all gap fillers of 1. Similar strategy to previous winners, adjusted numbers slightly for some variation
656 1 2 1 3 10 5 10 6 15 7 25 15 5 14 5 15 1 16 27 17 Tried to win castle 6, plus 2 of 7, 8, 9, 10 assuming that most contestants will go for 2 of 7, 8, 9, 10. Then scatter enough on 1-5 to pick up some points there.
657 2 1 5 2 5 2 9 2 11 10 2 26 21 28 26 2 31 2 I looked at the first battle you had, added up the total on each castle for the top entries, then divided proportionally. There seemed to be something vaguely bell-curve-derivative about the winners. Tried to win 7/8/9 in most cases, then need only 4 pts left for victory. 2 gaps help defeat all gap fillers of 1.
1 1 2 9 11 13 16 18 15 14 +1 to average May battles less on castles 1-3
658 2 1 4 1 5 10 7 10 9 15 11 25 13 5 15 5 16 1 18 27 Figured the most efficient distribution is 0.55 points per man. Applied the ideal to to each castle and rounded to the closest whole number.
659 2 2 5 2 5 2 9 2 11 14 10 24 26 27 28 23 2 2 My plan would be to take 54.5% of the points possible and put 88% of them toward that in order to help secure as many points as possible in the 6-9 range. Then have 2 soldiers at each other castle to hopefully catch people who don't value the lower valued castles or assume they are going to lose Castle 10 and don't put anyone there. I looked at the first battle you had, added up the total on each castle for the top entries, then divided proportionally. There seemed to be something vaguely bell-curve-derivative about the winners.
660 0 1 0 1 0 2 0 9 0 11 0 13 26 16 32 18 42 15 0 14 I only need to win 3 castles, assuming people focus on 10, I decided to ignore it an focus on the next three and then power creep 9 and 8 in case people had the same idea as I did. +1 to average May battles less on castles 1-3
680 3 2 6 4 6 7 9 15 11 18 2 21 27 0 31 2 2 0 3 31 Trying to bet 1 more than what I believe the majority of people will do based on your historical data. I dunno, I tried to win all the battles I picked. My strategy does well against last time's winners and beats the average distribution, I guess.
681 30 0 30 0 30 12 0 1 0 2 0 23 0 3 0 3 0 33 10 23 As I expect many to choose low troop numbers for the top castles, I deploy many soldiers there in order to hopefully take those three. After that, only one point is needed to win, so I chose to attack castle 10 in hopes that it is the least guarded. This appears to be a reasonable strategy based on the previous distribution. I used k-medoid clustering to find median strategies that represent the most common strategies, then found an allocation of soldiers that beat the 8 most common strategies. I then used that as an initial input to Robbie Ostrow's simulated annealing code from Part 2, which spat out the above.
682 2 0 4 0 7 12 15 0 18 0 21 26 0 2 0 0 29 31 33 I dunno, I tried to win all the battles I picked. My strategy does well against last time's winners and beats the average distribution, I guess. Choose just a few castles and maximize the chances of winning those.
0 0 12 1 2 23 3 3 33 23 I used k-medoid clustering to find median strategies that represent the most common strategies, then found an allocation of soldiers that beat the 8 most common strategies. I then used that as an initial input to Robbie Ostrow's simulated annealing code from Part 2, which spat out the above.
0 0 12 0 0 26 0 0 29 33 Choose just a few castles and maximize the chances of winning those.
683 1 3 4 9 6 18 8 18 6 27 Base: Assign soldier number equal to castle number using 55. Do it again using castle #-1 using the other 45. Adjust: disfavor odd # castles trying for wins in #4, 6, 8, and 10.
684 1 2 2 2 2 21 22 23 25 0
685 2 4 7 7 8 15 18 18 20 1 They can all go after the top castle all they want. I am giving them the top castle to strengthen my middle.
686 3 4 5 6 10 10 11 13 16 22 I wanted to use just enough troops on the earlier castles to win them , and wanted to win 9 and 10.
5 0 7 7 7 21 3 24 2 24 This strategy wins at least 24 points against an average opponent, and has the opportunity to take at least 4 points from castles that must be left largely unguarded. If an opponent takes 6, 8, or 10, then they likely used too many troops to adequately cover the mid-tier castles.
687 5 0 7 7 7 21 3 24 2 24 This strategy wins at least 24 points against an average opponent, and has the opportunity to take at least 4 points from castles that must be left largely unguarded. If an opponent takes 6, 8, or 10, then they likely used too many troops to adequately cover the mid-tier castles.
688 0 5 0 0 7 10 7 15 7 17 21 26 3 30 24 0 2 1 24 This strategy wins at least 24 points against an average opponent, and has the opportunity to take at least 4 points from castles that must be left largely unguarded. If an opponent takes 6, 8, or 10, then they likely used too many troops to adequately cover the mid-tier castles.
689 1 3 6 7 9 10 13 15 17 19 If F is a fraction of the troops, 1F+2F+...+9F+10F should equal 100. F is 100/55, or 1.81818...As there are no fractional people, I wanted to allocate the closest whole-number equivalents to 1F, 2F, etc. to the various castles, to minimize my ‘shortfall fraction’. So because some castles have an extra fractional person, the castles I chose to have a ‘shortfall’ were 1, 2, 4, 5 & 6.
700 5 1 5 3 8 5 8 7 10 9 17 11 20 13 23 15 2 17 2 19 Winning with the middle picks (maybe) didn't check the last results 2V-1. Assets (troops) distributed in proportion to cattle point values.
701 1 5 3 6 5 6 7 6 9 11 11 5 13 5 15 6 17 25 19 25 2V-1. Assets (troops) distributed in proportion to cattle point values. Performs well against round 2, wins more often than not against round 1...
702 5 2 6 3 6 4 6 5 11 5 5 15 5 15 6 25 25 25 1 Performs well against round 2, wins more often than not against round 1... I’m feeling lucky.
2 3 4 5 5 15 15 25 25 1 I’m feeling lucky.
703 2 4 5 7 9 11 13 15 16 18 Based on value of castles.
704 2 2 7 17 22 22 13 4 4 7 I am inevitable.
705 4 5 8 10 7 13 10 14 17 12 Mixed strategy
718 1 4 3 6 5 8 7 12 9 17 11 22 13 31 15 0 17 0 19 0 I split all my troops up equally based on each castles point value. Since there were a total of 55 points between all ten castles and I was given 100 troops there was no way to split up 100/55 straight up. Instead, I went with the equation 2(points)-1= soldiers. This leads to having exactly 100 troops distributed among the ten castles while assigning troops equally among each point value. Focus on the front 7, which adds up to 28, which gives you one more than your opponent, who takes 7,8,9 (total 27)
719 4 1 6 1 8 1 12 6 17 20 22 20 31 20 0 25 0 3 0 3 Focus on the front 7, which adds up to 28, which gives you one more than your opponent, who takes 7,8,9 (total 27) Looking at last time, if I wanted to beat that I would go for a bit more on the higher values and drop the lower ones. This should beat that by having a few more on 5-8, while also picking up 9 and 10 if people dump that, and beating 0s on 1-3
720 1 1 6 1 6 1 20 41 20 7 20 7 25 34 3 1 3 1 Looking at last time, if I wanted to beat that I would go for a bit more on the higher values and drop the lower ones. This should beat that by having a few more on 5-8, while also picking up 9 and 10 if people dump that, and beating 0s on 1-3 Starting with the goal of reaching 28 points, I went with a balance of offense and defense. The distribution I was shooting for was winning 2, 5, 6, 7, and 8. Leaving 9 and 10 pretty much open would let my opponent waste much of their capitol on those, leaving only 8 and 5 as 'battles,' but ones in which my opponent would have less to spend. Seeing the distributions of the previous 2 rounds, 6 and 7 seemed pretty safe, so I spent my soldiers on 5 and 8, leaving token 1's to leverage against random strategies with zeros.
1 6 1 1 41 7 7 34 1 1 Starting with the goal of reaching 28 points, I went with a balance of offense and defense. The distribution I was shooting for was winning 2, 5, 6, 7, and 8. Leaving 9 and 10 pretty much open would let my opponent waste much of their capitol on those, leaving only 8 and 5 as 'battles,' but ones in which my opponent would have less to spend. Seeing the distributions of the previous 2 rounds, 6 and 7 seemed pretty safe, so I spent my soldiers on 5 and 8, leaving token 1's to leverage against random strategies with zeros.
721 0 7 0 14 0 21 25 0 33 0 I considered strategies which are most efficient in usage of troops (ie. trying to get exactly 28 points) which would allow for ~3.57 troops per point value of the castle. Then I considered rounding error on the troops deployed - if others are also using 28-point strategies, then the best of them would be those that used the castles with small negative rounding errors. (ie. Castle 2 asks for ~7.14 troops but would be satisfied with 7). So I pick castle 2,4,6,7,&9 which leaves me with one leftover troop - I think Castle 9 might be the most competitive among 28-point strategies, so I drop the extra troop there.
2 8 8 8 8 30 2 30 2 2 Goal was to get 28 points. Abandon high value targets and hope that they draw many troops.
722 1 2 1 8 5 8 1 8 20 8 20 30 1 2 25 30 25 2 1 2 There's no way to win without taking at least 4 numbers with an average of 7 (need to sum up to 28 to win). I figure there will probably be a psychological bias towards playing a lot of troops on 10, and a psychological bias towards abandoning numbers not getting played for in strategies. The 1s are to pick up those abandoned numbers easily, and I figure plays of 20 on mid tier numbers have a high likelihood of winning. Goal was to get 28 points. Abandon high value targets and hope that they draw many troops.
723 10 1 10 1 10 5 10 1 10 20 25 20 25 1 0 25 0 25 0 1 There are 55 points up for grabs. To win, I would need 28 or more. I disregard castles 8, 9, and 10. That loses me 27 points. However, I deploy the remaining soldiers in the following manner - 1. Castles 6 and 7 get 25 soldiers each. Assuming that the opponent has committed most soldiers to castles 8, 9, and 10, I should be able to gain these two castles. 2. For the remaining castles, I will assign 10 soldiers each. The hope is that the opponent over-commits on the higher value castles while undervaluing the remaining castles. By flipping that thinking on its head, I hope to undermine the opponent's strategy. There's no way to win without taking at least 4 numbers with an average of 7 (need to sum up to 28 to win). I figure there will probably be a psychological bias towards playing a lot of troops on 10, and a psychological bias towards abandoning numbers not getting played for in strategies. The 1s are to pick up those abandoned numbers easily, and I figure plays of 20 on mid tier numbers have a high likelihood of winning.
724 3 10 3 10 3 10 7 10 7 10 6 25 6 25 15 0 30 0 20 0 My goal was to fight for every castle. A sizable investment in castle “9” and “10” was meant to punish any player who got too cheeky while also remaining competitive in the middle values. No castles for free to the opponent. There are 55 points up for grabs. To win, I would need 28 or more. I disregard castles 8, 9, and 10. That loses me 27 points. However, I deploy the remaining soldiers in the following manner - 1. Castles 6 and 7 get 25 soldiers each. Assuming that the opponent has committed most soldiers to castles 8, 9, and 10, I should be able to gain these two castles. 2. For the remaining castles, I will assign 10 soldiers each. The hope is that the opponent over-commits on the higher value castles while undervaluing the remaining castles. By flipping that thinking on its head, I hope to undermine the opponent's strategy.
729 0 0 0 5 6 7 8 22 25 27
730 0 0 8 10 12 14 17 19 20 0 I guessed that an distribution proportionate to point values will rarely win the 10 and will waste trips on the low-value castles, so I dropped the 10 and the bottom too and then loosely distributed them proportionally from there fight estimating as I wrote on some construction paper with a crayon.
731 17 11 11 11 12 15 20 1 1 1 The warlord can win with 1-7. Rather than targeting the high-point castles, target the low-point castles. In case our competitor tries the same strategy, we left one troop on each of 8-10, and loaded up on 1.
0 7 0 0 0 0 25 0 32 36
1 2 3 5 11 19 20 19 16 5 I tried for a bell curve with the peak between 7-8
732 1 0 1 7 3 0 5 0 7 0 13 0 16 25 22 0 15 32 17 36 Value weight plus noise
733 7 1 13 1 7 3 13 5 4 7 16 13 4 16 16 22 2 15 18 17 I was trying to guess the 100,000,000 number and this answer keeps coming up Value weight plus noise
734 6 7 7 13 9 7 12 13 16 4 21 16 26 4 1 16 1 2 1 18 Total of 55 VP to be won, and a player who wins the top 4 castles wins the game. Some will push really hard to win the top 4. Others will realize this and try to scoop up the low VP castles cheaply while still competing for some of the top 4. Honestly that's pretty much what I'm doing too, but rather than competing for the top 4, the idea is to scoop up the bottom 7, while tossing a bone to the top 3 castles to hopefully outdo anyone who is using a similar bottom-up strategy. The idea is that, while most people will invest a lot into the top castles (because they are valuable and because they expect others to do the same), many will not invest much into the bottom castles. This makes them (hopefully) cheap to obtain, and allows a pretty hefty force to go to castle 7 to (again, hopefully) outdo those who want castle 7, but who value it 4th most. I was trying to guess the 100,000,000 number and this answer keeps coming up
745 1 2 6 8 12 14 16 19 11 11
746 4 0 0 0 0 0 0 30 32 34 My plan hinges on capturing the most valuable castles, 8, 9 and 10, as well as capitalizing - hopefully - on a perceived deficiency in the lowest value castle, 1. The total value of 55 divided by 2 gets 27.5, so the magic number is 28. 10, 9, and 8 would get me to 27 already, so capturing 1 alone would put me over the top. If I lose any battle I've committed to, I lose. If I tie any battle I've committed to, I lose (other than 1, in which I'd tie). Hopefully all works out.
747 1 1 2 8 15 20 3 4 23 23
4 1 6 1 1 20 0 32 0 35 Goal is to take castles 1, 3, 6, 8, 10 for a winning 28 points. Single points in castles 2, 4, 5 are to tie with other people who put a single point in their castles or win against people who put 0 points in there castles. On a weighted percentage any opponent who puts more into castle 10, 8 or 6 is drastically overvaluing these castles (since you need half the points to tie any castle with more than double its weighted percentage is overvalued) and may beat me but will not be beating the majority of other opponents. I slightly undervalued castle 10 and castle 6, because I anticipate heavy investment in castles 8 and 9. Concerns are a skew to castle 3 in response to round 2 and that naive strategies (say 0 0 0 0 0 0 20 20 20 40) that are more top heavy are prevalent enough in the 538 reader base that I cannot win castles 10, 8, 6, and 3 consistently. Interestingly enough an even distribution of (10 10 10 10 10 10 10 10 10 10) beats my distribution and the top 5 distributions from round 2. I assume however that most of the 538 reader base will not submit such a simplistic submission. My distribution beats the top 5 from round 2, but loses to the 3 of the top 5 from round 1. I do not anticipate to win round 3, but am anticipating many readers will play similar strategies.
748 1 4 0 1 2 6 2 1 11 1 12 20 24 0 24 32 0 24 35 Goal is to take castles 1, 3, 6, 8, 10 for a winning 28 points. Single points in castles 2, 4, 5 are to tie with other people who put a single point in their castles or win against people who put 0 points in there castles. On a weighted percentage any opponent who puts more into castle 10, 8 or 6 is drastically overvaluing these castles (since you need half the points to tie any castle with more than double its weighted percentage is overvalued) and may beat me but will not be beating the majority of other opponents. I slightly undervalued castle 10 and castle 6, because I anticipate heavy investment in castles 8 and 9. Concerns are a skew to castle 3 in response to round 2 and that naive strategies (say 0 0 0 0 0 0 20 20 20 40) that are more top heavy are prevalent enough in the 538 reader base that I cannot win castles 10, 8, 6, and 3 consistently. Interestingly enough an even distribution of (10 10 10 10 10 10 10 10 10 10) beats my distribution and the top 5 distributions from round 2. I assume however that most of the 538 reader base will not submit such a simplistic submission. My distribution beats the top 5 from round 2, but loses to the 3 of the top 5 from round 1. I do not anticipate to win round 3, but am anticipating many readers will play similar strategies.
2 3 4 6 9 14 21 17 12 12 Focus on the valuable middle to high castles
749 2 1 2 0 2 3 2 3 11 11 12 16 24 31 24 3 0 27 24 this did ok when tried with a smaller group of students
0 10 0 10 5 10 15 20 10 20 My 11 year son is pretty sure this will win.
750 5 2 7 3 10 4 12 6 15 9 17 14 31 21 1 17 1 12 1 12 I wanted to guarantee victory on the first 7 castles. Briefly looking at past data, I estimated 28 victory points would be the number to aim for. Focus on the valuable middle to high castles
2 3 4 6 10 18 24 1 31 1 I wanted to obviously weigh the greater castles with more troops. I didn’t want to dump a lot of resources into 10 because people would target it. I also chose 9 instead of 8 due to previous results (in case that influenced other people’s picks)
751 3 2 5 2 7 2 10 3 15 3 22 11 28 16 2 31 4 3 4 27 Mostly abandon the top tier castles and focus my forces on the lower values. However, send what are hopefully slightly larger scouting parties to the high value targets. this did ok when tried with a smaller group of students
752 4 0 1 10 15 0 0 10 0 5 0 10 0 15 0 20 40 10 40 20 Only need 22.5 points to win. Figured 40 would win most of the time at 9 & 10, so I only need 3.5 My 11 year son is pretty sure this will win.
0 4 6 8 22 20 12 12 9 7 pure guess, did not look at previous games
753 1 5 1 7 6 10 10 12 20 15 25 17 20 31 15 1 1 1 Center around middle, most point per troop (don't want to waste at any point). At least one in each-points if ever left empty I wanted to guarantee victory on the first 7 castles. Briefly looking at past data, I estimated 28 victory points would be the number to aim for.
754 1 2 1 3 1 4 11 6 11 10 6 18 6 24 6 1 22 31 35 1 A hybrid strategy that attempts to guarantee Castle 10, and secure the remaining 18 points from poorly-guarded castles. Similar to last year's winners, but weakens the investment in Castle 9 in exchange for a moderate investment into Castles 6, 7, and 8 designed to reliably overwhelm token forces. This strategy edges out the points-per-solider distribution and the uniform distribution, as well as last game's 4-5-9-10 meta. I wanted to obviously weigh the greater castles with more troops. I didn’t want to dump a lot of resources into 10 because people would target it. I also chose 9 instead of 8 due to previous results (in case that influenced other people’s picks)
755 4 3 0 5 0 7 0 10 0 15 0 22 0 28 41 2 31 4 24 4 Magic Mostly abandon the top tier castles and focus my forces on the lower values. However, send what are hopefully slightly larger scouting parties to the high value targets.
767 0 0 5 0 1 0 1 0 0 1 0 2 35 2 30 3 30 The mini-me on my left shoulder There is 55 points total. 28 is what you need to win. So win 10,9,8 and 2. Focus on the minimum amount of effort to win. Win by a little or a lot, a win is a win.
768 0 1 0 3 1 4 16 13 21 15 2 18 25 1 3 20 29 22 3 Go hard on 4, 5, 6, 8, and 9.
769 1 0 1 0 1 0 1 2 1 12 1 16 40 0 26 33 15 34 13 3 inverse of the 7 down strat Trying to win 9, 8, 6, and 5, and hoping I can steal some of the others.
2 2 2 8 0 19 26 41 0 0 Avoid wasted troops at high value targets and low v; win on aggregate over sim.
770 0 0 0 1 3 16 5 21 23 2 16 25 13 3 17 29 23 3 Inverted bell curve for the top castles, leaving ineffective castles empty.
771 0 1 0 1 0 1 5 1 9 1 14 1 21 40 21 26 30 15 0 13 Ill sacrifice the extremes and try to take the bulk of the points in the middle inverse of the 7 down strat
772 3 2 6 2 7 2 1 8 2 0 22 19 22 26 2 41 2 0 33 0 -Always choose numbers of men above multiples of 5. -Shift focus away from 4 and 5, where large numbers were sent the previous two times -go back to focusing on 1, 2, and 3. -Finally, move focus away from castle 9 to 10. Avoid wasted troops at high value targets and low v; win on aggregate over sim.
776 2 3 2 2 2 3 3 2 8 2 22 2 22 15 28 21 35 I'm honestly really tired so email me if I win (I doubt it)
777 1 0 1 0 1 0 1 11 17 11 17 1 21 51 10 1 33 I assumed 10, being the most valuable, would be the most likely to see the bulk of enemy troops, by leaving only 1 soldier, I can still claim victory if they ignore it, but lose little to an attack. (Same theory for 1-4 and 7). Since 28 points are needed for victory, and I'm assuming a 10 point loss, the bulk of my troops are stationed at castle 9. With significant forces at 5, 6 and 8. If i can claim these four, i have victory. If i fail on some of these, the single soldiers in other forts hopefully claim unopposed victory.
778 0 5 0 4 0 6 0 0 16 0 16 0 18 35 35 30 5 30 28 is a win, so concentrate where you need to win, and win!
1 2 2 3 17 18 19 3 4 31 Because it's good. Done.
779 2 3 8 2 10 2 14 3 7 8 6 22 5 22 21 15 24 21 If I don't know what I'm doing than certainly no one else will
780 11 1 0 1 2 1 11 1 2 11 14 11 5 1 16 21 3 51 36 1 -Try to lock up 10 -While everyone else is going for 28, go for 29. It guarantees you a couple towers you want, and hopefully if they went all in on 8, 6, or 4, hopefully you can pick up the number beneath it and you still hit 28 I assumed 10, being the most valuable, would be the most likely to see the bulk of enemy troops, by leaving only 1 soldier, I can still claim victory if they ignore it, but lose little to an attack. (Same theory for 1-4 and 7). Since 28 points are needed for victory, and I'm assuming a 10 point loss, the bulk of my troops are stationed at castle 9. With significant forces at 5, 6 and 8. If i can claim these four, i have victory. If i fail on some of these, the single soldiers in other forts hopefully claim unopposed victory.
781 0 5 0 9 4 12 6 13 0 14 16 0 16 0 18 21 35 26 5 The strategy I chose is a tweaked version of “distribute troops proportional to the value of the castle, while abandoning the highest conflict Castles (historically 7 & 8) and the lowest point castle (Castle 1). I tweaked the exact numbers to fit my liking though. My goal with this deployment was not to beat the top performers - it was to beat the field. Beating the #1 warlord is the same as beating anyone else after all. I decided on this strategy by coming up with several theories on how to win, and testing them against an approximation of “the field” I created using the data provided by the previous contests and a Gaussian number generator. 333 “participants” were based off of the data from the first contest, 666 from the second, each of the top 5 strategies got 15 entries, and to make it an even 1150 the last participant placed 10’s in each castle. Hopefully there aren’t too many people who copy-paste the winning lists, otherwise I’ll lose! While I calculated a roughly 70-75% win chance in total vs the field, and a solid 80% win chance vs the initial top 5, I literally lose to each of the most recent top 5. So... good luck to me? Hopefully this won’t blow up in my face!
786 0 1 5 9 4 12 8 21 8 19 12 5 12 5 16 0 15 24 19 My brother worked on this, and I think he was on the right track. But he failed to account for how many will just use variations of the plans that won last time. I used a set of info Thomas made from your last two warlord games and made a strategy that works almost as well, but specifically targets the winners of the previous two games. My goal here is to have just one or two more soldiers than my enemy in the areas I'm fighting, and abandon the places where my enemy puts the most soldiers. My basic strategy was to distribute the troops in a proportion equal to the percentage of total points that each castle holds, rounded, with a twist! Each of these proportions were (1/55 * castle#). I believe this is the best mathematical solution, but I thought that others might have thought the same, so I conspired to beat them. For each even castle I added 1 troop, and subtracted 1 from each odd castle. This way, I will win ties against those who shared my thought process.
787 1 2 6 4 0 6 10 11 0 12 15 13 5 14 19 17 21 20 23 Value is highest at 10, I presume that the lower values castles 5 and below are expendable. I try to get the best of both worlds, as much as possible, by sending big battallions to the largest castles while still having a good chance of grabbing the even-numbered lower ones by punting on odd numbered low castles. It's a bizarre strategy that does well against the average strategies from both the other years as well as the winning strategies from those years. I do have to punt on one of the bigger numbers, so I choose 7 since I think people tend to "randomly" select that one a lot, plus 7 is "big enough to be important but not so big that others will get it, so I will". I do still send 5 troops there to avoid losing to other strategies that punt there.
788 0 0 0 0 0 15 10 20 10 0 10 40 35 25 35 0 A gross misunderstanding of all logic Choose four castles whose total point value is 28. Go all out for them.
3 6 6 16 19 12 12 20 3 3 I found the average troop deployment of the top 5 placers from both of the last tournaments, and then I found a strategy that would beat them both on average.
1 1 3 3 3 4 19 24 20 22 I would like to say I performed a complex game-theory simulation to optimize the outcome, but I basically eyeballed it to weight toward higher victory points without abandoning any castles; since the two previous contests had both the 7/8 and 9/10 focus strategies winning, I did not exclusively focus on either.
5 6 8 10 1 16 21 31 1 1 In previous battles the winners took two different approaches. The first round the winners focused on castles 4,5,7,8. In the second the focus was on 4,5,9,10. My idea was to focus on 6/7/8. then capturing as many little castles as I could.
789 2 4 4 9 5 4 12 4 12 4 12 4 2 4 3 33 23 32 23 Ensure I could beat both previous winners. This game is transitive, right?! It would be fun to know all the results! Maybe you can share the a google spreadsheet with everyone's answers, but maybe not our names and emails? :) I understand the changes between the last two games to show that my fellow warlords are smart but not going down the path of "if I do this then she does this then I'll do this and then she'll do this." Basically, they're making first-order adjustments. This deployment will hopefully work against both the average players and also the ones making first-order adjustments. That's shown clearly in the second digit of all my guesses--I think people naturally go for round numbers, and then smart players go one over round numbers to beat the round number players, so I'm going three over to beat the first-order guesses. I also focused on return on investment. Theoretically I can win most of the smaller castles with this deployment, and then I only need to win one or two of the big ones.
790 5 0 6 5 8 9 12 20 21 20 19 12 5 8 5 6 0 5 24 Split from the middle, easier to concede the higher and lower My brother worked on this, and I think he was on the right track. But he failed to account for how many will just use variations of the plans that won last time. I used a set of info Thomas made from your last two warlord games and made a strategy that works almost as well, but specifically targets the winners of the previous two games. My goal here is to have just one or two more soldiers than my enemy in the areas I'm fighting, and abandon the places where my enemy puts the most soldiers.
791 5 1 5 2 5 4 5 6 0 11 0 12 0 13 10 14 30 17 40 20 Intuition and guesswork based on the past data. Most generals had more even distributions and none of the top 10 had any allocations above 40. So if I capture the highest value prizes and a few of the smaller ones that garner less attention, I figure I should be in pretty good shape. Value is highest at 10, I presume that the lower values castles 5 and below are expendable.
817 0 0 8 11 2 0 2 0 2 7 32 7 2 7 35 34 9 34 8 I don't want to lose any large castle by a narrow margin, as this would be a significant waste of troops. If I win a large castle narrowly, this is the best scenario, but an overwhelming loss is also acceptable (since it will cost my opponent many troops to achieve this, and therefore give me numerical superiority elsewhere). It's like the electoral college! In the previous rounds, players deployed troop amounts on the large castles that were either very small or very large. My strategy depends on my expectation that this pattern will repeat itself. I chose all of my troop placements with this in mind, determined not to lose any large castle narrowly against either of those strategies. I invested heavily into castles 9 and 10, expecting to win their points almost every time. If I win one or both of them narrowly, then this is a significant boon to my efficiency. If I win them overwhelmingly, this is not as good, but for 19 points I'm willing to take the risk. I expect to defeat most players who conduct a predictable attack on one or both of these castles. If I lose either of these castles after such a large investment then I probably lose the match. I expect to do well in castles 3, 6, 7, and 8. I'm vulnerable to opponents who attack three or more of these simultaneously with medium-sized forces while conceding castles 9 and 10, as some top finishers did in the first round, but it's a risk I'm willing to take. Any two of these mid-range castles, plus the 19 points above will give me the 28 points necessary for the win. Castles 4 and 5 seem to have been highly overvalued in the earlier rounds, so I did not contest them at all. I am hoping to take an overwhelming loss here against opponents who try this again. If I lose them narrowly, that's unfortunate, but it won't matter too much. My path to 28 points is fairly difficult to block even without them. hope most people ignore castle 9 and 10, and then go over 27 with castles 8 and 6
818 0 1 11 2 11 4 11 11 16 11 20 11 21 11 16 11 5 12 4 leave out the 1 and always beat the mean Short the larger castles where some may devote a lot of resources, focus on winning more of the castles in the middle. Pretty much the opposite of NBA shot optimization.
819 0 2 0 7 11 0 0 22 7 3 7 1 7 33 34 32 34 10+9+6+3 = 28 and both 6 & 3 are not common choices in previous editions. I don't want to lose any large castle by a narrow margin, as this would be a significant waste of troops. If I win a large castle narrowly, this is the best scenario, but an overwhelming loss is also acceptable (since it will cost my opponent many troops to achieve this, and therefore give me numerical superiority elsewhere). It's like the electoral college! In the previous rounds, players deployed troop amounts on the large castles that were either very small or very large. My strategy depends on my expectation that this pattern will repeat itself. I chose all of my troop placements with this in mind, determined not to lose any large castle narrowly against either of those strategies. I invested heavily into castles 9 and 10, expecting to win their points almost every time. If I win one or both of them narrowly, then this is a significant boon to my efficiency. If I win them overwhelmingly, this is not as good, but for 19 points I'm willing to take the risk. I expect to defeat most players who conduct a predictable attack on one or both of these castles. If I lose either of these castles after such a large investment then I probably lose the match. I expect to do well in castles 3, 6, 7, and 8. I'm vulnerable to opponents who attack three or more of these simultaneously with medium-sized forces while conceding castles 9 and 10, as some top finishers did in the first round, but it's a risk I'm willing to take. Any two of these mid-range castles, plus the 19 points above will give me the 28 points necessary for the win. Castles 4 and 5 seem to have been highly overvalued in the earlier rounds, so I did not contest them at all. I am hoping to take an overwhelming loss here against opponents who try this again. If I lose them narrowly, that's unfortunate, but it won't matter too much. My path to 28 points is fairly difficult to block even without them.
10 10 10 10 10 10 10 10 10 10 Equal distribution beats the game theory.
820 0 0 11 2 11 30 11 2 11 30 11 2 11 34 11 0 11 0 12 Three eyed raven told me leave out the 1 and always beat the mean
821 0 0 2 0 7 10 0 0 0 22 0 3 30 1 25 33 35 32 Just a hunch I had based on previous editions 10+9+6+3 = 28 and both 6 & 3 are not common choices in previous editions.
822 3 10 5 10 1 10 11 10 10 15 10 15 10 20 10 17 10 3 10 idk it’s 5am Equal distribution beats the game theory.
828 0 2 1 3 3 3 7 7 10 7 14 8 18 22 21 23 18 26 4 I figured I'd look at what strategy riddlers used last time. I looked at both the mean and the median. I started with the median set and increased most of the numbers 1. I also compared this number set to the mean. It won 35 of the 55 points. So, why not go with that?
829 0 3 0 5 0 7 13 9 1 11 21 12 2 14 23 17 3 19 37 3 Felt right :) Forfeit the 10 points and win the others
830 2 0 2 1 2 3 4 3 4 7 19 7 19 8 22 23 3 26 Must beat Jason Weisman!!! Considered how he thinks and deployed troops to beat him. Also looked at previous results and guessed.
2 4 5 7 9 11 13 15 16 18 Each point is worth about 1.8 troops. Distributing troops so as to pay approximately their value for each point led to this distribution. Seems to me that anyone overpaying elsewhere will spend more troops than they should for a castle, allowing me to pick up a different castle(s) at near troop value. The more they overspend anywhere, the worse this becomes for them.
831 1 0 2 0 2 0 5 13 7 1 13 21 19 2 21 23 14 3 16 37 Felt right :)
832 7 2 0 2 0 2 0 4 0 4 0 19 0 19 31 22 31 23 31 3 28 to 27 Must beat Jason Weisman!!! Considered how he thinks and deployed troops to beat him. Also looked at previous results and guessed.
833 0 2 1 4 2 5 8 7 3 9 15 11 18 13 20 15 3 16 30 18 Fancied a go aye Each point is worth about 1.8 troops. Distributing troops so as to pay approximately their value for each point led to this distribution. Seems to me that anyone overpaying elsewhere will spend more troops than they should for a castle, allowing me to pick up a different castle(s) at near troop value. The more they overspend anywhere, the worse this becomes for them.
835 2 7 1 0 6 0 7 0 12 0 16 0 22 0 1 31 31 2 31 28 to 27
836 0 0 1 0 2 0 8 0 3 17 15 18 30 20 35 3 0 30 Fancied a go aye
837 0 5 0 7 0 10 0 12 0 14 0 17 0 19 30 21 35 0 30 1 and 2 are low-value; 10 will be too heavily contested No modelling, just a ten second guess on what others would do on average. (It's a no stakes game.) 28 is needed to win. 10 + 9 + 8 + 1 suffices. Naturally you'd expect them to be hotly contested, but this is well above the average content of those castles so let's let the last two round's data suggest it is worth a go attacking them. So let's sacrifice losing to players that take alternative strategies to see if this wins enough rounds against common submissions. And taking a complete guess that the peak of the contest will move from castle 8 to castle 9.
2 0 6 1 0 0 22 0 40 29 55 points to win, this is a race to 28. The quickest way to that is winning 9 & 10 and then then figuring how best to win one big-ish castle and win/split a small-ish (but not smallest) one. I focused on 7 because I thought the battle would be bigger for 8, and then 3 to win or split. That takes me to at least 27.5 with the hope that one of the other towers breaks my way (particularly the 1 point as a win or split).
838 1 2 3 1 4 6 1 7 1 12 4 16 6 22 8 1 38 31 34 2 A few simulations to find good strategies, and then searching for one that would perform well against those.
839 1 0 1 0 1 0 13 0 1 0 1 17 22 18 27 30 32 35 1 0 28 points are needed to win so I decided to invest all of my soldiers in taking castles 4,7,8, and 9 for a total of 28 points. I decided this combination was less obvious than ones including 10, which I think will receive heavy investment from opponents, but still uses to smallest number of castles. A point is worth about 1.8 soldiers so I expect investing 3.2 soldiers per point in my castles to take them will win. I also put one point in each castle to have a win condition if I lose one of my castles to a player also play a concentrated strategy.
840 1 0 1 0 2 7 2 10 15 12 11 14 0 17 5 19 33 21 30 0 Worked against the 10 previous winners, plus uniform, plus heavy uniform, plus strategies from a friend. 1 and 2 are low-value; 10 will be too heavily contested
864 0 5 2 5 2 5 4 5 1 5 18 10 19 10 19 15 14 15 21 25 I ran 100000 different random combinations that summed to 100 against 500 random opposing combinations and then chose the distribution that resulted in the highest average point total against its 500 imaginary opponents. If I can commit enough to with with higher value forts then the rest don't matter.
865 1 0 6 2 2 16 4 3 1 26 18 8 19 32 19 3 14 3 21 I put 3 at 9 & 10, noting how many winners had put 2 there in previous years, and then assuming others would borrow their strategy. I then overloaded on the even numbers to try to eke out victory. I ran 100000 different random combinations that summed to 100 against 500 random opposing combinations and then chose the distribution that resulted in the highest average point total against its 500 imaginary opponents.
866 3 1 5 6 7 2 17 16 10 3 16 26 19 8 15 32 5 3 3 I reviewed and added both of the table of previous winners to an excel spreadsheet and manipulated the numbers until I won most matchups in against both sets of winners. The second winners appear to essentially concede 27 points (1,2,3,6,7,8) while the first winners in general sought their points in the 5-9 range. Unfortunately, you won't get an awesome math answer for my choices. I put 3 at 9 & 10, noting how many winners had put 2 there in previous years, and then assuming others would borrow their strategy. I then overloaded on the even numbers to try to eke out victory.
2 4 10 12 14 16 18 20 2 2 Strategy :)
867 1 3 2 5 6 7 20 17 20 10 20 16 26 19 1 15 2 5 2 3 Getting 3 to 7 is sufficient for victory, so all others are just token moves in case the enemy didn't defend. I reviewed and added both of the table of previous winners to an excel spreadsheet and manipulated the numbers until I won most matchups in against both sets of winners. The second winners appear to essentially concede 27 points (1,2,3,6,7,8) while the first winners in general sought their points in the 5-9 range. Unfortunately, you won't get an awesome math answer for my choices.
1 3 5 7 9 11 13 15 17 19 Gave more to more valuable castles without writing any off
868 1 2 1 4 6 10 9 12 1 14 13 16 26 18 4 20 4 2 35 2 A lot of people seem to be going for castles 7 and 8 or 9 and 10, so I thought I would try to create a set-up to consistently win 7 and 10 and steal whichever of 8 and 9 they didn't go for. The rest of the distribution was designed to just tack on a few extra points--giving up castle 5 allowed me to put bigger point totals elsewhere. Strategy :)
869 5 1 5 2 5 6 10 20 20 25 20 30 26 0 1 0 2 0 2 trying for a plausible counter-intuitive plan Getting 3 to 7 is sufficient for victory, so all others are just token moves in case the enemy didn't defend.
0 0 1 1 2 3 6 12 25 50 Keep cutting my troops in half starting from top to bottom
870 7 1 0 3 0 5 0 7 0 9 0 11 0 13 26 15 31 17 36 19 Protect the bag Gave more to more valuable castles without writing any off
871 2 1 3 1 4 6 5 9 8 1 12 13 16 26 24 4 26 4 0 35 hit the higher valued castles harder, except for 10, which I believe my opponent will overvalue. A lot of people seem to be going for castles 7 and 8 or 9 and 10, so I thought I would try to create a set-up to consistently win 7 and 10 and steal whichever of 8 and 9 they didn't go for. The rest of the distribution was designed to just tack on a few extra points--giving up castle 5 allowed me to put bigger point totals elsewhere.
872 0 5 0 5 0 5 7 10 23 20 5 25 4 30 3 0 34 0 24 0 Beat the top player from last time then designed a strategy to beat that then designed a strategy to beat that trying for a plausible counter-intuitive plan
906 1 0 5 1 6 1 9 2 5 2 4 20 10 11 20 24 0 11 40 28 I've done these things before, and I know that people stack the second-highest value. I decided to go a more conservative approach and split a lot of things, stacking on those where less soldiers would be and retreat where others would stack. It's a bifurcated attack on the previous two seasons.
907 0 1 1 5 1 5 2 5 2 5 20 5 11 5 24 5 11 32 28 32 It's a bifurcated attack on the previous two seasons. Put a lot on high value targets + pick up the forgotten points. We'll see how it goes.
908 1 5 3 5 5 7 5 9 5 11 5 13 5 15 32 17 32 19 Put a lot on high value targets + pick up the forgotten points. We'll see how it goes. Gave more to more valuable castles without writing any off
1 3 5 7 9 11 13 15 17 19 Gave more to more valuable castles without writing any off
909 1 1 1 1 23 6 11 11 23 22 First, leave nothing undefended. Next, beat an naive even distribution (10 everywhere) and a distribution that concedes the first 5 and doubles up on the rest. Bonus that it beats most of the previous winners and the top 10 from 10 million random strategies I ran on the computer.
910 1 5 1 1 1 1 1 10 30 15 1 10 31 34 30 26 My ideal war is pretty obvious :P I didn't come up with this through a strategy or anything fancy. To misquote _Macbeth_, all hail Zach who shall be king hereafter! Looking at the last two top deployments and data breakdowns, the top deployments were throwing the bank at 9 and slightly less for 10. My strategy is top-heavy; it is very dependent on winning the top end and all but sacrificing the lower end (one soldier per castle for the bottom five will claim undefended territories and nothing else). The focus was on beating the winning strategies from the last cycle. 34 for castle 9 and 26 for castle 10 beats the top four cleanly, for a cost of 60 soldiers. Castle 7 gets some value play, too, so 15 goes there, and 10 each for castles 6 and 8. This leaves five soldiers to pick off anything undefended; our strategy is to win all or nearly all of the top 5, and then anything below is gravy. Weaknesses are if they can claim the 6-8 and not sacrifice the bottom to do so; a tie or better on one of those three and winning 9 and 10 should bring victory.
911 1 0 1 0 1 0 1 4 1 4 10 15 17 10 28 34 32 26 5 Looking at the last two top deployments and data breakdowns, the top deployments were throwing the bank at 9 and slightly less for 10. My strategy is top-heavy; it is very dependent on winning the top end and all but sacrificing the lower end (one soldier per castle for the bottom five will claim undefended territories and nothing else). The focus was on beating the winning strategies from the last cycle. 34 for castle 9 and 26 for castle 10 beats the top four cleanly, for a cost of 60 soldiers. Castle 7 gets some value play, too, so 15 goes there, and 10 each for castles 6 and 8. This leaves five soldiers to pick off anything undefended; our strategy is to win all or nearly all of the top 5, and then anything below is gravy. Weaknesses are if they can claim the 6-8 and not sacrifice the bottom to do so; a tie or better on one of those three and winning 9 and 10 should bring victory. The additional deployment scheme was won with emphasis on castles 7 and 8 .. and in the reprise (second) simulation, the winning submission emphasized Castle #9 and #10. By putting 0 soldiers in Castle #1, 2 and 3, I am going to concentrate my forces in Castles #6 - #9 with just putting enough soldiers in Castle #10 to avoid giving it away cheaply. In addition, I am putting 4 soldiers each in Castles #4 and #5 as a way to score a few "cheap" points against people who concentrate almost exclusively in Castles #6 - 10.
912 0 1 0 2 0 2 4 2 4 11 10 15 17 28 22 32 15 5 13 The additional deployment scheme was won with emphasis on castles 7 and 8 .. and in the reprise (second) simulation, the winning submission emphasized Castle #9 and #10. By putting 0 soldiers in Castle #1, 2 and 3, I am going to concentrate my forces in Castles #6 - #9 with just putting enough soldiers in Castle #10 to avoid giving it away cheaply. In addition, I am putting 4 soldiers each in Castles #4 and #5 as a way to score a few "cheap" points against people who concentrate almost exclusively in Castles #6 - 10. COC
1 2 2 2 11 15 17 22 15 13 COC
913 11 3 11 7 11 10 12 14 14 18 15 22 16 26 0 0 0 I went for 28 out of 55 points by selecting the lowest values that add to 28. I aimed to win 28 points (minimum for a simple majority out of 55), and targeted the lowest value castles to reach a 28-point total while avoiding committing troops to the high-value targets. My goal was to pay just over 3 troops per point.
914 3 0 7 10 1 14 0 18 0 22 1 26 28 0 1 0 33 0 29 I aimed to win 28 points (minimum for a simple majority out of 55), and targeted the lowest value castles to reach a 28-point total while avoiding committing troops to the high-value targets. My goal was to pay just over 3 troops per point. I took one of the better performing solutions from last simulation that seemed to work well against the other top solutions and tweaked it slightly.
915 0 1 7 1 1 0 0 0 1 15 28 20 1 31 33 30 29 2 I took one of the better performing solutions from last simulation that seemed to work well against the other top solutions and tweaked it slightly. I figured most people would favor Castle 10, so I instead heavily reinforced Castles 8 and 9. I also left several troops in Castles 6 and 7. If I can win the middle numbers, I will be in good shape.
916 1 2 1 5 0 10 0 10 0 15 15 20 31 23 30 0 2 0 I figured most people would favor Castle 10, so I instead heavily reinforced Castles 8 and 9. I also left several troops in Castles 6 and 7. If I can win the middle numbers, I will be in good shape. Trumpian Electoral college: ignore NY and CA, go for TX, PA, FL
917 2 5 5 10 5 10 5 15 10 15 10 20 23 20 0 10 0 10 Trumpian Electoral college: ignore NY and CA, go for TX, PA, FL
918 5 23 5 0 5 2 5 1 10 1 10 1 20 1 20 23 10 24 10 24 I placed at least 1 troop to every castle except for 2. I assume that my enemy sends at least 1 troop to every castle and therefore will give me the best chance to win 3. Next I assume the point of the game is to get 28 as there a total of 55 points. By dividing up all other amounts amongst the quickest way to make 28, (10+9+8+1) I have given myself the best chance to win those numbers.
23 0 2 1 1 1 1 23 24 24 I placed at least 1 troop to every castle except for 2. I assume that my enemy sends at least 1 troop to every castle and therefore will give me the best chance to win 3. Next I assume the point of the game is to get 28 as there a total of 55 points. By dividing up all other amounts amongst the quickest way to make 28, (10+9+8+1) I have given myself the best chance to win those numbers.
919 2 3 7 9 10 10 18 20 6 15 Adds to 100
920 11 11 11 11 14 21 21 0 0 0 I expect most people to put most of their troops in the higher numbered castles, so my strategy is to win the lowest 7.
921 1 1 1 11 11 20 25 30 0 0 castle 9 and 10 would be the most valuable so should get the largest number of troops assigned to them by the other overlords so fighting over them would be the most pointless allocation of troops since you're most likely to lose there. castles 1-3 are of limited value so while they could safely be ignored you could steal one of them with minimal troop numbers. combining those 5 castles gives you 25 points which won't be enough to win. castles 6-8 are the most valuable as far as being high enough to want to take but not so high that you would risk sending all your troops to, so 20-30% of your forces should be enough to win those three, especially castle 8 as you've conceded 9 and 10 already so you have to win castle 8 . castles 4 and 5 are the risky ones as losing either one means you lose, but again aren't valuable enough for large troop dispositions. however in the event of the enemy dividing his troops evenly among all 10 castles I need to commit more than 10 troops to ensure victory. doing things this way should give me a 30-25 victory
1 1 1 1 9 9 1 21 26 30 Trying to optimize from the second iteration, should perform well against people who go for the low castle value strategy
1 1 3 20 4 3 16 3 28 21 Wanted to send at least a few to every castle. Focused on the biggest ones but couldn't go all out. I did look at previous winners but still feels like a total guess.
922 0 1 2 1 2 1 16 1 21 9 11 9 26 1 16 21 3 26 3 30 Trying to pick 1 more than round numbers. Concentrating on the mid-value castles Trying to optimize from the second iteration, should perform well against people who go for the low castle value strategy
923 2 1 4 1 6 3 12 20 16 4 18 3 20 16 22 3 0 28 0 21 Wanted to send at least a few to every castle. Focused on the biggest ones but couldn't go all out. I did look at previous winners but still feels like a total guess.
924 0 0 2 0 2 20 16 20 21 20 11 20 26 20 16 0 3 0 3 Why not? Trying to pick 1 more than round numbers. Concentrating on the mid-value castles
943 0 1 1 5 3 11 13 1 14 1 5 22 1 26 2 3 35 3 26 27 Similar strategy as Round 2 winners, with some small shifts that seek to contest castles 9 and 10 more vigorously while devoting a few more troops to potentially undervalued castles like castle 6.
944 3 3 3 11 3 2 3 6 5 12 15 31 20 1 20 28 25 Looked at previous good ones, made some guesses on how people would respond this time around
945 3 0 4 1 4 5 4 20 24 4 6 10 6 0 7 10 8 10 34 40 Last time people frequently went with a strategy where they stacked castles that gave them exactly 28 points. I'm trying to steal one of the ones they stacked, while picking up the ones they left relatively undefended. Random
1 5 11 1 1 22 26 3 3 27
946 3 0 3 0 3 2 3 3 20 5 20 15 20 20 2 20 2 25 31 Looked at previous good ones, made some guesses on how people would respond this time around Castles 8 and 9 received a lot of attention in the previous two iterations, respectively, because of various assumptions about the other players. We’ll see if this will work, but 10/7/6/5 are enough to win, and I’m gambling on any deployment that beats one of those splitting other castles with me.
947 0 1 0 5 0 20 0 4 6 10 5 0 11 10 18 10 28 40 32 Random Top Heavy
948 0 0 2 3 2 20 5 20 5 20 29 2 1 2 1 31 55 Castles 8 and 9 received a lot of attention in the previous two iterations, respectively, because of various assumptions about the other players. We’ll see if this will work, but 10/7/6/5 are enough to win, and I’m gambling on any deployment that beats one of those splitting other castles with me. winning #10 cancels out the first 4 if lost. then 567 > 89 so put more there.
977 4 7 5 11 7 11 11 13 12 15 21 18 21 25 2 1 2 1 2 My starting point was to look at the number of men that would be needed to beat the averages from both previous battles -- {4 5 7 9 11 14 17 20 17 13}. Then, I figured out the cheapest way to get 28 points with that number of men in each castle -- I came up with {0 0 0 9 11 0 0 0 17 13}, using 50 men. I then tried to counter that strategy, eventually deciding on punting the "most valuable" castles 9 and 10 and reinforcing the castles I felt I needed to do best in (4, 5, and 8). To counter groups focusing too much on higher value castles and also those who may send nobody to them.
978 5 1 6 2 7 5 8 17 9 11 10 13 11 16 12 18 14 0 18 17 Trying to balance protecting/winning the high-value targets and preventing token squads from picking off the low-value forts Counter positions of most successful players from last time, while exceeding averages.
979 7 0 11 0 11 2 11 3 12 10 21 15 21 17 2 17 2 18 2 18 To counter groups focusing too much on higher value castles and also those who may send nobody to them. Because in the last battle the most successful warlords targeted the middle and top numbered castles with an overwhelming number of troops, I wanted to spread my points more evenly across castles with a value of five or higher (because even if you conquer the lower castles you still lose). This general strategy might be susceptible to players who cluster their soldiers at the top, but I am hoping to split the difference and more evenly spread my troops in the hope that when the smoke clears I can - to paraphrase Varys from Game of Thrones - be king of the ashes.
1 2 5 17 11 13 16 18 0 17 Counter positions of most successful players from last time, while exceeding averages.
980 0 1 0 1 2 1 3 12 10 20 15 20 17 21 17 20 18 2 18 2 Because in the last battle the most successful warlords targeted the middle and top numbered castles with an overwhelming number of troops, I wanted to spread my points more evenly across castles with a value of five or higher (because even if you conquer the lower castles you still lose). This general strategy might be susceptible to players who cluster their soldiers at the top, but I am hoping to split the difference and more evenly spread my troops in the hope that when the smoke clears I can - to paraphrase Varys from Game of Thrones - be king of the ashes. Optimize the middle values assuming they are under deployed
981 1 2 1 1 2 12 5 20 5 20 21 20 20 2 25 2 0 Optimize the middle values assuming they are under deployed Assuming the opposing warlord would place the highest value on Castle 10, I instead tried to capitalize on castles 6 to 9 in order to try and solidify my points gains.
982 2 0 1 0 2 0 5 0 5 0 20 25 20 25 20 25 25 0 Assuming the opposing warlord would place the highest value on Castle 10, I instead tried to capitalize on castles 6 to 9 in order to try and solidify my points gains.
985 2 3 4 3 5 3 7 3 9 3 11 17 13 17 15 17 16 17 18 17 I chose a simple strategy: based on the total points available, determine the number of points per soldier, and deploy the appropriate number of soldiers to each castle assuming they would win that number of points. While this strategy does not account for the slight differences in over and undervaluing deployment if one is rounding up or rounding down (since only whole numbers of soldiers can be deployed), it should (in theory) help to appropriate weight the value of all castles and penalize opponents who skew their distribution of soldiers too heavily in any direction. This strategy is to spread a wide net. Which clearly hasn't worked so far. But lets try it
986 3 2 3 2 3 2 3 10 3 10 17 20 17 2 17 2 17 25 17 25 This strategy is to spread a wide net. Which clearly hasn't worked so far. But lets try it Basically, I assume people will see what happened last time (lots of troops in 4,5,9, and 9) and avoid those this time. So I put troops there.
987 2 2 3 6 3 11 14 3 18 26 25 18 25 26 2 4 6 Why all the pearls? Why all the hair? Why anything? Target middle value castles (5, 6, 7, 8) with larger forces while deploying a midsized force to castle 10.
2 2 2 10 10 20 2 2 25 25 Basically, I assume people will see what happened last time (lots of troops in 4,5,9, and 9) and avoid those this time. So I put troops there.
988 2 1 2 3 2 3 14 4 18 6 25 9 25 14 2 22 6 37 Target middle value castles (5, 6, 7, 8) with larger forces while deploying a midsized force to castle 10. fibonacci is awesome so fibonacci +1 must be better
989 1 0 2 3 2 6 3 11 4 13 6 16 9 0 14 51 22 0 37 0 fibonacci is awesome so fibonacci +1 must be better Because you need to get to 28 to win so maximum chance of getting to 28
990 0 1 3 1 6 1 11 1 13 1 16 1 0 14 51 25 0 25 0 30 Because you need to get to 28 to win so maximum chance of getting to 28 Concentrated on high value targets
991 1 10 1 14 1 14 1 14 1 14 1 14 14 20 25 0 25 0 30 0 Concentrated on high value targets Total of 55 points. Need 28 to Win.
992 10 0 14 0 14 10 14 0 14 22 14 0 20 0 0 0 34 0 34 Total of 55 points. Need 28 to Win. I only need 28 points to win and castles 9&10 seemed undervalued by the average player. I’ve gone all in on four castles.
993 0 20 0 10 10 0 11 22 12 0 15 0 22 0 34 0 34 0 I only need 28 points to win and castles 9&10 seemed undervalued by the average player. I’ve gone all in on four castles. It is a race to 28 points. Chosen locations least likely to be fought for.
20 10 10 11 12 15 22 0 0 0 It is a race to 28 points. Chosen locations least likely to be fought for.
994 1 2 4 6 9 11 21 22 22 2 I'm guessing people will over deploy to 10, so I'm sacrificing it to strengthen 7-9, with the suspicion that people will also go for round numbers like 20, or go 1 over that. Otherwise a proportional distribution slightly less weighted at the start, where I suspect people will underdeploy.
995 6 5 5 25 18 13 10 7 6 5
996 2 4 5 7 9 10 13 15 16 19 Proportional representation of the troops based on the points of the castle
1020 0 0 12 0 0 0 0 6 25 16 25 21 0 26 33 31 //Spam troops at only locations that add up to 28. Sacrifice castle 9 because it was too hot in the previous round, take castles 10, 8, 7, and 3.
1021 2 1 2 1 2 1 8 1 2 19 2 19 20 19 26 19 34 19 2 1 4, 7, 8, 9 and sneak a couple of others. Surrender 10 and 1-4 against all but 0 troop deployment strategies, and evenly spread remaining troops for best chance of taking 5-9 which together (35) exceed the points total of the other castles (20).
1022 3 7 3 13 3 9 3 4 3 12 3 14 3 8 26 13 26 9 27 11 Trying to maximize value at the bottom side poaching empty castles while still having a shot against most who split their forces to 25 or less. Pi
0 0 0 0 0 6 16 21 26 31
1 1 1 1 19 19 19 19 19 1 Surrender 10 and 1-4 against all but 0 troop deployment strategies, and evenly spread remaining troops for best chance of taking 5-9 which together (35) exceed the points total of the other castles (20).
1023 7 0 13 1 9 1 4 1 12 2 14 23 8 23 13 23 9 23 11 3 Pi Hoped others would prioritize castle 10 and I could win without it, built a monte carlo model to evaluate many outcomes to optimize general strategy
0 1 1 1 2 23 23 23 23 3 Hoped others would prioritize castle 10 and I could win without it, built a monte carlo model to evaluate many outcomes to optimize general strategy
1024 1 3 5 7 9 11 13 15 17 19 Troops proportional to point value
1025 1 3 6 12 20 3 25 20 4 6 I tried to guess where the biggest battles would be, avoid them, and then go a bit above where people would put low troop counts. There was a decent amount of guessing.
1026 2 5 5 2 2 16 2 2 32 32
1027 3 2 5 18 9 18 6 15 6 18 Trying to get to 27 against various previous methods.
1028 0 0 0 0 0 10 20 30 40 0 Most people will try locking in 10, I'd rather let them spend their points since 9 is almost equal. Further it allows me to hit a few more relatively high value targets further down
1029 3 1 3 4 4 5 12 11 14 12 16 0 18 15 20 12 18 19 2 21 Concede 10, try to win on castles 4-9 Not really sure
1 4 5 11 12 0 15 12 19 21 Not really sure
1030 4 4 4 18 23 0 13 0 34 0 I concentrated on winning more of the lower value castles.
1031 0 0 1 15 1 1 26 26 30 0 I just tried to ensure I had 28 points and didn't want to invest in 10 or 1/2
1032 0 0 2 2 22 4 22 22 4 22
1038 1 0 1 10 1 3 1 3 2 18 2 3 2 3 5 29 41 29 45 Focused on winning these 4 battles to get to 28 as 3&6 have been under focused in past battles. Focus almost entirely on the big castles, but spread some soldiers out for easy pickups.
1039 0 2 1 3 1 5 1 7 2 11 2 3 2 15 5 18 41 27 45 9 Focus almost entirely on the big castles, but spread some soldiers out for easy pickups.
1040 2 1 3 1 5 1 7 6 11 1 3 19 15 19 18 26 27 1 9 25 Counter
1 1 1 6 1 19 19 26 1 25 Counter
1041 0 9 0 0 2 1 29 1 31 27 Used a genetic algorithm which slowly replaced the original entries with the newly generated ones, hopefully optimising against everyone optimising for the previous round.
1042 3 1 5 1 8 1 10 17 1 10 14 21 18 5 20 5 18 35 2 4 Gut. Noticing that winning strategies go big on 2 high value castles and 2 low midvalue castles. Decided to go all in on 1 high value castle - and try 3 midlevel castles that would be split evenly lower for anyone throwing points at a secondary high value castle. And raised the lower bar up to 4 for castles >3 points as easy gimmes in case people copy last winning strategy.
1043 1 0 1 0 1 0 17 5 10 5 21 15 5 15 5 15 35 20 4 25 Noticing that winning strategies go big on 2 high value castles and 2 low midvalue castles. Decided to go all in on 1 high value castle - and try 3 midlevel castles that would be split evenly lower for anyone throwing points at a secondary high value castle. And raised the lower bar up to 4 for castles >3 points as easy gimmes in case people copy last winning strategy. Random
1044 0 0 0 5 5 15 15 15 20 25 Random
1045 0 1 0 3 0 5 17 5 20 15 0 15 0 15 3 20 28 25 28 Random Divination by dreams (and some code that seemed to make sense but I can't really explain)
1 3 0 17 20 0 0 3 28 28 Divination by dreams (and some code that seemed to make sense but I can't really explain)
0 0 2 16 21 3 2 2 32 22 Best of last two plus some ai
1046 5 0 5 0 5 2 5 16 16 21 17 3 18 2 19 2 5 32 5 22 It takes 28 points to win the battle. The easy way to do that is to win 8, 9, and 10 (allowing you to win by winning any of the other castles). But if a large number of people go with that strategy, you can get a decent number by winning 5, 6, and 7 and hoping to clean up the last ten points by having enough guarding 1-4. I am hoping that 19 points will be enough to have a shot at winning 8, and if not that those going with a top heavy strategy will not have enough left for any of the other castles. Best of last two plus some ai
1047 9 5 10 5 12 5 15 5 16 17 18 1 19 1 5 1 5 the bottom seven castles win against the top three by one point, so if i concentrate all my men on the bottom 7 castles ill win against any opponent who splits their soldiers across all 10 castles. Added one guy to the top three to beat anyone who uses this strategy but completely abandons the top castles It takes 28 points to win the battle. The easy way to do that is to win 8, 9, and 10 (allowing you to win by winning any of the other castles). But if a large number of people go with that strategy, you can get a decent number by winning 5, 6, and 7 and hoping to clean up the last ten points by having enough guarding 1-4. I am hoping that 19 points will be enough to have a shot at winning 8, and if not that those going with a top heavy strategy will not have enough left for any of the other castles.
1048 0 9 0 10 5 12 18 15 20 16 1 17 25 18 26 1 3 1 2 1 focus mainly on the the middle castes, sacraficing castles to increase distribution to castles 8,9 the bottom seven castles win against the top three by one point, so if i concentrate all my men on the bottom 7 castles ill win against any opponent who splits their soldiers across all 10 castles. Added one guy to the top three to beat anyone who uses this strategy but completely abandons the top castles
1049 0 2 0 6 5 4 18 8 20 5 1 20 25 12 26 23 3 20 2 focus mainly on the the middle castes, sacraficing castles to increase distribution to castles 8,9
1050 0 5 2 7 6 9 4 11 8 21 5 0 20 21 12 0 23 26 20 2, 3, 4 instead of 9, and then and 3 of 5,6,8, and 10
0 0 3 0 0 14 14 5 33 31 I tried to come up with a troop arrangement that would outscore the top five deployments (averaged out) and the top deployments from the previous rounds. It was mostly a matter of trial-and-error. And I didn't quite succeed in my goal (my deployment beats the "average" 36-19 and the second round winner 43.5-11.5, but loses to the first round winner 25-30). But I feel good about my choices of castles to attack with strength (9, 10) and about my decision to emphasize attacking castles 6 and 7 at the expense of castles 4 and 5. I am a little bit uneasy about my decision to make only a modest 5-troop deployment to castle 8 as there may be a rush by others to scoop up those points this round. But I think the decision to abandon castles 1 and 2 in favor of a token 3-troop deployment to castle 3 is sensible.
1051 1 0 2 5 3 7 5 9 1 11 11 21 20 0 26 21 0 32 26 Because it'll win? 2, 3, 4 instead of 9, and then and 3 of 5,6,8, and 10
1052 1 0 1 0 3 10 0 20 0 20 14 20 14 10 5 10 33 5 31 I tried to put troops in the middle where points would be high, but not so high that everyone would attack there first I tried to come up with a troop arrangement that would outscore the top five deployments (averaged out) and the top deployments from the previous rounds. It was mostly a matter of trial-and-error. And I didn't quite succeed in my goal (my deployment beats the "average" 36-19 and the second round winner 43.5-11.5, but loses to the first round winner 25-30). But I feel good about my choices of castles to attack with strength (9, 10) and about my decision to emphasize attacking castles 6 and 7 at the expense of castles 4 and 5. I am a little bit uneasy about my decision to make only a modest 5-troop deployment to castle 8 as there may be a rush by others to scoop up those points this round. But I think the decision to abandon castles 1 and 2 in favor of a token 3-troop deployment to castle 3 is sensible.
1053 0 1 1 1 3 1 10 1 20 4 20 9 20 14 10 25 10 44 5 Guessing I tried to put troops in the middle where points would be high, but not so high that everyone would attack there first
1064 0 0 0 15 0 15 8 0 2 0 25 0 30 35 35 0 We go all in on the minimum value to win.
1065 2 0 2 0 2 0 17 15 18 15 18 0 18 0 20 0 2 35 2 35 All in on 4-8 for a total of 30 points. We go all in on the minimum value to win.
1066 2 1 1 17 0 31 0 33 4 11 I'd like to rescind my previous submission! I've now looked at the previous two metas. I'm trying to anticipate the next 28-set and stake out a slightly different 28-set, with the guess that 10 will skew low again.
1 0 0 16 22 1 2 3 33 23 Based it off the last winner
0 1 1 16 21 3 2 1 32 23 better than Vince hahaha
1067 0 2 1 4 1 14 16 15 21 5 3 5 2 5 1 33 32 17 23 better than Winder better than Vince hahaha
1068 0 0 2 0 4 15 14 18 15 1 5 1 5 1 5 32 33 32 17 better than Derek better than Winder
2 3 3 17 17 3 4 4 23 24 better than Eric
1069 2 0 2 0 2 0 2 15 13 18 15 1 19 1 22 1 19 32 4 32 better than Derek
1070 0 2 0 3 0 3 15 17 21 17 0 3 0 4 0 4 36 23 28 24 Better than Mike better than Eric
5 5 8 10 14 14 12 17 15 0 Sending more men To the higher castles is more important than the others down the list. Ten isn’t worth it.
5 5 8 10 14 14 12 17 15 0 Sending more men To the higher castles is more important than the others down the list. Ten isn’t worth it.
1071 0 2 2 3 2 4 2 16 13 6 15 16 19 16 22 11 19 26 4 I noticed that multiples of five were popular answers in the first round so chose numbers just above those.
1072 1 0 2 0 2 0 2 15 19 21 15 0 15 0 16 0 1 36 27 28 I threw some numbers together that would win against each of last iteration's top five plans. Better than Mike
1073 0 5 1 5 9 8 0 10 0 14 19 14 6 12 0 17 35 15 30 0 I went with my gut Sending more men To the higher castles is more important than the others down the list. Ten isn’t worth it.
1129 2 10 2 10 2 10 12 10 17 10 17 10 17 10 17 10 7 10 7 10 Go for the middle point values, hope it works.
1130 0 2 0 2 0 2 0 12 0 17 0 17 20 17 23 17 27 7 30 7 Determine the maximum number of castles that can be abandoned while still achieving net victory assuming individual victories at the remaining castles. sum(i, i = 1 .. 10) = 55, sum(i, i = 7 .. 10) = 34, sum(i, i = 1 .. 6) = 21. 34-21 = 13, therefore only castles 7-10 need to be won. Soldiers were distributed approximately proportionally to the point value of the castle, but preferentially rounding down for lower value castles and up for higher values. Go for the middle point values, hope it works.
1131 5 0 6 0 7 0 8 0 9 0 11 0 12 20 13 23 14 27 15 30 laziness Determine the maximum number of castles that can be abandoned while still achieving net victory assuming individual victories at the remaining castles. sum(i, i = 1 .. 10) = 55, sum(i, i = 7 .. 10) = 34, sum(i, i = 1 .. 6) = 21. 34-21 = 13, therefore only castles 7-10 need to be won. Soldiers were distributed approximately proportionally to the point value of the castle, but preferentially rounding down for lower value castles and up for higher values.
1 2 7 11 14 17 2 3 21 22 I wrote a Python program to randomly generate troop deployments, match troop deployments against each other, and then match the winners against other winners. My submission was my overall winner.
1132 0 5 0 6 2 7 5 8 17 9 5 11 17 12 17 13 33 14 4 15 I want to win a number of castles. I tried to adjust for the adjustments people would make when comparing the two previous winners. laziness
1133 4 1 8 2 12 7 15 11 19 14 22 17 4 2 5 3 5 21 6 22 From the previous round of this game, two peaks are observed: those at the low quantities from those who barely defend and those at the high quantities from those who value the castle. If I can stay just ahead of those barely defending, then I distribute the remaining troops as possible to attack the well-defended. I wrote a Python program to randomly generate troop deployments, match troop deployments against each other, and then match the winners against other winners. My submission was my overall winner.
1134 3 0 3 0 3 2 17 5 17 17 5 17 17 3 33 3 4 total guess I want to win a number of castles. I tried to adjust for the adjustments people would make when comparing the two previous winners.
1160 6 9 12 16 19 22 4 4 4 4 This is a joke entry, but I may not have the time to create a serious entry, so this is what you get.
1161 10 0 0 0 0 0 0 30 30 30 Adds up to 28
1162 0 4 5 5 5 7 8 11 20 35 I wanted no Castle to contain more than 40 troops. The higher the point value of the Castle, the more troops deployed. An even distribution would have yielded 10 troops per castle, so I had 3.5X that amount for my highest-point Castle, and 2X that amount for my 2nd highest-point Castle. One more than that amount for my third-best Castle.
4 1 7 2 3 19 3 31 3 28 Modified earlier answer based on skim of prior data. Seeking to optimize vs. all previous submissions.
1163 2 2 3 5 8 10 10 15 20 25 Put more troops on castles worth more points
1164 5 0 1 10 9 12 5 0 18 40 I ran a program that simulated a thousand rounds of battles with 20,000 participants and made random updates to each strategy after each round based on how well the players performed on the previous round. This was the winner of the last round.
1165 0 2 3 3 13 13 21 20 0 25 I consulted Mars the God of War and he suggested this.
1167 0 1 0 1 0 2 15 2 20 2 20 14 20 25 0 30 0 3 Figuring the enemy would over commit to the larger value castles. I chose the deployment that would win.
1168 1 0 1 4 2 5 2 2 12 14 19 20 2 25 2 30 24 3 30 I chose the deployment that would win. To win you need 28 victory points which gives about 3.5 troops per point (which suggests it is not worth sending more than 3.5 troops per castle point). Finally the last two rounds showed a the field adopting the previous strategy and the winners planing to win against it. Assuming that people are still seeking patterns and have detected the shift and will now have the default as the shift, whilst still keeping some value on the high value castles. Also from examining the averages the 7,8 castles are over valued compared to the 9,10's suggesting a strategy strong on these will do well. Also this means that if both of these are won only an additional nine points need to be picked up elsewhere. Finally the minimum should always be 2 as it beats both zero and the cheap guess which beats 0. Except for one because I believe that 2 soliders will have a more effective return elsewhere
1169 0 4 2 5 2 2 4 12 7 19 15 2 15 2 25 24 3 30 27 To win you need 28 victory points which gives about 3.5 troops per point (which suggests it is not worth sending more than 3.5 troops per castle point). Finally the last two rounds showed a the field adopting the previous strategy and the winners planing to win against it. Assuming that people are still seeking patterns and have detected the shift and will now have the default as the shift, whilst still keeping some value on the high value castles. Also from examining the averages the 7,8 castles are over valued compared to the 9,10's suggesting a strategy strong on these will do well. Also this means that if both of these are won only an additional nine points need to be picked up elsewhere. Finally the minimum should always be 2 as it beats both zero and the cheap guess which beats 0. Except for one because I believe that 2 soliders will have a more effective return elsewhere The best defense is a good offense.
0 0 0 4 0 6 0 34 0 36 Gematria
1170 0 2 1 2 11 4 3 7 2 15 22 15 2 25 2 3 29 27 28 The best defense is a good offense. Win enough castles to get to 28. Put enough in non target castles to pickup if unmatched.
1171 0 1 1 2 11 4 3 7 2 13 22 12 2 15 2 3 29 22 28 21 Win enough castles to get to 28. Put enough in non target castles to pickup if unmatched. In consulted my 9 month old and this is what he suggested after simulation with his toys.
1 2 4 7 13 12 15 3 22 21 In consulted my 9 month old and this is what he suggested after simulation with his toys.
1172 1 3 5 0 0 14 19 2 24 32 To avoid overvaluing castles 4 and 5, I chose a strategy that cedes 4, 5, and the hotly contested 8. 28 points are needed to win, and if I win every castle I am invested in I will come ahead with 38. This allows me to lose even my most valuable castle and still win.
1173 1 1 3 6 12 13 18 31 2 13 Based on past strategies I distributed my troops closer to the middle, but I also went a little hard for number 10.
1174 5 3 9 2 18 3 0 0 29 31 It's a race to 28! I broke down the data from the last two editions, determined WITTW for each castle at 90-95% level, and targeted castles with better value per soldier-required. 7&8 are bloodbaths - I'm staying away.
1180 0 0 0 12 0 0 18 30 40 0 28 is the minimum number of points to win. I sent the least number to castle 4 because I anticipated that it would not need to be taken with higher numbers in most scenarios.
1181 0 3 5 0 10 16 25 21 20 0 I just picked ones I thought would win
1182 7 2 2 11 0 6 24 5 33 10 random & fudging & top loading
0 0 7 3 5 2 16 17 28 22 hope
1183 1 0 1 0 1 7 8 3 8 5 16 2 16 22 17 22 28 5 22 I think that castle 10 will be overvalued, and castles 1 to 3 will be overvalued. If I can win 9,8,7, and 6 without ties then I will win every battle. hope
1184 0 1 0 1 0 1 10 8 10 8 12 16 14 16 16 22 18 22 20 5 I am anticipating others wasting troops on the low value targets, which I will abandon. I assigned troops to each other site based on their value alone, anticipating the others at this point would overthink and leave the high value targets undefended(but in an unpredictable way) I think that castle 10 will be overvalued, and castles 1 to 3 will be overvalued. If I can win 9,8,7, and 6 without ties then I will win every battle.
1185 2 0 4 0 6 0 7 10 9 10 11 12 13 14 14 16 16 18 18 20 I figure each soldier at .55 points and distributed in a way that most approaches that mean. It is an exploitable strategy, but I am expecting more people to try to exploit gambits than exploiting the obvious answer. I am anticipating others wasting troops on the low value targets, which I will abandon. I assigned troops to each other site based on their value alone, anticipating the others at this point would overthink and leave the high value targets undefended(but in an unpredictable way)
1188 1 0 1 0 1 3 1 1 12 1 17 50 2 25 31 12 2 7 32 Inverse of 7 down strategy Well, the first time the winners targeted 7 and 8, and the second time the winners targeted 9 and 10. So I'm going to target 8 and 10 - as long as I win those and break even on 1 through 6, I should beat the copy cats from last time, and anyone who hopes to beat the copycats by one-upping them on key castles. In order to break even or better on 1 through 6, I'm targeting 5 and 6. After that, I've got 8 armies left to split among the remaining castles, in case I lose some of the others. I ignore 1 and 2, which aren't worth much, in favor of taking advantage of those who leave some higher-value castles empty or close to empty. I also made sure that my solution beats most typical solutions (i.e. even splits, or assigning armies proportional to value), as well as most of the winner's solutions (although admittedly Jim Skloda's submission from the first time counters mine pretty perfectly). I also think it's worth going for numbers that are 1 or 2 mod 5, since many people will submit nice round numbers, as proven by the winning submissions from the previous contests.
1189 2 1 2 1 2 1 12 1 3 1 3 1 26 50 3 25 26 12 21 7 This is left as an exercise for the reader. Inverse of 7 down strategy
1190 1 2 1 2 3 2 6 12 12 3 17 3 16 26 18 3 23 26 3 21 This is left as an exercise for the reader.
1 5 1 1 17 23 24 25 1 2 2,5,6,7,8 for the win
1191 1 1 2 3 6 0 12 0 17 27 16 30 18 33 23 0 3
1192 0 1 1 5 2 1 16 1 21 17 2 23 3 24 1 25 32 1 22 2 This is almost an exact replica from the dataset that the winner submitted last time, except one troop moving from Castle 6 to Castle 7. It won 84% of it's games against the database, plus over 95% of the games against the partial optimal database that my father and I created. 2,5,6,7,8 for the win
1193 1 9 1 9 2 8 6 1 0 7 0 2 27 6 30 3 33 54 0 Because I am The Warlord!
1194 0 0 1 1 2 1 16 22 21 24 2 1 3 4 1 25 32 22 I wrote a half-baked genetic algorithm that evaluated strategies against random strategies, entries from the previous contests, and the top strategies from the previous generation, and then chose the strategy that most often received the highest fitness of its generation. This is almost an exact replica from the dataset that the winner submitted last time, except one troop moving from Castle 6 to Castle 7. It won 84% of it's games against the database, plus over 95% of the games against the partial optimal database that my father and I created.
1195 10 1 0 9 0 9 0 8 0 1 0 7 0 2 25 6 37 3 28 54 To win just over 50% of the points with the least number of castles by deploying enough troops to four castles to win 28/55 points and abandoning the other six Because I am The Warlord!
1 6 9 12 15 2 2 2 24 27 Targeted ones that were worth the most points per average soldier assigned in previous rounds (2-5, 9-10).
1196 1 0 3 0 3 1 4 1 4 22 14 24 12 1 19 4 24 25 16 22 You have to win the high value castles to win it all, but should still defend the low level ones as well. I wrote a half-baked genetic algorithm that evaluated strategies against random strategies, entries from the previous contests, and the top strategies from the previous generation, and then chose the strategy that most often received the highest fitness of its generation.
1197 1 10 2 0 8 0 1 0 5 0 5 0 14 0 19 25 8 37 37 28 Not having much time to figure out what to do this time, I decided to play heavy for 10, and most likely try to pick up a victory on the back of 10-8-7-3, but also have a little bit of contesting other places in case I could get some very cheap points. Somehow this seems wrong, especially from what I remember when I worked out what to do last time, but oh well. To win just over 50% of the points with the least number of castles by deploying enough troops to four castles to win 28/55 points and abandoning the other six
1198 0 1 0 6 0 9 5 12 12 15 16 2 18 2 24 2 25 24 0 27 The top one and bottom 3 are simply not worth the manpower. Targeted ones that were worth the most points per average soldier assigned in previous rounds (2-5, 9-10).
1204 0 2 0 2 0 5 0 5 0 5 0 5 10 20 20 24 30 6 40 26 Higher value=more soldiers, keep it simple Decided to abandon Castle 9 with the aim to win the battles for Castles 7, 8 and 10. With a possible 55 points on the board, winning a guaranteed 25 and hoping to steal one more castle of at least 3 points should give me the win in most matchups
1205 6 0 8 0 11 14 11 17 1 20 6 22 6 34 6 1 6 0 A slightly altered version of my 'joke' entry. Definitely no 'evolved' entry coming like in previous battles. Trying to win the lowest number of castles that reach 28 points, with maximum force at higher numbered castles where more enemy attacks can be expected. We hope to take away castle 8 from anyone who is focusing on the top castles, and win some cheaply.
1206 1 0 1 0 13 0 1 0 1 0 23 0 2 10 3 20 26 30 29 40 Thought the 10,9,5,4 strategy might be overused because of success last time so went with 10,9,6,3 Higher value=more soldiers, keep it simple
1 1 1 9 22 24 24 6 6 6 I tried to guess what would beat the people who tried to guess how to beat the last winning strategy. 1 up the people who tried to 1 up the low number of soldiers for the high valued towers. Assume I win one one of those which means I can lose towers 1, 2, 3 and sometimes 4 depending on which high value tower I won.
1207 1 6 2 8 3 11 2 14 22 17 4 20 3 6 3 6 34 6 25 6 Dominate the last winner, then dominate that. A slightly altered version of my 'joke' entry. Definitely no 'evolved' entry coming like in previous battles.
1208 2 1 2 1 2 13 2 1 2 1 20 23 24 2 24 3 20 26 2 29 I wanted to beat anyone trying to be crafty sending just one person to each castle while beating anyone who didn't commit to the higher valued castles. I gave up on castle 10 thinking some players will just send all of them to 10 in some circumstances. Thought the 10,9,5,4 strategy might be overused because of success last time so went with 10,9,6,3
1209 0 1 4 1 1 3 9 19 22 10 24 12 24 7 6 12 6 32 6 I ran a genetic algorithm starting from the best solutions from Riddler Nation Battle Royale round 2, and testing against both round 1 and 2 deployments. The one I submitted is just the deployment with the most wins after a bunch of iterations. I tried to guess what would beat the people who tried to guess how to beat the last winning strategy. 1 up the people who tried to 1 up the low number of soldiers for the high valued towers. Assume I win one one of those which means I can lose towers 1, 2, 3 and sometimes 4 depending on which high value tower I won.
1217 1 0 1 15 2 20 6 20 15 20 10 20 27 1 32 1 4 1 3 I will assume that castles 8 - 10 will be heavily fought over. I will assume loss in each of these. Although, if a person decides not to send anyone to a castle I can still win that caste. I did the same with Castles 1 & 2 bc they are not worth enough. I then spread my forces evenly across the middle. I was willing to give up castles 9 and 10 and lose those by large margins, while still winning those slightly against players who completely abandoned them. Instead, I focused on the other large numbers (5, 6, 7, 8).
1218 0 1 0 1 10 15 0 20 0 20 0 20 10 20 20 1 25 1 35 1 The focus is on on reducing the battlefield down to enough castles to get 28 victory points, and then identifying the set of castles that make up 28 points that past players have shown the least interest in competing for. I will assume that castles 8 - 10 will be heavily fought over. I will assume loss in each of these. Although, if a person decides not to send anyone to a castle I can still win that caste. I did the same with Castles 1 & 2 bc they are not worth enough. I then spread my forces evenly across the middle.
1219 2 0 3 0 3 10 6 0 6 0 10 0 10 20 20 25 20 35 diversified deployment with more troops sent to higher castles, placing slightly higher relative value on even numbered castles. The focus is on on reducing the battlefield down to enough castles to get 28 victory points, and then identifying the set of castles that make up 28 points that past players have shown the least interest in competing for.
0 1 10 0 2 1 20 29 6 31 try to win 10 8 7 3, then some random backups
1220 1 2 1 3 3 3 6 3 6 17 10 17 10 3 20 20 32 20 target 6,7,9 and 10 while still picking up pts from 0's from others diversified deployment with more troops sent to higher castles, placing slightly higher relative value on even numbered castles.
0 0 0 1 17 23 28 3 4 24 Castle 8 and 9 are highly contested, so you have to put in a lot of troops to gain a high probability of winning them. However, if your strategy is 9-10 heavy, 8 is weak for you and I might win or tie with a few there; if your strategy is more focused on 8-10 or lower values, I might snag a tie or win with a couple troops in 9. Overall, the winning strategy is 5-6-7-10. If I lose 10, I hope to win 8 or 9, and tie or win a few of the lower ones. I will definitely lose games, but the hope is that I can win against a bunch of strategies. For instance, this beats about half of last years' winners.
1221 3 0 0 1 0 10 0 0 2 0 1 0 20 31 29 33 6 33 31 all or nothing try to win 10 8 7 3, then some random backups
1222 2 1 3 1 4 3 10 3 2 3 24 17 20 17 2 3 3 20 30 32 I think most people will cycle back to strategy 1 but I think one could use that to take many 10's back. Otherwise, concentrating on the middle again - but not contesting the highest contested castles. target 6,7,9 and 10 while still picking up pts from 0's from others
1223 2 0 2 0 6 0 3 1 3 17 21 23 21 28 18 3 3 4 21 24 I am mixing a few low-effort and high effort attacks with a medium effort thrown in to test low-level dedication. Castle 8 and 9 are highly contested, so you have to put in a lot of troops to gain a high probability of winning them. However, if your strategy is 9-10 heavy, 8 is weak for you and I might win or tie with a few there; if your strategy is more focused on 8-10 or lower values, I might snag a tie or win with a couple troops in 9. Overall, the winning strategy is 5-6-7-10. If I lose 10, I hope to win 8 or 9, and tie or win a few of the lower ones. I will definitely lose games, but the hope is that I can win against a bunch of strategies. For instance, this beats about half of last years' winners.
1231 1 3 1 5 1 7 0 9 0 11 20 13 20 15 22 17 35 19 0 Each castle has just under twice their point value in troops.
1232 0 6 0 1 0 2 16 2 21 1 1 3 2 6 1 24 35 34 24 21 Optimised against top fives from both runs and median from the first. Depends on snatching the top two bolstered by four and five, these four wins would total a bare minimum of 28 of 55 points. Sometimes snatches the 6–8. If most strengthened the top prizes a bit, yeah, I'm screwed. Didn't want to do a deep dive into the complete data. Previous battle victories seemed to be all-or-nothing attempts to get 28 pts from the fewest castles to maximize troop strengths. That's fine. If four castles is what it takes, that's what it takes. My goal in this round is to make Castle 1 mean something! Assuming you're a real warlord, going in order, you want to get that first victory to make your troops follow you. Besides that thought, I used no formulas or special computations. I just looked at what went before and decided this looked reasonable enough.
1233 2 1 2 3 3 5 11 7 11 9 16 11 16 13 16 15 21 17 2 19 Never put 0, conceede castle 10, focus on 4-9, and put castle values 1 higher than common values (1, 10, 15, 20) Each castle has just under twice their point value in troops.
1 1 8 19 6 20 18 22 3 2 hope to get my points in random places
1234 0 1 0 2 0 3 16 16 21 19 1 22 2 5 1 6 35 26 24 Try to win castle 10. Put one more than 25 there, thinking that some people will go for the even number. Add 5, 6 and 7 as a strategy to get 28 with 10. Try to capture the other numbers a fair fraction of the time when nobody targets them, but don't overspend on low numbers. Optimised against top fives from both runs and median from the first. Depends on snatching the top two bolstered by four and five, these four wins would total a bare minimum of 28 of 55 points. Sometimes snatches the 6–8. If most strengthened the top prizes a bit, yeah, I'm screwed. Didn't want to do a deep dive into the complete data.
1235 0 2 0 2 0 3 10 11 10 11 25 16 25 16 15 16 10 21 5 2 Because the middle will be ignored Never put 0, conceede castle 10, focus on 4-9, and put castle values 1 higher than common values (1, 10, 15, 20)
1236 3 1 0 1 6 8 8 19 15 6 22 20 4 18 3 22 31 3 8 2 a computer told me to hope to get my points in random places
1238 0 3 0 3 0 12 10 12 10 17 25 12 25 17 15 12 10 12 5 Looking at the data from the first two iterations, castles 6 and 8 seemed most likely to be winnable. I focused on 12s and 17s as I assume others like to throw in a lot of 11s and 16s to get 1 army over those who put in 10s and 15s. Because the middle will be ignored
1239 5 3 0 0 6 12 8 0 15 13 22 0 4 30 3 35 31 5 8 Trying to secure a baseline of 17 and steal either 10 or 7+3 as well as the first castle a computer told me to
1240 0 0 3 3 5 12 11 12 13 17 21 12 22 17 14 12 11 12 Kind of a guess, really Looking at the data from the first two iterations, castles 6 and 8 seemed most likely to be winnable. I focused on 12s and 17s as I assume others like to throw in a lot of 11s and 16s to get 1 army over those who put in 10s and 15s.
1 1 1 1 16 16 2 29 30 3
1241 1 5 1 0 2 0 16 12 20 0 2 13 3 0 1 30 32 35 22 5 This worked last time? Trying to secure a baseline of 17 and steal either 10 or 7+3 as well as the first castle
1242 1 0 1 0 1 3 1 5 1 11 15 13 18 21 26 22 34 14 2 11 Guesswork Kind of a guess, really
1243 2 1 11 1 11 1 11 1 11 16 11 16 12 2 12 29 17 30 2 3 I tailored my placement to counter what I believe will be popular strategies. One strategy being placing at least one soldier on each castle, another being splitting them evenly at 10 soldiers a piece, and another being overloading castle 10.
1259 1 1 1 1 20 1 20 1 24 13 1 40 1 40 30 1 I need to get to 28. The minimum to get there is four castles. I want to pick the four that add to 28 and will be the least defended by my opponents. 10 is obvious, but for this reason may be overlooked by others, so I choose it. Ineed 18 more, so I pick 5,6,7. 1 to every castle to ensure I capture any uncontested castle. Most people will likely focus on the highest value castles and you need 28 total points to win so castles 8/9/10 would do it and splitting troops 3 ways to grab those I would still take 8 and 9.
1260 2 0 1 0 4 0 1 0 17 0 6 0 21 12 6 12 36 12 6 64 focused highly on the highest valued castles
1261 2 7 4 8 5 2 7 15 9 17 11 14 13 24 15 5 16 3 18 5 The number of troops at each castle is roughly equal to the ratio of each castle's value relative to the total number of available points I did a brute force excel simulation and this strategy did alright. It won ~most~ of its battles.
1 1 1 1 1 1 3 27 30 34 Proportional alignment based off points needed to win + at least 1 troop at every castle
2 4 5 6 6 6 28 6 6 31 ay81o
1262 4 1 0 1 5 1 0 1 2 20 2 20 18 24 30 1 20 1 19 30 Developed a troop deployment that beat 1386 out of 1387 of the castle-solutions.csv from two years ago. I need to get to 28. The minimum to get there is four castles. I want to pick the four that add to 28 and will be the least defended by my opponents. 10 is obvious, but for this reason may be overlooked by others, so I choose it. Ineed 18 more, so I pick 5,6,7.
1263 1 2 1 3 4 5 1 7 17 9 6 17 21 21 6 3 36 33 6 stochastic approximation
1264 1 2 2 4 3 5 2 7 3 9 12 11 21 13 26 15 26 16 4 18 Good chance to win 7,8,9 plus beating all the people that give up (0 or 1 army) on other castles. The number of troops at each castle is roughly equal to the ratio of each castle's value relative to the total number of available points
1298 3 1 3 1 7 1 11 1 14 1 16 6 19 13 22 19 3 25 3 32 Didn't want to put less than three in any castle, to prevent seceding it to someone who played 2 to beat a 1. Went for the midrange and lower castles to bolster points. 2. 75 men per point after eliminating 10, 9, 1 and 2. I wanted to have at least one soldier for every castle. However, even if one were to win castles 1 through 5, that's only 27% of the total points. Castles 6-10 were incrementally weighted.
1299 5 4 2 6 5 4 7 12 22 2 23 17 22 18 2 27 2 5 10 5 I based my numbers on the 2017 distributions, hoping history would repeat and not a ton would pore over the results much. In that data set, there were a lot of clusters in the 1-4 range at the higher and lower castles, so my castles 1-3 and 9-10 all hovered at or around 5 troops to cover. In the middle castles, I figured I'd sacrifice one to put each of the rest in play.
1300 0 4 3 4 3 8 8 6 5 7 19 15 19 18 20 6 20 18 3 14 Created two sets of the 1000 top results out of 1000 random arrays compared against themselves. Then compared the top performing array sets. The above was the best performing solution. Performed with SAS, using SQL and the datastep. Run time was about 20m. Ran a bunch of simulations in Excel to pick the ideal strategy based on past results and then ran a final simulation designed to beat the "ideal"
3 3 3 3 3 3 3 26 26 27 The top 3 castles are worth the same as the other 7, so I focused troops there and equally disbursed troops in the other 7 castles to pick up any that they didn't attack with much force.
1301 1 4 1 6 1 7 1 1 1 14 23 17 70 20 1 17 1 13 Maybe the worst idea I thought of is the best. Ran a bunch of simulations in Excel
1302 3 1 5 1 1 9 7 17 10 13 10 15 20 19 0 11 20 7 30 Odd numbers between 1 and 19, centered on Castle 8 and distributed around it in descending order. In order to win any game, a player only needs to score 28 points, so I tried to teach 28 with the fewest possible castles. But really I built a simulation and tested out a variety of strategies against a computer to see what I liked best. It really comes down to if I use the least used strategy that provides the most wins. Plus a little bit of razzle dazzle. Cheers.
1303 0 5 1 2 2 5 16 7 21 22 2 23 3 22 1 2 32 2 22 10 I built myself a fancy excel spreadsheet of all of the previous submissions, and then attempted to optimize against those.
1305 1 3 1 3 1 3 5 3 5 3 15 3 16 3 1 26 24 26 31 27 My approach: generate a bunch of random strategies with the requirement that they can beat the 'uniform' strategy of evenly deployed troops, then set them against each other to see which one wins out. I won't account for expected human choices, but I will allow the previous winners to be represented on the battle field to see how they do. My expectation is this will be close to a GTO approach in the sense that it will be hard for others to guess and exploit the strategy. On the other hand, since we'll be playing against a bunch of other humans, it wouldn't surprise me if I get killed by an exploitive strategy. FWIW, this field crushed my initial guess at a good strategy (focus on 10, 9, 6, 3 to get to 28 points). This deployment was based on results from a 60,000 random assortment. p.s. I know I'm late ... hope you find it in your heart to allow the entry anyway. p.p.s. Also happy to share my python code for this. The top 3 castles are worth the same as the other 7, so I focused troops there and equally disbursed troops in the other 7 castles to pick up any that they didn't attack with much force.
1306 1 3 2 5 4 1 10 9 21 17 12 13 26 15 16 19 4 11 4 7 Contest everything, but don't commit heavy to the point-heavy (castles 9 & 10) obvious grab strategies that people are likely to employ (similar to the first round of the contest, but countered in round two with a lot of people choosing a 4,5,9,10 strategy). Deployment had to defeat/tie some of the default, non-strategic assignments (e.g., 10 everywhere, 25s in each 7-10, % assignment based on value). Castles 5 (main counter to round two strategies), 7 (main counter to round one strategies), and 8 (some round one strategies) can break a lot of opponent strategies so contesting them is where my main investment took place. It is a bit of a gamble to pick up stray points in low commit castles when my other investments aren't high enough to offset opponent high commits. Odd numbers between 1 and 19, centered on Castle 8 and distributed around it in descending order.
1307 2 0 4 1 6 2 9 16 0 21 3 2 3 21 1 24 32 28 22 I chose something that held up well against different scenarios like previous winners and averages. I built myself a fancy excel spreadsheet of all of the previous submissions, and then attempted to optimize against those.
3 3 7 4 4 24 5 34 8 8 I spent way too long on this and I still hate my answer.
1308 5 2 5 2 5 3 5 5 6 8 6 10 6 15 6 20 6 30 to test whether multiple submissions are allowed Guessing, I guess...
1309 5 1 5 1 5 1 5 5 6 15 6 16 6 1 6 24 6 31 to test whether multiple submissions are allowed My approach: generate a bunch of random strategies with the requirement that they can beat the 'uniform' strategy of evenly deployed troops, then set them against each other to see which one wins out. I won't account for expected human choices, but I will allow the previous winners to be represented on the battle field to see how they do. My expectation is this will be close to a GTO approach in the sense that it will be hard for others to guess and exploit the strategy. On the other hand, since we'll be playing against a bunch of other humans, it wouldn't surprise me if I get killed by an exploitive strategy. FWIW, this field crushed my initial guess at a good strategy (focus on 10, 9, 6, 3 to get to 28 points). This deployment was based on results from a 60,000 random assortment. p.s. I know I'm late ... hope you find it in your heart to allow the entry anyway. p.p.s. Also happy to share my python code for this.
1310 5 1 5 2 5 4 5 10 5 21 6 12 6 26 6 16 6 4 6 4 to test whether multiple submissions are allowed Contest everything, but don't commit heavy to the point-heavy (castles 9 & 10) obvious grab strategies that people are likely to employ (similar to the first round of the contest, but countered in round two with a lot of people choosing a 4,5,9,10 strategy). Deployment had to defeat/tie some of the default, non-strategic assignments (e.g., 10 everywhere, 25s in each 7-10, % assignment based on value). Castles 5 (main counter to round two strategies), 7 (main counter to round one strategies), and 8 (some round one strategies) can break a lot of opponent strategies so contesting them is where my main investment took place. It is a bit of a gamble to pick up stray points in low commit castles when my other investments aren't high enough to offset opponent high commits.
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riddler-castles/castle-solutions-4.csv
View File

@@ -1,8 +1,6 @@
Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9,Castle 10
0,0,12,1,1,23,3,3,33,24
5,8,0,17,17,16,16,0,23,0
0,0,0,10,13,15,18,20,24,0
6,7,8,16,17,2,2,2,25,25
0,12,0,0,20,21,23,24,0,0
1,2,2,4,8,12,14,16,19,22
0,0,0,5,15,20,20,18,22,0
@@ -16,7 +14,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,10,0,0,0,0,0,28,30,32
8,10,12,14,16,19,21,0,0,0
0,0,0,0,15,17,17,17,17,17
4,5,6,9,0,13,13,17,17,17
6,6,10,13,14,0,25,0,0,26
1,1,1,5,1,1,20,20,25,25
0,8,0,0,15,19,27,31,0,0
@@ -50,7 +47,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,4,8,8,13,3,3,23,4,31
0,0,0,10,10,0,15,20,20,25
0,0,0,0,10,0,0,30,30,30
6,7,13,14,118,21,21,1,1,1
1,3,5,7,9,11,13,15,17,19
0,0,0,0,6,16,18,18,20,22
0,8,0,14,0,22,0,26,0,30
@@ -64,7 +60,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,1,0,0,0,0,0,31,32,33
0,3,5,11,13,14,15,14,13,12
3,5,7,10,12,1,26,30,3,3
0,0,0,0,0,22,22,22,22,22
0,0,5,0,10,13,15,19,19,19
2,4,4,6,25,2,22,24,6,5
0,0,0,5,8,16,14,18,19,20
@@ -73,7 +68,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
10,0,0,0,0,0,0,30,30,30
0,0,0,0,10,13,14,22,21,20
1,1,2,2,11,14,16,17,18,18
2,2,3,6,10,14,17,20,15,10
1,4,6,0,0,20,0,21,33,15
2,4,6,6,15,13,6,6,21,21
0,0,5,8,12,16,17,2,20,20
@@ -97,7 +91,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,1,1,1,20,24,25,25
2,5,2,5,11,13,13,21,18,10
2,3,4,5,6,10,15,19,18,18
2,3,5,6,7,11,15,16,18,19
3,5,7,10,12,0,17,0,22,24
1,3,5,7,9,11,13,15,17,19
0,0,0,0,10,16,17,18,19,20
@@ -107,7 +100,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,2,0,0,0,18,19,19,19,21
0,0,0,15,0,0,25,30,30,0
0,1,4,11,11,17,18,4,6,28
2,3,5,7,9,11,13,15,16,18
1,1,1,1,1,15,20,20,20,20
2,2,0,0,0,18,18,19,20,21
7,8,10,12,15,20,25,1,1,1
@@ -124,7 +116,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,5,1,9,1,11,20,12,20,20
1,1,2,4,13,8,26,7,33,5
7,10,10,15,22,23,2,3,4,4
2,4,6,8,10,10,10,10,17,17
2,2,6,8,12,18,3,2,21,26
0,1,14,1,1,1,25,25,1,31
3,4,5,8,0,12,13,17,18,20
@@ -141,7 +132,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,2,2,5,8,16,16,16,17,17
7,8,10,12,14,0,0,0,23,26
0,1,2,4,6,10,12,18,21,26
1,3,5,5,5,10,25,25,25,1
1,1,2,3,4,21,27,28,6,7
6,0,0,0,0,0,0,32,32,30
3,4,8,8,8,1,1,1,33,33
@@ -179,7 +169,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,5,0,15,20,0,0,0,30,30
0,0,0,0,0,0,20,25,25,30
0,0,0,0,11,11,0,39,39,0
1.1,2.1,3.1,4.1,6.1,7.1,15.1,16.1,20.1,25.1
4,6,8,14,18,24,26,0,0,0
3,5,5,0,0,15,18,18,19,17
10,10,10,10,10,25,25,0,0,0
@@ -190,7 +179,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,15,1,1,25,25,30,0
0,0,0,18,18,0,0,0,32,32
1,1,1,1,1,1,20,22,24,28
1,2,4,5,13,15,16,22,23,0
1,1,8,11,14,17,1,1,1,45
1,3,4,6,8,13,14,18,18,15
1,1,1,1,1,27,27,27,7,7
@@ -205,7 +193,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,10,10,10,20,18,0,0,0,30
2,2,2,2,12,15,20,23,20,2
5,5,5,5,0,14,16,20,8,22
0,9,11,0,0,23,29,0,0,27
2,4,5,7,9,11,13,15,16,18
2,4,5,7,9,11,13,15,16,18
2,0,6,0,0,0,14,22,26,30
@@ -219,8 +206,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,2,2,2,3,16,17,18,19,20
0,0,0,0,14,18,1,32,34,1
0,0,3,10,3,19,6,1,26,32
4,5,7,9,1,13,16,18,15,13
3,4,6,7,11,14,14,17,17,16
1,1,1,1,15,20,1,20,20,20
1,3,5,7,9,11,13,15,17,19
2,3,4,7,9,12,12,16,18,17
@@ -230,29 +215,23 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
8,8,11,13,15,18,21,2,2,2
6,7,12,15,18,20,22,0,0,0
5,0,0,0,0,0,0,32,32,31
1,1,1,1,1,1,20,21,25,25
0,0,7,10,12,14,17,19,21,0
2,2,4,5,7,10,16,18,18,18
1,1,2,2,3,15,19,19,19,19
0,0,5,12,1,0,23,2,20,28
0,0,0,0,0,20,20,20,20,20
2,1,3,7,10,5,15,20,19,18
2,3,5,7,9,12,14,17,16,15
1,1,1,6,8,11,15,17,19,21
11,8,12,12,12,12,12,11,12,10
3,5,6,9,11,11,13,16,18,8
7,0,0,0,0,0,0,31,31,31
3,4,5,8,10,13,15,20,20,2
1,1,3,5,11,14,17,20,15,18
1,2,2,5,10,13,14,18,18,17
0,0,0,0,0,0,20,25,25,30
2,2,2,7,9,15,17,17,17,12
7,9,11,13,16,18,20,3,2,1
0,4,4,4,5,6,14,17,23,19
0,0,0,0,0,20,20,20,20,20
6,7,9,10,13,17,1,1,1,35
2,5,10,10,20,21,21,0,11,0
1,5,3,9,5,15,7,21,8,24
0,1,7,8,9,15,6,6,28,20
0,0,0,0,21,23,25,0,0,31
0,9,1,1,11,13,26,38,0,1
@@ -275,15 +254,12 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
4,0,0,0,0,0,0,32,32,32
2,3,3,7,14,15,17,19,19,1
5,5,5,7,10,15,20,0,0,33
0,5,7,9,11,14,16,18,20,O
0,0,0,0,0,20,20,20,20,20
0,3,5,7,9,11,16,18,18,13
12,0,0,0,0,0,0,29,29,30
1,1,4,7,6,15,20,23,13,10
2,3,4,7,9,13,16,18,15,13
5,0,0,0,0,0,0,31,32,32
2,3,5,7,11,14,15,17,18,16
0,0,0,14,15,15,22,22,22,0
0,0,0,17,18,0,0,0,35,30
1,2,10,13,22,24,1,1,1,25
10,1,1,1,1,1,1,25,28,31
@@ -292,7 +268,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,4,5,1,10,13,14,11,20,19
1,1,3,5,10,14,17,20,17,12
0,4,7,9,11,14,17,19,18,1
1,0,0,0,9,17,19,21,21,13
0,0,0,13,2,22,1,5,34,23
10,8,4,10,15,5,15,17,6,10
0,0,4,14,16,18,22,26,0,0
@@ -330,7 +305,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,2,3,3,8,12,25,30,15,0
5,7,7,12,0,0,0,21,23,25
0,5,6,8,1,20,40,20,0,0
2,4,3,8,8,14,15,20,15,12
4,0,0,0,0,0,0,32,32,32
0,8,0,12,16,0,25,0,0,39
0,0,0,0,10,14,16,18,20,22
@@ -345,7 +319,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,2,5,3,13,1,27,31,11,4
5,6,7,0,0,0,19,20,21,22
3,3,3,3,3,21,21,21,21,1
1,1,6,8,12,13,17,0,20,20
4,5,5,0,0,0,25,23,20,18
4,4,5,8,10,14,15,2,19,19
1,2,4,7,8,13,15,18,15,17
@@ -392,7 +365,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,7,7,8,4,13,16,19,22,1
1,1,1,1,1,15,20,20,20,20
0,0,0,0,16,18,0,19,24,23
3,3,4,8,9,12,15,16,16,16
0,0,0,14,3,14,15,5,25,24
2,6,9,4,10,12,14,15,14,14
3,6,2,11,12,9,15,15,14,13
@@ -429,7 +401,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,19,1,1,19,19,1,1,19,19
0,0,2,9,15,6,5,6,35,22
10,10,10,10,20,20,20,0,0,0
1,1,1,19,19,1,1,19,19,49
0,0,0,0,0,18,19,20,21,22
1,1,1,19,19,1,1,19,19,19
5,7,9,15,18,22,24,0,0,0
@@ -464,13 +435,11 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
6,6,3,3,2,15,14,17,17,17
0,4,0,13,0,25,0,37,0,21
0,0,0,0,17,21,29,0,0,33
2,4,3,3,3,16,19,22,0,25
2,3,6,1,1,1,15,20,23,28
2,2,13,1,16,1,26,3,4,32
0,0,5,18,18,19,20,20,0,0
0,0,0,20,20,20,20,20,0,0
5,6,6,7,8,9,9,8,3,39
5,7,7,15,18,22,25,1,1,1
1,5,7,2,12,14,17,2,20,20
0,0,0,0,0,0,25,25,25,25
3,5,5,0,10,10,15,18,17,17
@@ -495,7 +464,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,1,1,1,1,31,31,31
0,0,0,0,18,20,28,0,0,34
4,4,7,9,11,14,17,20,14,0
1.1,4.1,7.1,2.1,16.1,3.1,3.1,16.1,29.1,28.1
6,8,10,12,14,16,18,7,7,2
1,3,4,7,9,11,13,15,16,21
0,0,0,5,7,18,18,18,20,14
@@ -507,7 +475,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
5,0,0,0,0,0,0,27,34,34
3,3,5,7,9,12,15,18,15,13
0,0,0,0,0,15,19,24,23,19
4,8,10,12,14,20,23,3,3,4
8,10,10,10,12,25,0,0,0,25
4,0,6,0,16,0,0,0,36,38
0,0,20,0,0,0,25,25,0,30
@@ -532,7 +499,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,2,4,10,15,20,22,23,4
0,0,0,0,0,17,18,22,22,21
1,1,3,4,5,12,15,24,24,11
0,0,12,16,20,26,0,0,0,32
1,1,1,1,11,14,15,19,19,18
0,2,3,10,5,13,17,12,20,18
0,0,10,0,0,0,20,30,0,40
@@ -552,7 +518,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,5,8,10,13,1,26,30,2,2
0,0,0,17,17,0,0,0,33,33
0,0,0,4,14,12,16,17,18,19
6,8,10,14,18,22,24,0,0,0
5,5,8,10,3,3,21,22,21,2
0,9,0,0,16,21,26,26,1,1
10,0,0,0,0,0,0,30,30,30
@@ -563,15 +528,12 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,5,7,1,7,14,21,15,19,10
1,1,6,10,10,13,18,18,18,5
2,3,4,7,9,12,13,17,17,16
100,100,100,100,100,100,100,100,100,100
0,8,1,1,1,1,1,29,29,29
0,0,6,8,10,12,16,17,16,15
5,6,7,12,13,16,19,22,0,0
1,1,1,1,19,20,20,20,7,10
5,5,6,9,5,5,6,9,25,25
1,2,4,3,3,21,4,4,25,28
0,0,0,12,19,2,3,3,35,26
5,6,6,11,12,2,2,1,28,28
2,5,10,12,15,23,30,1,1,1
1,2,1,16,16,1,28,1,28,6
5,2,0,0,0,0,0,30,31,32
@@ -584,9 +546,7 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,9,16,20,20,1,1,1,30
6,6,6,11,11,16,21,19,2,2
6,6,0,0,0,28,0,0,30,30
2,3,3,3,3,3,15,27,56,1
2,2,5,2,7,12,15,27,2,26
3,3,4,12,10,14,12,18,16,18
2,5,6,10,13,20,20,20,2,2
0,0,3,6,15,17,0,20,20,19
0,0,0,0,18,24,26,0,0,32
@@ -600,7 +560,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
5,5,0,0,0,0,0,30,30,30
6,0,0,0,0,0,0,31,31,32
1,1,1,6,15,15,20,20,20,1
0,0,11,11,0,15,25,37,0,0
1,2,5,7,9,13,15,18,16,14
0,0,0,14,0,18,0,20,23,25
1,2,3,5,7,12,15,17,18,20
@@ -620,11 +579,9 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,3,5,7,9,10,13,15,16,20
0,2,4,6,8,11,19,17,17,16
3,3,4,6,12,8,13,18,17,16
3,4,5,8,10,13,15,18,18,7
0,0,10,13,21,24,3,1,2,26
0,0,0,14,18,0,0,0,34,34
3,4,7,9,13,16,3,5,20,20
10,10,10,10,20,0,20,20,0,15
1,2,2,2,2,3,7,13,25,43
1,1,0,1,1,3,24,6,36,27
0,0,0,0,0,0,0,32,34,34
@@ -640,7 +597,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,1,2,4,10,12,14,17,19,21
0,5,0,11,13,19,22,22,4,4
2,4,4,5,9,11,12,18,17,18
1,1,5,6,16,18,22,3,4,25
1,2,3,5,8,9,16,17,19,20
8,0,0,0,0,0,0,28,30,34
0,0,4,0,10,15,15,18,18,20
@@ -662,13 +618,11 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,0,31,31,0,0,38
3,1,9,2,3,18,4,24,5,31
4,5,6,10,15,18,0,0,24,18
2,2,2,3,15,15,15,15,15,15
30,25,20,15,5,1,1,1,1,1
1,3,5,7,9,11,13,15,17,19
2,3,8,12,12,23,6,4,7,23
0,0,10,0,0,20,0,0,35,35
0,0,0,10,10,15,15,0,25,25
1,1,2,4,7,9,13,17,22,25
5,8,0,0,0,0,0,28,29,30
0,0,0,0,0,20,23,27,30,0
1,2,2,3,4,8,15,18,23,24
@@ -678,7 +632,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
5,7,8,10,15,15,20,0,0,20
0,0,0,0,0,0,25,25,25,25
2,4,5,7,9,11,13,15,16,18
3,5,7,9,11,13,15,17,19,0
0,0,0,0,0,0,24,25,25,26
1,1,1,17,18,19,20,21,1,1
2,2,2,0,8,15,14,19,19,19
@@ -695,9 +648,7 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
8,8,11,13,16,21,23,0,0,0
14,0,0,0,0,0,0,28,28,30
0,0,0,0,0,19,19,19,20,23
30,30,30,30,40,40,40,50,50,50
10,0,0,0,0,0,0,30,30,30
1,1,2,3,4,16,17,18,19,20
0,0,12,0,0,22,0,0,34,32
0,0,12,1,2,23,3,3,33,23
3,0,6,8,15,22,4,3,31,8
@@ -729,19 +680,15 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,7,1,13,18,21,36,1,1
0,7,9,17,3,3,4,3,22,32
0,1,12,2,2,23,3,2,33,22
0,0,0,13,0,0,21,23,25,28
4,8,12,16,20,0,0,0,20,20
22,0,0,0,0,0,0,24,26,28
2,3,5,8,10,13,14,15,14,15
1,3,5,7,8,10,12,14,20,20
0,0,0,0,0,0,25,25,25,25
0,0,0,0,20,20,20,20,0,20
5,10,12,15,16,20,22,0,0,0
5,10,10,0,0,0,0,25,25,25
0,0,2,2,1,20,26,26,20,4
2,2,2,2,2,2,17,23,23,25
0,0,0,14,17,20,23,26,0,0
4,5,8,10,13,2,26,30,3,3
0,0,10,2,3,22,3,3,32,25
0,5,0,10,10,5,0,18,26,26
2,2,2,7,5,15,13,19,18,17
@@ -750,7 +697,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,0,0,23,24,26,27
0,0,0,0,0,20,20,20,20,20
7,0,0,0,0,0,0,30,31,32
1,3,5,8,9,13,16,16,19,0
0,0,0,10,12,19,22,0,0,37
0,0,1,2,6,20,22,1,24,24
1,1,1,1,1,1,23,23,24,24
@@ -773,7 +719,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,0,20,20,20,20,20
0,0,9,0,0,0,0,30,31,30
4,4,0,0,0,0,0,32,30,30
0,2,2,11,4,15,2,17,4,24
1,17,1,18,1,19,1,20,1,21
3,4,6,8,10,17,24,28,0,0
1,2,3,1,2,2,2,28,29,30
@@ -798,7 +743,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,0,16,20,20,20,24
3,5,7,13,0,20,23,0,0,29
0,0,0,0,0,15,20,20,20,25
2,2,12,9,2,20,27,20,2,2
1,0,2,5,12,17,25,5,1,32
8,0,0,0,0,0,0,27,30,35
1,3,0,4,3,17,23,0,23,26
@@ -810,7 +754,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
6,9,10,11,14,12,11,10,9,8
0,0,0,17,21,0,0,0,32,30
2,3,3,8,13,6,26,31,4,4
1,16,1,1,1,3,20,2200,27,28
1,10,10,1,1,2,19,3,27,26
3,3,5,6,8,12,14,16,17,16
0,0,0,0,18,19,20,21,0,22
@@ -821,14 +764,10 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
4,5,5,5,7,9,16,15,18,16
0,5,6,0,0,22,26,0,0,41
2,3,5,10,12,16,19,21,11,1
3,4,6,8,12,13,14,17,13,11
9,0,0,0,0,0,0,30,31,30
2,2,4,7,9,17,11,22,15,11
3,0,1,1,9,10,17,1,25,33
0,0,4,0,0,0,19,19,19,19
0,0,0,0,25,25,25,0,0,25
5,0,0,0,0,0,0,31,32,42
0,0,4,4,6,6,10,20,30,30
0,0,0,9,14,0,19,10,22,26
10,10,10,10,10,14,16,20,0,0
1,7,10,10,15,15,20,20,1,1
@@ -850,7 +789,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
4,5,4,6,12,22,21,3,18,5
1,2,3,6,9,12,14,18,18,17
3,5,8,10,13,1,26,30,2,2
0,2,2,2,4,4,17,20,23,26 30
4,5,6,1,1,1,1,24,27,30
0,0,0,3,11,14,17,20,18,17
0,2,4,8,9,12,15,19,19,12
@@ -862,18 +800,14 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,5,7,7,10,11,20,20,20
0,0,12,1,1,22,3,3,33,25
0,0,10,16,0,20,25,29,0,0
0.1,0.1,10.1,15.1,0,20.2,25.1,29.3,0,0
0,0,6,0,0,22,22,25,25,0
1,2,8,10,15,22,5,4,9,24
5,0,0,0,0,0,0,25,30,40
2,4,6,9,11,14,16,19,19,0
0,0,0,0,0,28,0,36,36,0
0,0,11,0,0,7,7,7,34,34
0,0,0,0,17,22,0,29,33,0
0,7,11,16,0,0,0,0,35,31
3,3,5,5,0,20,20,21,0,23
0,0,2,14,18,2,3,3,32,36
0,7,0,0,0,0,18,0,25,52
4,0,0,0,0,0,0,28,32,36
0,0,2,8,2,15,3,28,7,35
2,3,6,6,6,6,6,6,33,26
@@ -924,8 +858,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,1,11,2,2,1,22,32,5,24
4,5,7,9,12,24,26,2,5,6
0,5,7,9,12,14,16,0,19,18
1,2,5,9,9,14,15,14,15,14
0,0,0,0,0,18,20,22,20,18
2,2,18,4,2,19,3,4,20,26
8,9,12,14,16,18,20,1,1,1
0,0,0,0,0,100,0,0,0,0
@@ -939,20 +871,17 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,2,2,10,10,21,26,26
10,10,10,10,10,10,15,15,10,0
0,1,1,15,18,1,3,2,35,24
5,5,9,11,0,0,20,0,20,20
0,0,0,5,15,17,20,21,22,0
1,3,5,7,9,11,13,15,17,19
10,0,0,0,0,0,0,30,30,30
3,5,6,8,11,14,15,0,19,19
6,0,0,4,0,10,0,31,31,18
1,1,1,1,14,17,26,3,34,2
1,1,1,8,10,13,14,15,15,23
4,4,4,8,15,15,15,20,15,0
0,1,11,1,1,22,3,3,34,24
2,3,4,9,19,19,1,1,21,21
0,7,9,17,24,2,8,8,0,25
2,5,8,1,10,2,17,3,26,26
0,0,0,0,14,15,0,23,24,25
0,0,0,0,15,20,0,28,37,0
8,0,0,0,0,0,0,27,31,34
0,0,0,8,12,0,17,20,21,22
@@ -962,8 +891,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
10,10,12,14,16,18,20,0,0,0
6,1,1,1,1,1,1,30,30,28
2,4,4,5,10,15,20,0,20,20
2,1,2,2,2,17,19,1,27,26
3,4,6,8,10,12,15,17,14,12
2,2,4,6,6,14,16,0,24,26
8,8,8,14,17,20,25,0,0,0
4,4,6,8,8,15,15,6,18,16
@@ -976,14 +903,12 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
5,7,9,11,15,21,25,2,2,3
0,2,3,7,14,16,17,18,3,20
2,2,2,2,2,2,0,29,30,29
0,0,0,0,0,0,18,15,22,46
4,0,0,0,0,0,0,32,32,32
3,4,7,10,13,2,27,31,1,2
3,3,6,2,2,19,9,22,13,21
0,2,2,3,16,0,19,22,5,31
1,0,0,0,6,0,10,21,29,33
5,0,0,0,0,0,0,28,32,35
5,1,1,1,1,1,1,30,30,30
2,8,2,13,18,2,2,23,28,2
0,0,1,2,12,22,3,22,33,5
2,3,3,5,10,13,14,26,13,11
@@ -1011,4 +936,4 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,3,5,6,11,13,24,3,29,3
0,5,7,12,12,21,1,31,4,7
0,0,0,5,15,8,4,13,30,25
6,4,6,9,14,14,1,33,7,6
6,4,6,9,14,14,1,33,7,6
1 Castle 1 Castle 2 Castle 3 Castle 4 Castle 5 Castle 6 Castle 7 Castle 8 Castle 9 Castle 10
2 0 0 12 1 1 23 3 3 33 24
5 8 0 17 17 16 16 0 23 0
3 0 0 0 10 13 15 18 20 24 0
6 7 8 16 17 2 2 2 25 25
4 0 12 0 0 20 21 23 24 0 0
5 1 2 2 4 8 12 14 16 19 22
6 0 0 0 5 15 20 20 18 22 0
14 0 10 0 0 0 0 0 28 30 32
15 8 10 12 14 16 19 21 0 0 0
16 0 0 0 0 15 17 17 17 17 17
4 5 6 9 0 13 13 17 17 17
17 6 6 10 13 14 0 25 0 0 26
18 1 1 1 5 1 1 20 20 25 25
19 0 8 0 0 15 19 27 31 0 0
47 3 4 8 8 13 3 3 23 4 31
48 0 0 0 10 10 0 15 20 20 25
49 0 0 0 0 10 0 0 30 30 30
6 7 13 14 118 21 21 1 1 1
50 1 3 5 7 9 11 13 15 17 19
51 0 0 0 0 6 16 18 18 20 22
52 0 8 0 14 0 22 0 26 0 30
60 3 1 0 0 0 0 0 31 32 33
61 0 3 5 11 13 14 15 14 13 12
62 3 5 7 10 12 1 26 30 3 3
0 0 0 0 0 22 22 22 22 22
63 0 0 5 0 10 13 15 19 19 19
64 2 4 4 6 25 2 22 24 6 5
65 0 0 0 5 8 16 14 18 19 20
68 10 0 0 0 0 0 0 30 30 30
69 0 0 0 0 10 13 14 22 21 20
70 1 1 2 2 11 14 16 17 18 18
2 2 3 6 10 14 17 20 15 10
71 1 4 6 0 0 20 0 21 33 15
72 2 4 6 6 15 13 6 6 21 21
73 0 0 5 8 12 16 17 2 20 20
91 1 1 1 1 1 1 20 24 25 25
92 2 5 2 5 11 13 13 21 18 10
93 2 3 4 5 6 10 15 19 18 18
2 3 5 6 7 11 15 16 18 19
94 3 5 7 10 12 0 17 0 22 24
95 1 3 5 7 9 11 13 15 17 19
96 0 0 0 0 10 16 17 18 19 20
100 2 2 0 0 0 18 19 19 19 21
101 0 0 0 15 0 0 25 30 30 0
102 0 1 4 11 11 17 18 4 6 28
2 3 5 7 9 11 13 15 16 18
103 1 1 1 1 1 15 20 20 20 20
104 2 2 0 0 0 18 18 19 20 21
105 7 8 10 12 15 20 25 1 1 1
116 1 5 1 9 1 11 20 12 20 20
117 1 1 2 4 13 8 26 7 33 5
118 7 10 10 15 22 23 2 3 4 4
2 4 6 8 10 10 10 10 17 17
119 2 2 6 8 12 18 3 2 21 26
120 0 1 14 1 1 1 25 25 1 31
121 3 4 5 8 0 12 13 17 18 20
132 1 2 2 5 8 16 16 16 17 17
133 7 8 10 12 14 0 0 0 23 26
134 0 1 2 4 6 10 12 18 21 26
1 3 5 5 5 10 25 25 25 1
135 1 1 2 3 4 21 27 28 6 7
136 6 0 0 0 0 0 0 32 32 30
137 3 4 8 8 8 1 1 1 33 33
169 0 5 0 15 20 0 0 0 30 30
170 0 0 0 0 0 0 20 25 25 30
171 0 0 0 0 11 11 0 39 39 0
1.1 2.1 3.1 4.1 6.1 7.1 15.1 16.1 20.1 25.1
172 4 6 8 14 18 24 26 0 0 0
173 3 5 5 0 0 15 18 18 19 17
174 10 10 10 10 10 25 25 0 0 0
179 1 1 1 15 1 1 25 25 30 0
180 0 0 0 18 18 0 0 0 32 32
181 1 1 1 1 1 1 20 22 24 28
1 2 4 5 13 15 16 22 23 0
182 1 1 8 11 14 17 1 1 1 45
183 1 3 4 6 8 13 14 18 18 15
184 1 1 1 1 1 27 27 27 7 7
193 2 10 10 10 20 18 0 0 0 30
194 2 2 2 2 12 15 20 23 20 2
195 5 5 5 5 0 14 16 20 8 22
0 9 11 0 0 23 29 0 0 27
196 2 4 5 7 9 11 13 15 16 18
197 2 4 5 7 9 11 13 15 16 18
198 2 0 6 0 0 0 14 22 26 30
206 1 2 2 2 3 16 17 18 19 20
207 0 0 0 0 14 18 1 32 34 1
208 0 0 3 10 3 19 6 1 26 32
4 5 7 9 1 13 16 18 15 13
3 4 6 7 11 14 14 17 17 16
209 1 1 1 1 15 20 1 20 20 20
210 1 3 5 7 9 11 13 15 17 19
211 2 3 4 7 9 12 12 16 18 17
215 8 8 11 13 15 18 21 2 2 2
216 6 7 12 15 18 20 22 0 0 0
217 5 0 0 0 0 0 0 32 32 31
1 1 1 1 1 1 20 21 25 25
218 0 0 7 10 12 14 17 19 21 0
219 2 2 4 5 7 10 16 18 18 18
220 1 1 2 2 3 15 19 19 19 19
0 0 5 12 1 0 23 2 20 28
221 0 0 0 0 0 20 20 20 20 20
222 2 1 3 7 10 5 15 20 19 18
223 2 3 5 7 9 12 14 17 16 15
224 1 1 1 6 8 11 15 17 19 21
11 8 12 12 12 12 12 11 12 10
225 3 5 6 9 11 11 13 16 18 8
226 7 0 0 0 0 0 0 31 31 31
227 3 4 5 8 10 13 15 20 20 2
1 1 3 5 11 14 17 20 15 18
228 1 2 2 5 10 13 14 18 18 17
229 0 0 0 0 0 0 20 25 25 30
230 2 2 2 7 9 15 17 17 17 12
231 7 9 11 13 16 18 20 3 2 1
0 4 4 4 5 6 14 17 23 19
232 0 0 0 0 0 20 20 20 20 20
233 6 7 9 10 13 17 1 1 1 35
234 2 5 10 10 20 21 21 0 11 0
1 5 3 9 5 15 7 21 8 24
235 0 1 7 8 9 15 6 6 28 20
236 0 0 0 0 21 23 25 0 0 31
237 0 9 1 1 11 13 26 38 0 1
254 4 0 0 0 0 0 0 32 32 32
255 2 3 3 7 14 15 17 19 19 1
256 5 5 5 7 10 15 20 0 0 33
0 5 7 9 11 14 16 18 20 O
257 0 0 0 0 0 20 20 20 20 20
258 0 3 5 7 9 11 16 18 18 13
259 12 0 0 0 0 0 0 29 29 30
260 1 1 4 7 6 15 20 23 13 10
261 2 3 4 7 9 13 16 18 15 13
262 5 0 0 0 0 0 0 31 32 32
2 3 5 7 11 14 15 17 18 16
0 0 0 14 15 15 22 22 22 0
263 0 0 0 17 18 0 0 0 35 30
264 1 2 10 13 22 24 1 1 1 25
265 10 1 1 1 1 1 1 25 28 31
268 3 4 5 1 10 13 14 11 20 19
269 1 1 3 5 10 14 17 20 17 12
270 0 4 7 9 11 14 17 19 18 1
1 0 0 0 9 17 19 21 21 13
271 0 0 0 13 2 22 1 5 34 23
272 10 8 4 10 15 5 15 17 6 10
273 0 0 4 14 16 18 22 26 0 0
305 2 2 3 3 8 12 25 30 15 0
306 5 7 7 12 0 0 0 21 23 25
307 0 5 6 8 1 20 40 20 0 0
2 4 3 8 8 14 15 20 15 12
308 4 0 0 0 0 0 0 32 32 32
309 0 8 0 12 16 0 25 0 0 39
310 0 0 0 0 10 14 16 18 20 22
319 3 2 5 3 13 1 27 31 11 4
320 5 6 7 0 0 0 19 20 21 22
321 3 3 3 3 3 21 21 21 21 1
1 1 6 8 12 13 17 0 20 20
322 4 5 5 0 0 0 25 23 20 18
323 4 4 5 8 10 14 15 2 19 19
324 1 2 4 7 8 13 15 18 15 17
365 3 7 7 8 4 13 16 19 22 1
366 1 1 1 1 1 15 20 20 20 20
367 0 0 0 0 16 18 0 19 24 23
3 3 4 8 9 12 15 16 16 16
368 0 0 0 14 3 14 15 5 25 24
369 2 6 9 4 10 12 14 15 14 14
370 3 6 2 11 12 9 15 15 14 13
401 1 19 1 1 19 19 1 1 19 19
402 0 0 2 9 15 6 5 6 35 22
403 10 10 10 10 20 20 20 0 0 0
1 1 1 19 19 1 1 19 19 49
404 0 0 0 0 0 18 19 20 21 22
405 1 1 1 19 19 1 1 19 19 19
406 5 7 9 15 18 22 24 0 0 0
435 6 6 3 3 2 15 14 17 17 17
436 0 4 0 13 0 25 0 37 0 21
437 0 0 0 0 17 21 29 0 0 33
2 4 3 3 3 16 19 22 0 25
438 2 3 6 1 1 1 15 20 23 28
439 2 2 13 1 16 1 26 3 4 32
440 0 0 5 18 18 19 20 20 0 0
441 0 0 0 20 20 20 20 20 0 0
442 5 6 6 7 8 9 9 8 3 39
5 7 7 15 18 22 25 1 1 1
443 1 5 7 2 12 14 17 2 20 20
444 0 0 0 0 0 0 25 25 25 25
445 3 5 5 0 10 10 15 18 17 17
464 1 1 1 1 1 1 1 31 31 31
465 0 0 0 0 18 20 28 0 0 34
466 4 4 7 9 11 14 17 20 14 0
1.1 4.1 7.1 2.1 16.1 3.1 3.1 16.1 29.1 28.1
467 6 8 10 12 14 16 18 7 7 2
468 1 3 4 7 9 11 13 15 16 21
469 0 0 0 5 7 18 18 18 20 14
475 5 0 0 0 0 0 0 27 34 34
476 3 3 5 7 9 12 15 18 15 13
477 0 0 0 0 0 15 19 24 23 19
4 8 10 12 14 20 23 3 3 4
478 8 10 10 10 12 25 0 0 0 25
479 4 0 6 0 16 0 0 0 36 38
480 0 0 20 0 0 0 25 25 0 30
499 0 0 2 4 10 15 20 22 23 4
500 0 0 0 0 0 17 18 22 22 21
501 1 1 3 4 5 12 15 24 24 11
0 0 12 16 20 26 0 0 0 32
502 1 1 1 1 11 14 15 19 19 18
503 0 2 3 10 5 13 17 12 20 18
504 0 0 10 0 0 0 20 30 0 40
518 3 5 8 10 13 1 26 30 2 2
519 0 0 0 17 17 0 0 0 33 33
520 0 0 0 4 14 12 16 17 18 19
6 8 10 14 18 22 24 0 0 0
521 5 5 8 10 3 3 21 22 21 2
522 0 9 0 0 16 21 26 26 1 1
523 10 0 0 0 0 0 0 30 30 30
528 1 5 7 1 7 14 21 15 19 10
529 1 1 6 10 10 13 18 18 18 5
530 2 3 4 7 9 12 13 17 17 16
100 100 100 100 100 100 100 100 100 100
531 0 8 1 1 1 1 1 29 29 29
532 0 0 6 8 10 12 16 17 16 15
533 5 6 7 12 13 16 19 22 0 0
534 1 1 1 1 19 20 20 20 7 10
535 5 5 6 9 5 5 6 9 25 25
1 2 4 3 3 21 4 4 25 28
536 0 0 0 12 19 2 3 3 35 26
5 6 6 11 12 2 2 1 28 28
537 2 5 10 12 15 23 30 1 1 1
538 1 2 1 16 16 1 28 1 28 6
539 5 2 0 0 0 0 0 30 31 32
546 1 1 9 16 20 20 1 1 1 30
547 6 6 6 11 11 16 21 19 2 2
548 6 6 0 0 0 28 0 0 30 30
2 3 3 3 3 3 15 27 56 1
549 2 2 5 2 7 12 15 27 2 26
3 3 4 12 10 14 12 18 16 18
550 2 5 6 10 13 20 20 20 2 2
551 0 0 3 6 15 17 0 20 20 19
552 0 0 0 0 18 24 26 0 0 32
560 5 5 0 0 0 0 0 30 30 30
561 6 0 0 0 0 0 0 31 31 32
562 1 1 1 6 15 15 20 20 20 1
0 0 11 11 0 15 25 37 0 0
563 1 2 5 7 9 13 15 18 16 14
564 0 0 0 14 0 18 0 20 23 25
565 1 2 3 5 7 12 15 17 18 20
579 2 3 5 7 9 10 13 15 16 20
580 0 2 4 6 8 11 19 17 17 16
581 3 3 4 6 12 8 13 18 17 16
3 4 5 8 10 13 15 18 18 7
582 0 0 10 13 21 24 3 1 2 26
583 0 0 0 14 18 0 0 0 34 34
584 3 4 7 9 13 16 3 5 20 20
10 10 10 10 20 0 20 20 0 15
585 1 2 2 2 2 3 7 13 25 43
586 1 1 0 1 1 3 24 6 36 27
587 0 0 0 0 0 0 0 32 34 34
597 0 1 2 4 10 12 14 17 19 21
598 0 5 0 11 13 19 22 22 4 4
599 2 4 4 5 9 11 12 18 17 18
1 1 5 6 16 18 22 3 4 25
600 1 2 3 5 8 9 16 17 19 20
601 8 0 0 0 0 0 0 28 30 34
602 0 0 4 0 10 15 15 18 18 20
618 0 0 0 0 0 31 31 0 0 38
619 3 1 9 2 3 18 4 24 5 31
620 4 5 6 10 15 18 0 0 24 18
2 2 2 3 15 15 15 15 15 15
621 30 25 20 15 5 1 1 1 1 1
622 1 3 5 7 9 11 13 15 17 19
623 2 3 8 12 12 23 6 4 7 23
624 0 0 10 0 0 20 0 0 35 35
625 0 0 0 10 10 15 15 0 25 25
1 1 2 4 7 9 13 17 22 25
626 5 8 0 0 0 0 0 28 29 30
627 0 0 0 0 0 20 23 27 30 0
628 1 2 2 3 4 8 15 18 23 24
632 5 7 8 10 15 15 20 0 0 20
633 0 0 0 0 0 0 25 25 25 25
634 2 4 5 7 9 11 13 15 16 18
3 5 7 9 11 13 15 17 19 0
635 0 0 0 0 0 0 24 25 25 26
636 1 1 1 17 18 19 20 21 1 1
637 2 2 2 0 8 15 14 19 19 19
648 8 8 11 13 16 21 23 0 0 0
649 14 0 0 0 0 0 0 28 28 30
650 0 0 0 0 0 19 19 19 20 23
30 30 30 30 40 40 40 50 50 50
651 10 0 0 0 0 0 0 30 30 30
1 1 2 3 4 16 17 18 19 20
652 0 0 12 0 0 22 0 0 34 32
653 0 0 12 1 2 23 3 3 33 23
654 3 0 6 8 15 22 4 3 31 8
680 1 1 7 1 13 18 21 36 1 1
681 0 7 9 17 3 3 4 3 22 32
682 0 1 12 2 2 23 3 2 33 22
0 0 0 13 0 0 21 23 25 28
683 4 8 12 16 20 0 0 0 20 20
684 22 0 0 0 0 0 0 24 26 28
2 3 5 8 10 13 14 15 14 15
685 1 3 5 7 8 10 12 14 20 20
686 0 0 0 0 0 0 25 25 25 25
687 0 0 0 0 20 20 20 20 0 20
688 5 10 12 15 16 20 22 0 0 0
689 5 10 10 0 0 0 0 25 25 25
0 0 2 2 1 20 26 26 20 4
690 2 2 2 2 2 2 17 23 23 25
691 0 0 0 14 17 20 23 26 0 0
4 5 8 10 13 2 26 30 3 3
692 0 0 10 2 3 22 3 3 32 25
693 0 5 0 10 10 5 0 18 26 26
694 2 2 2 7 5 15 13 19 18 17
697 0 0 0 0 0 0 23 24 26 27
698 0 0 0 0 0 20 20 20 20 20
699 7 0 0 0 0 0 0 30 31 32
1 3 5 8 9 13 16 16 19 0
700 0 0 0 10 12 19 22 0 0 37
701 0 0 1 2 6 20 22 1 24 24
702 1 1 1 1 1 1 23 23 24 24
719 0 0 0 0 0 20 20 20 20 20
720 0 0 9 0 0 0 0 30 31 30
721 4 4 0 0 0 0 0 32 30 30
0 2 2 11 4 15 2 17 4 24
722 1 17 1 18 1 19 1 20 1 21
723 3 4 6 8 10 17 24 28 0 0
724 1 2 3 1 2 2 2 28 29 30
743 0 0 0 0 0 16 20 20 20 24
744 3 5 7 13 0 20 23 0 0 29
745 0 0 0 0 0 15 20 20 20 25
2 2 12 9 2 20 27 20 2 2
746 1 0 2 5 12 17 25 5 1 32
747 8 0 0 0 0 0 0 27 30 35
748 1 3 0 4 3 17 23 0 23 26
754 6 9 10 11 14 12 11 10 9 8
755 0 0 0 17 21 0 0 0 32 30
756 2 3 3 8 13 6 26 31 4 4
1 16 1 1 1 3 20 2200 27 28
757 1 10 10 1 1 2 19 3 27 26
758 3 3 5 6 8 12 14 16 17 16
759 0 0 0 0 18 19 20 21 0 22
764 4 5 5 5 7 9 16 15 18 16
765 0 5 6 0 0 22 26 0 0 41
766 2 3 5 10 12 16 19 21 11 1
3 4 6 8 12 13 14 17 13 11
767 9 0 0 0 0 0 0 30 31 30
768 2 2 4 7 9 17 11 22 15 11
769 3 0 1 1 9 10 17 1 25 33
0 0 4 0 0 0 19 19 19 19
770 0 0 0 0 25 25 25 0 0 25
5 0 0 0 0 0 0 31 32 42
0 0 4 4 6 6 10 20 30 30
771 0 0 0 9 14 0 19 10 22 26
772 10 10 10 10 10 14 16 20 0 0
773 1 7 10 10 15 15 20 20 1 1
789 4 5 4 6 12 22 21 3 18 5
790 1 2 3 6 9 12 14 18 18 17
791 3 5 8 10 13 1 26 30 2 2
0 2 2 2 4 4 17 20 23 26 30
792 4 5 6 1 1 1 1 24 27 30
793 0 0 0 3 11 14 17 20 18 17
794 0 2 4 8 9 12 15 19 19 12
800 0 0 5 7 7 10 11 20 20 20
801 0 0 12 1 1 22 3 3 33 25
802 0 0 10 16 0 20 25 29 0 0
0.1 0.1 10.1 15.1 0 20.2 25.1 29.3 0 0
803 0 0 6 0 0 22 22 25 25 0
804 1 2 8 10 15 22 5 4 9 24
805 5 0 0 0 0 0 0 25 30 40
806 2 4 6 9 11 14 16 19 19 0
807 0 0 0 0 0 28 0 36 36 0
808 0 0 11 0 0 7 7 7 34 34
0 0 0 0 17 22 0 29 33 0
809 0 7 11 16 0 0 0 0 35 31
810 3 3 5 5 0 20 20 21 0 23
0 0 2 14 18 2 3 3 32 36
0 7 0 0 0 0 18 0 25 52
811 4 0 0 0 0 0 0 28 32 36
812 0 0 2 8 2 15 3 28 7 35
813 2 3 6 6 6 6 6 6 33 26
858 0 1 11 2 2 1 22 32 5 24
859 4 5 7 9 12 24 26 2 5 6
860 0 5 7 9 12 14 16 0 19 18
1 2 5 9 9 14 15 14 15 14
0 0 0 0 0 18 20 22 20 18
861 2 2 18 4 2 19 3 4 20 26
862 8 9 12 14 16 18 20 1 1 1
863 0 0 0 0 0 100 0 0 0 0
871 1 1 1 2 2 10 10 21 26 26
872 10 10 10 10 10 10 15 15 10 0
873 0 1 1 15 18 1 3 2 35 24
5 5 9 11 0 0 20 0 20 20
874 0 0 0 5 15 17 20 21 22 0
875 1 3 5 7 9 11 13 15 17 19
876 10 0 0 0 0 0 0 30 30 30
877 3 5 6 8 11 14 15 0 19 19
878 6 0 0 4 0 10 0 31 31 18
879 1 1 1 1 14 17 26 3 34 2
1 1 1 8 10 13 14 15 15 23
880 4 4 4 8 15 15 15 20 15 0
881 0 1 11 1 1 22 3 3 34 24
882 2 3 4 9 19 19 1 1 21 21
883 0 7 9 17 24 2 8 8 0 25
884 2 5 8 1 10 2 17 3 26 26
0 0 0 0 14 15 0 23 24 25
885 0 0 0 0 15 20 0 28 37 0
886 8 0 0 0 0 0 0 27 31 34
887 0 0 0 8 12 0 17 20 21 22
891 10 10 12 14 16 18 20 0 0 0
892 6 1 1 1 1 1 1 30 30 28
893 2 4 4 5 10 15 20 0 20 20
2 1 2 2 2 17 19 1 27 26
3 4 6 8 10 12 15 17 14 12
894 2 2 4 6 6 14 16 0 24 26
895 8 8 8 14 17 20 25 0 0 0
896 4 4 6 8 8 15 15 6 18 16
903 5 7 9 11 15 21 25 2 2 3
904 0 2 3 7 14 16 17 18 3 20
905 2 2 2 2 2 2 0 29 30 29
0 0 0 0 0 0 18 15 22 46
906 4 0 0 0 0 0 0 32 32 32
907 3 4 7 10 13 2 27 31 1 2
908 3 3 6 2 2 19 9 22 13 21
909 0 2 2 3 16 0 19 22 5 31
910 1 0 0 0 6 0 10 21 29 33
911 5 0 0 0 0 0 0 28 32 35
5 1 1 1 1 1 1 30 30 30
912 2 8 2 13 18 2 2 23 28 2
913 0 0 1 2 12 22 3 22 33 5
914 2 3 3 5 10 13 14 26 13 11
936 3 3 5 6 11 13 24 3 29 3
937 0 5 7 12 12 21 1 31 4 7
938 0 0 0 5 15 8 4 13 30 25
939 6 4 6 9 14 14 1 33 7 6

70
riddler-castles/castle-solutions-5.csv
View File

@@ -16,7 +16,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,2,2,1,1,20,30,30,3,3,3,3
0,5,6,0,0,13,15,17,19,0,23,0,2
0,0,0,0,0,0,1,1,15,16,20,22,25
1,1,2,2,2,15,15,15,15,0,0,0,31
1,1,3,2,2,15,15,15,15,0,0,0,31
1,1,5,2,2,13,13,13,13,2,2,2,31
1,1,3,1,1,13,14,15,16,1,1,1,32
@@ -35,7 +34,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,1,5,3,7,5,9,7,11,9,14,10,17
1,2,3,4,6,7,8,9,10,11,12,13,14
1,3,4,6,8,9,11,12,14,15,17,0,0
2,0,6,0,10,0,14,0,18,1,22,1,24
1,1,1,2,3,5,7,11,15,18,22,12,2
1,2,3,4,6,7,8,9,10,11,12,13,14
1,1,1,1,1,12,1,16,18,1,22,24,1
@@ -63,7 +61,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,2,2,4,11,11,25,26,14,3,2
0,0,0,8,2,2,2,13,17,2,2,31,21
1,1,2,2,3,3,3,15,20,20,20,5,5
2,0,0,0,9,10,11,13,7,23,0,26,0
2,0,0,0,9,10,11,12,7,23,0,26,0
0,0,0,0,0,0,2,2,2,15,19,33,27
0,0,0,1,1,10,11,1,1,24,22,28,1
@@ -90,7 +87,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,1,3,5,3,6,7,16,29,12,6,12
8,9,3,5,6,0,7,15,1,10,11,12,13
0,0,0,2,4,7,10,12,13,15,17,18,2
1,1,1,1,1,2,3,5,8,13,21,34,29
0,0,0,16,16,0,17,0,17,17,17,0,0
4,0,0,0,0,0,16,16,16,23,23,1,1
0,4,6,0,11,13,0,17,0,22,0,27,0
@@ -102,7 +98,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,1,7,8,9,11,13,14,16,17,1
1,2,2,3,5,4,4,5,2,21,19,17,15
0,0,0,0,0,0,0,0,0,23,24,26,27
3,3,3,3,3,3,0,15,16,0,21,21,0
0,0,0,2,3,4,7,9,12,13,17,17,16
5,6,7,8,9,11,12,13,14,15,0,0,0
10,10,10,10,10,10,10,10,10,10,0,0,0
@@ -120,12 +115,10 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,0,12,1,17,19,0,23,27,1
0,0,6,0,0,0,11,0,0,0,23,27,33
0,0,8,0,9,10,2,2,15,3,22,28,1
2,7,10,4,2,4,3,11,12,11,3,15,12
0,0,0,0,0,13,0,13,13,0,30,31,0
1,1,1,3,4,5,8,13,21,31,2,4,6
2,4,4,8,8,8,2,12,16,16,2,16,2
0,2,5,2,3,6,4,1,12,23,6,9,27
1,0,0,0,0,0,0,0,3,22,24,27,24
0,1,0,1,0,13,15,0,0,21,23,26,0
2,3,3,0,0,1,15,17,20,21,16,1,1
0,0,3,3,3,7,9,10,11,12,13,14,15
@@ -136,14 +129,10 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,3,3,1,10,11,13,14,16,3,19,3,3
0,0,0,0,0,0,0,0,0,19,24,30,27
0,0,4,0,0,8,11,15,0,4,0,32,26
10,10,9,8,7,6,2,6,6,8,9,10,10
10,10,9,8,7,6,2,6,6,8,9,10,10
10,10,9,8,7,6,2,6,6,8,9,10,10
2,1,1,1,3,10,6,11,1,16,20,22,6
0,1,1,3,6,10,16,3,3,21,8,23,5
2,3,4,5,1,1,2,8,9,11,15,19,20
1,1,1,2,2,2,2,5,6,15,15,20,28
2,2,3,5,1,1,1,14,1,19,24,1,28
1,1,1,1,1,1,10,12,1,14,16,21,20
0,0,0,0,3,4,1,1,1,21,15,28,26
1,2,3,4,5,6,7,9,10,11,13,14,15
@@ -153,7 +142,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,5,0,0,15,15,0,20,20,25,0,0
1,2,3,4,5,7,8,9,10,11,12,13,15
1,1,1,10,1,15,1,1,1,25,21,21,1
2,2,2,2,2,9,10,2,15,2,22,27,2
7,7,8,9,10,12,13,14,1,16,1,1,1
1,1,1,1,1,1,1,1,1,20,22,24,25
0,1,0,0,9,5,0,4,27,5,9,21,19
@@ -170,7 +158,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,6,6,3,3,3,5,6,6,30,32
0,0,0,4,8,1,5,2,6,5,7,30,32
0,0,0,3,6,1,5,1,8,5,7,32,32
2,4,0,2,14,1,21,1,10,2,23,2,22
2,3,4,5,7,8,9,10,11,12,13,14,2
1,1,4,6,8,9,10,11,13,15,16,3,3
0,0,0,8,0,12,0,0,0,0,26,27,27
@@ -179,7 +166,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
6,6,8,8,8,8,8,8,8,8,8,8,8
0,0,0,0,0,0,0,0,20,20,20,20,20
1,0,2,2,5,3,15,18,22,24,2,2,4
1,2,3,4,5,7,8,9,10,11,12,13,14
2,2,3,5,7,9,13,1,1,24,27,3,3
2,2,1,1,1,3,10,12,15,19,30,2,2
3,3,3,0,10,0,11,12,21,1,34,1,1
@@ -191,7 +177,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,2,2,2,2,2,2,2,2,2,26,26,28
0,0,0,0,0,0,0,14,17,21,23,25,0
2,12,1,4,6,1,19,10,5,13,6,11,10
0,2,0,3,3,1,15,10,20,15,5,28,1
2,3,3,3,3,8,8,8,12,12,12,12,14
0,0,0,0,0,0,0,0,0,20,25,25,30
0,0,0,0,1,1,1,1,1,14,26,27,28
@@ -205,7 +190,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,5,3,3,8,9,10,10,11,25,4,4,5
3,0,2,2,2,11,13,15,16,26,3,3,4
2,0,0,0,5,13,14,15,16,17,18,0,0
8,11,4,8,7,11,8,9,4,6,9,5,6
2,3,2,6,2,14,6,11,10,7,12,13,12
1,0,7,6,11,9,13,15,13,11,9,4,1
1,1,1,2,3,5,7,9,12,15,19,25,0
@@ -229,11 +213,9 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,4,5,6,8,8,8,8,8,9,10,11,12
1,1,0,0,3,11,7,9,7,7,16,17,21
2,2,2,2,6,7,8,9,10,26,26,0,0
0,0,0,0,0,5,5,0,0,26,24,23,22
1,1,4,10,12,14,16,18,20,1,1,1,1
0,3,0,6,0,11,15,18,21,26,0,0,0
0,0,0,1,1,6,6,2,1,26,26,29,2
0,0,1,2,2,6,7,9,15,20,20,20,2
0,0,0,0,0,0,0,5,5,12,24,26,28
0,0,0,0,0,0,0,0,0,20,22,29,29
0,0,0,0,0,0,1,1,1,23,23,26,25
@@ -245,21 +227,10 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,2,5,9,7,8,14,7,16,9,13,8
0,1,4,3,3,6,7,7,18,19,14,2,16
1,2,3,4,5,6,7,8,10,12,13,14,15
12,12,42,32,9,4,5,6,1,13,12,12,2
2,2,3,3,5,5,7,9,13,14,14,13,10
0,1,2,1,5,0,3,15,17,20,13,23,0
1,1,3,5,7,10,12,15,16,2,3,3,22
0,0,0,1,1,1,7,11,12,13,14,15,16
1,2,3,4,6,7,8,9,10,11,12,13,14
0,0,0,1,1,5,9,10,11,12,13,14,15
0,0,0,1,1,1,1,12,13,14,15,16,17
0,0,0,1,1,1,1,7,14,15,16,17,18
0,0,10,11,0,12,13,14,15,16,0,0,0
0,0,8,8,0,13,14,15,16,17,0,0,0
0,0,5,6,0,14,15,16,17,18,0,0,0
0,0,10,11,12,0,13,14,15,16,0,0,0
0,0,9,10,11,0,13,15,16,17,0,0,0
0,0,7,8,9,0,13,16,17,18,0,0,0
0,0,10,11,12,0,15,16,17,19,0,0,0
0,0,10,11,12,15,16,17,0,0,0,0,19
1,1,1,1,1,15,15,15,15,15,16,2,2
@@ -268,7 +239,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,2,2,2,2,2,2,3,3,20,20,20,20
0,0,0,0,0,0,0,0,0,0,0,0,100
7,7,7,7,7,7,7,7,7,8,9,10,10
1,1,1,1,20,20,20,17,5,1,5,1,4
1,2,3,4,6,7,8,9,10,11,12,13,14
1,1,1,2,2,2,7,10,14,18,21,18,3
0,0,0,21,0,0,0,0,0,0,79,0,0
@@ -292,15 +262,12 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
6,7,12,12,7,3,10,1,3,11,1,16,11
1,1,1,1,1,1,1,6,11,16,21,16,23
0,0,0,0,0,11,13,16,2,3,3,29,23
1,4,3,0,0,0,16,0,18,0,26,32,1
1,1,1,1,1,1,1,1,14,15,17,27,19
1,1,7,8,9,10,11,12,1,19,0,21,0
0,0,0,0,7,1,16,1,17,1,1,27,29
2,4,6,8,10,14,16,20,0,0,0,8,12
0,0,0,0,1,1,1,1,14,14,14,40,14
6,5,9,7,5,13,14,6,5,5,14,7,5
1,1,7,3,3,3,16,17,4,4,4,32,5
0,0,0,0,8,1,2,15,2,22,24,26,1
0,1,2,3,6,7,8,10,12,13,13,13,12
1,1,2,4,7,9,10,12,15,16,18,3,2
1,2,3,4,6,7,8,9,10,11,12,13,14
@@ -325,7 +292,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,2,2,5,2,5,2,8,5,15,16,17,19
0,1,1,1,2,2,16,17,18,18,2,20,2
0,0,0,0,0,0,0,0,12,19,21,23,25
1,2,3,4,5,6,7,8,9,10,13,13,20
1,1,5,7,2,2,12,15,19,3,26,3,4
0,1,1,2,2,2,2,3,4,5,31,45,2
1,1,1,1,1,1,1,6,6,20,40,20,1
@@ -345,7 +311,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,3,3,9,10,11,12,13,0,36,0,0,0
0,2,3,5,7,2,10,11,3,12,25,5,15
0,3,0,0,10,13,0,18,0,0,24,32,0
-1112,101,101,101,101,101,101,101,101,101,101,101,101
0,0,0,7,1,0,12,1,0,22,3,27,27
0,0,0,0,4,14,12,1,2,2,18,27,20
1,1,1,1,2,2,3,3,4,20,20,21,21
@@ -381,7 +346,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,2,2,2,2,2,2,10,15,20,20,20,1
1,0,0,0,11,11,11,11,11,11,11,11,11
0,0,0,0,0,0,15,16,19,23,0,27,0
2,2,2,2,2,4,6,8,10,13,15,17,19
0,1,1,11,11,11,11,11,11,11,21,0,0
10,10,10,10,10,10,10,10,10,10,0,0,0
1,1,1,1,1,1,1,1,1,19,20,26,26
@@ -390,11 +354,9 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
13,12,11,10,9,8,7,6,5,4,3,2,10
1,1,1,7,9,11,13,16,18,20,1,1,1
1,1,1,7,9,11,13,16,18,20,1,1,1
0,1,6,1,10,2,14,16,18,3,23,3,4
0,1,6,1,10,2,14,16,18,3,23,3,3
0,0,0,0,0,0,10,11,15,16,19,18,11
2,1,2,6,8,8,8,6,10,8,12,11,18
0,0,0,0,0,0,0,0,0,26,26,25,22
2,2,2,2,2,2,2,25,25,30,2,2,2
1,1,1,3,5,6,6,11,13,15,17,19,2
0,0,0,0,0,0,0,0,0,25,25,25,25
@@ -425,7 +387,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,14,0,0,20,0,21,22,23,0
0,0,0,0,5,5,10,15,30,15,10,5,5
0,0,8,3,10,10,14,1,1,1,1,28,23
0,0,0,0,0,0,0,0,0,0,0,0,0
1,1,1,3,6,9,10,6,7,15,15,16,10
2,2,2,2,2,2,2,2,8,21,26,21,8
1,1,1,1,1,1,1,1,1,16,21,25,29
@@ -436,7 +397,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,3,5,7,10,12,2,15,2,3,17,19,3
4,1,1,0,0,8,14,15,17,18,20,1,1
0,0,0,0,3,1,1,16,17,27,3,3,29
0,1,1,0,0,13,4,11,15,19,14,15,10
1,1,4,6,8,10,13,16,18,20,1,1,1
0,0,0,0,0,0,12,15,20,24,0,29,0
0,0,0,0,0,0,0,0,0,22,24,26,28
@@ -468,13 +428,11 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,3,4,5,6,7,8,9,19,0,0,37,0
1,1,1,1,1,1,1,1,1,1,29,30,31
0,0,0,7,1,0,0,1,10,26,26,28,1
10,11,12,13,7,7,10,10,3,2,1,12,3
1,1,1,3,4,5,5,8,10,15,17,19,11
0,2,3,3,0,6,10,15,18,18,15,5,5
0,0,0,0,0,0,0,0,0,23,24,26,27
4,2,2,1,1,2,14,12,15,8,4,18,17
0,0,0,1,6,9,14,15,15,16,16,4,4
1,1,1,1,1,1,1,0,1,20,20,25,25
0,0,1,1,1,13,3,16,18,0,23,24,0
1,1,1,2,2,2,2,2,2,14,15,22,34
2,2,2,2,5,8,11,13,15,17,19,2,2
@@ -485,7 +443,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,2,6,8,2,2,3,18,20,22,7,8
4,0,0,0,11,12,13,14,20,26,0,0,0
1,2,2,2,6,2,3,14,18,25,16,4,5
0,0,0,0,5,0,0,0,0,19,19,19,19
1,1,2,1,3,7,11,11,10,13,13,14,13
0,0,0,0,0,0,0,0,0,0,0,50,50
1,1,2,4,4,6,8,10,12,16,14,12,10
@@ -499,7 +456,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,1,9,10,8,10,10,14,14,13,11
1,1,2,4,4,4,4,9,11,12,16,16,16
1,1,6,8,1,12,14,16,18,20,1,1,1
1,1,1,5,5,6,6,8,10,12,12,15,17
0,0,0,0,0,0,0,0,0,25,25,25,25
0,0,0,0,0,0,0,15,20,20,20,25,0
0,0,0,0,0,0,20,20,20,20,0,20,0
@@ -509,11 +465,9 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,1,2,2,9,11,14,3,3,3,26,26
0,0,0,1,2,2,12,15,15,22,2,27,2
2,4,4,1,3,3,3,18,3,24,30,3,2
0,1,1,2,3,4,5,7,10,24,31,13,1
2,4,5,7,9,11,13,15,16,18,0,0,0
2,2,2,2,9,2,2,9,2,12,27,27,2
6,7,8,9,11,12,13,14,1,16,1,1,1
2,2,2,2,2,2,2,2,2,18,18,18,18
2,2,2,2,2,2,2,2,2,20,20,21,21
0,0,1,1,2,1,1,2,2,20,20,20,30
0,0,0,0,0,0,6,4,14,10,22,18,26
@@ -608,7 +562,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
6,6,6,7,8,8,8,8,8,8,9,9,9
5,5,5,5,5,10,11,11,2,35,2,2,2
1,2,2,2,2,2,12,15,17,19,20,3,3
1,1,1,2,0,0,9,13,18,22,27,0,0
1,1,1,1,1,1,1,1,80,9,1,1,1
2,2,3,6,7,8,8,11,11,12,12,9,9
2,2,2,2,2,6,10,15,15,2,2,20,20
@@ -627,7 +580,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,0,7,10,2,3,24,26,28,0
3,6,9,13,10,7,4,7,10,13,9,6,3
0,0,0,2,2,6,6,2,2,26,26,26,2
5,5,5,5,5,20,5,20,5,5,5,5,5
0,0,3,12,2,1,4,1,15,22,10,15,15
2,2,2,2,12,12,13,14,16,16,3,3,3
0,0,0,0,0,0,0,1,2,20,23,27,27
@@ -647,7 +599,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,1,1,9,4,8,7,6,8,11,13,15,17
1,2,4,6,4,8,13,13,2,20,15,5,7
0,1,5,7,2,2,10,14,2,2,14,24,17
4,4,3,10,11,5,12,1,7,4,6,16,16
0,0,0,0,9,14,10,1,2,1,15,28,20
0,0,0,1,1,8,9,2,18,2,33,2,24
2,4,5,4,7,9,9,9,11,10,10,10,10
@@ -661,12 +612,10 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,3,5,6,8,10,12,14,16,20,1,3
0,0,0,1,1,1,1,1,19,19,19,19,19
2,0,0,0,14,14,14,15,15,26,0,0,0
3,2,2,3,4,5,10,12,147,16,20,4,5
0,0,0,11,0,11,12,12,0,27,27,0,0
3,2,2,5,3,4,4,5,13,17,18,22,2
0,1,2,4,1,10,15,1,14,2,4,22,24
0,0,0,0,0,0,0,0,0,25,25,25,25
4,5,6,7,9,12,15,17,0,26,0,0,0
1,1,1,1,1,12,14,1,18,1,22,1,26
13,13,18,6,1,7,13,5,6,7,2,0,9
2,4,6,8,10,12,14,13,11,8,6,4,2
@@ -679,7 +628,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
3,4,6,9,11,13,15,17,1,21,0,0,0
1,1,2,3,3,3,3,8,8,12,22,22,12
2,0,0,5,6,7,8,9,10,11,13,14,15
2,3,4,5,6,8,9,10,11,12,13,14,1
1,2,2,3,7,7,13,7,11,8,29,5,5
0,0,0,9,10,11,12,13,14,15,16,0,0
0,0,1,1,11,1,15,2,17,2,1,22,27
@@ -688,7 +636,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
4,2,2,2,3,7,9,11,15,20,25,0,0
2,4,6,8,10,12,14,21,23,0,0,0,0
0,2,0,0,0,0,0,0,10,20,0,34,34
0,0,0,6,6,8,10,12,17,18,19,5,5
1,1,5,2,10,3,1,18,20,1,11,12,15
1,2,7,5,12,8,10,8,16,14,3,11,3
1,1,1,2,5,5,10,15,15,15,10,10,10
@@ -716,11 +663,9 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,0,0,2,2,0,0,24,24,24,24
0,0,4,6,2,8,8,7,13,10,17,15,10
0,1,0,4,8,2,11,3,3,12,21,10,25
1,1,1,5,1,12,12,18,20,1,1,25,1
2,2,2,2,2,2,14,12,14,5,18,20,5
2,3,3,4,5,8,12,12,12,13,13,2,11
1,1,4,5,5,10,6,15,9,6,7,15,16
0,0,0,1,1,13,1,16,18,25,1,1,25
1,1,1,1,1,1,4,20,20,20,26,2,2
0,0,0,0,0,0,10,10,10,12,14,18,26
1,1,1,1,1,1,1,1,7,15,20,25,25
@@ -771,7 +716,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,1,1,1,1,18,18,18,21,17,1
0,0,0,1,12,1,1,17,1,19,22,26,0
1,1,1,1,11,11,11,12,22,1,26,1,1
3,4,3,12,16,13,8,11,7,4,6,6,6
0,0,0,0,2,10,11,11,1,3,2,34,26
8,13,6,8,6,1,14,3,13,2,11,6,9
2,3,4,5,6,7,7,8,10,11,14,12,11
@@ -781,15 +725,12 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,1,1,1,13,16,16,16,16,16,1
1,1,1,1,1,1,1,1,12,20,20,20,20
1,1,6,1,7,1,20,1,20,1,20,1,20
7,7,7,7,7,7,7,7,7,7,7,19,7
1,2,3,3,3,4,5,9,12,15,15,15,13
1,1,1,5,5,5,1,1,1,1,26,26,26
2,2,2,4,4,2,2,2,2,20,20,20,20
1,2,2,3,3,4,11,11,16,16,16,14,1
0,0,0,9,1,1,1,14,1,18,23,2,30
2,3,3,3,5,5,9,9,9,12,13,13,14
1,1,1,1,2,7,0,12,16,21,0,18,20
0,0,0,15,0,0,14,16,16,27,27,0,0
1,1,1,1,3,3,20,2,22,2,22,2,20
0,0,3,4,0,1,1,11,13,26,3,35,3
3,4,5,6,7,8,9,10,11,12,9,8,8
@@ -799,7 +740,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
0,0,0,7,8,10,12,14,16,18,15,0,0
15,1,1,1,15,1,15,1,16,1,16,1,16
0,0,5,7,1,13,1,17,3,2,1,24,26
0,0,1,1,2,3,4,5,5,32,33,6,6
1,2,3,4,6,7,8,9,10,11,12,13,14
0,0,0,6,6,6,6,6,6,26,26,6,6
0,0,0,1,1,3,3,3,15,21,24,27,2
@@ -834,7 +774,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,1,1,1,1,18,18,18,18,19,2
5,5,7,7,9,9,8,8,8,8,8,9,9
3,0,5,0,7,0,14,0,21,0,24,26,0
1,1,1,1,3,9,12,10,16,16,18,12,2
0,0,1,0,1,0,16,13,14,22,0,32,1
0,0,1,1,1,9,3,18,18,1,28,18,2
0,0,0,3,4,13,15,4,4,16,16,20,5
@@ -850,7 +789,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,0,0,0,0,16,16,16,16,17,18,0,0
8,1,1,1,1,1,17,17,17,17,17,1,1
0,1,2,6,9,10,12,14,17,26,1,1,1
0,2,0,3,0,6,7,8,9,15,15,15,15
1,1,1,1,1,22,23,23,22,1,1,1,2
0,1,1,3,4,8,12,11,14,2,1,17,26
1,2,1,2,4,9,11,11,13,21,21,2,2
@@ -876,7 +814,6 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
2,0,0,0,0,7,8,9,10,16,16,16,16
2,2,2,7,8,2,11,13,17,18,5,6,7
1,1,3,4,9,10,12,14,16,19,3,3,5
0,1,1,3,7,7,7,15,14,15,15,15,2
0,0,0,0,0,0,0,0,0,25,25,25,25
5,5,5,5,5,5,5,5,5,55,0,0,0
0,0,0,0,0,2,12,13,16,21,4,26,6
@@ -895,12 +832,9 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,3,3,8,13,14,0,0,0,17,0,20,21
0,0,0,0,13,15,15,2,4,3,3,25,20
1,2,2,3,4,6,6,11,11,11,11,16,16
9,9,10,10,10,10,10,10,2,13,2,2,2
0,0,1,0,1,0,5,0,1,28,20,25,19
1,2,3,4,6,7,8,9,10,11,12,13,15
4,4,4,4,4,4,5,15,15,26,5,5,5
0,0,0,0,0,10,10,0,0,15,20,25,20
2,2,2,2,2,12,16,17,18,19,3,3,3
2,3,1,5,2,8,7,11,15,15,15,1,15
7,7,7,7,8,8,8,8,8,8,8,8,8
0,0,0,0,0,0,0,16,16,17,17,17,17
@@ -931,14 +865,12 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
6,6,6,5,3,11,14,3,4,6,9,7,20
0,1,1,1,1,1,1,1,1,20,22,24,26
1,2,3,4,5,6,7,9,10,11,13,14,15
0,1,2,3,5,6,6,7,10,12,14,16,17
0,0,0,0,0,16,18,20,22,24,0,0,0
0,1,2,3,4,5,11,12,13,15,16,17,1
0,1,3,5,6,7,9,11,13,14,15,16,0
0,0,0,0,0,0,0,0,0,31,23,23,23
0,0,0,1,1,1,12,14,16,21,3,28,3
1,2,3,4,4,0,0,0,0,24,28,34,0
2,3,3,9,3,5,13,19,24,3,6,5,6
0,0,0,0,0,0,0,0,0,22,24,26,28
2,2,2,2,1,1,12,14,16,22,24,1,1
0,0,0,0,0,0,0,0,0,25,25,25,25
@@ -961,4 +893,4 @@ Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9
1,1,1,1,1,1,1,1,1,23,22,23,23
2,2,5,7,10,9,15,2,12,16,16,2,2
1,2,3,4,5,7,8,9,10,11,12,13,15
1,1,1,2,2,3,10,8,5,5,30,30,2
1,1,1,2,2,3,10,8,5,5,30,30,2
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21 1 1 3 1 1 13 14 15 16 1 1 1 32
34 2 1 5 3 7 5 9 7 11 9 14 10 17
35 1 2 3 4 6 7 8 9 10 11 12 13 14
36 1 3 4 6 8 9 11 12 14 15 17 0 0
2 0 6 0 10 0 14 0 18 1 22 1 24
37 1 1 1 2 3 5 7 11 15 18 22 12 2
38 1 2 3 4 6 7 8 9 10 11 12 13 14
39 1 1 1 1 1 12 1 16 18 1 22 24 1
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792 1 1 1 1 1 22 23 23 22 1 1 1 2
793 0 1 1 3 4 8 12 11 14 2 1 17 26
794 1 2 1 2 4 9 11 11 13 21 21 2 2
814 2 0 0 0 0 7 8 9 10 16 16 16 16
815 2 2 2 7 8 2 11 13 17 18 5 6 7
816 1 1 3 4 9 10 12 14 16 19 3 3 5
0 1 1 3 7 7 7 15 14 15 15 15 2
817 0 0 0 0 0 0 0 0 0 25 25 25 25
818 5 5 5 5 5 5 5 5 5 55 0 0 0
819 0 0 0 0 0 2 12 13 16 21 4 26 6
832 1 3 3 8 13 14 0 0 0 17 0 20 21
833 0 0 0 0 13 15 15 2 4 3 3 25 20
834 1 2 2 3 4 6 6 11 11 11 11 16 16
9 9 10 10 10 10 10 10 2 13 2 2 2
835 0 0 1 0 1 0 5 0 1 28 20 25 19
1 2 3 4 6 7 8 9 10 11 12 13 15
836 4 4 4 4 4 4 5 15 15 26 5 5 5
837 0 0 0 0 0 10 10 0 0 15 20 25 20
2 2 2 2 2 12 16 17 18 19 3 3 3
838 2 3 1 5 2 8 7 11 15 15 15 1 15
839 7 7 7 7 8 8 8 8 8 8 8 8 8
840 0 0 0 0 0 0 0 16 16 17 17 17 17
865 6 6 6 5 3 11 14 3 4 6 9 7 20
866 0 1 1 1 1 1 1 1 1 20 22 24 26
867 1 2 3 4 5 6 7 9 10 11 13 14 15
0 1 2 3 5 6 6 7 10 12 14 16 17
868 0 0 0 0 0 16 18 20 22 24 0 0 0
869 0 1 2 3 4 5 11 12 13 15 16 17 1
870 0 1 3 5 6 7 9 11 13 14 15 16 0
871 0 0 0 0 0 0 0 0 0 31 23 23 23
872 0 0 0 1 1 1 12 14 16 21 3 28 3
873 1 2 3 4 4 0 0 0 0 24 28 34 0
2 3 3 9 3 5 13 19 24 3 6 5 6
874 0 0 0 0 0 0 0 0 0 22 24 26 28
875 2 2 2 2 1 1 12 14 16 22 24 1 1
876 0 0 0 0 0 0 0 0 0 25 25 25 25
893 1 1 1 1 1 1 1 1 1 23 22 23 23
894 2 2 5 7 10 9 15 2 12 16 16 2 2
895 1 2 3 4 5 7 8 9 10 11 12 13 15
896 1 1 1 2 2 3 10 8 5 5 30 30 2

53
riddler-castles/castle-solutions.csv
View File

@@ -10,7 +10,6 @@ Notice that the key is not beating a randomly generated opponent, but beating th
The method I've devised will beat ""10s all around"" and has a shot at beating folks who go all in on another strategy. I expect to get beaten a lot, though, by folks who pick a different set of castles they want to win. Oh well. I've already spent too long on this. If nothing else, I've given you another weird data point! :)"
26,26,26,16,1,1,1,1,1,1,The top 3 are necessary for a majority and the 4th is also needed. The rest are filled in case my opponent leaves them empty.
26,5,5,5,6,7,26,0,0,0,"Most people will focus on high number, but castles 1-7 equal 28 points, enough to win. Realizing that someone may attempt to take castles 8-10 and castle 1, i redeployed troops to castle 1 to thwart that strategy. "
25,0,0,0,0,0,0,25,25,25,"The total points up for grabs is 55, and to win the war I need 28 points. I want to get 28 points by using the least number of castles, so I can put more soldiers in each castle and increase my odds of winning that castle. I can earn 28 points by winning castles 1, 8, 9, and 10. So I will put 25 soldiers each in castles 1, 8, 9, and 10 to maximize my odds of winning each of those castles simultaneously."
25,0,0,0,0,0,0,25,25,25,Submission #4. A variation of my third submission. Equally divided among just enough points to win. (Not convinced this will win either).
25,0,0,0,0,0,0,25,25,25,"There are 55 points up for grabs, so 28 are needed to win. Winning castles 1,8,9,10 are the fewest number of castles needed reach 28 points. Castle 1 is as important as castle 10 for getting to 28 points. "
@@ -28,7 +27,6 @@ But this won't work because the other castles will be undefended and an enemy co
So Castle 1 is defended by 19 soldier to be able to defended the rest of the castles with 1 soldier.
Running a simulation with a random number generator gives me a 98% chances of winning with this combination, althought it is sunday night and I might have made some fundamental mistake in the code"
18,18,2,18,18,18,2,2,2,2,To disrupt strategies that rely on lower value castles.
18,16,14,12,10,8,6,4,2,1,
16,16,16,16,16,16,1,1,1,1,"Evenly distributing troops at 6 castles gives me a great chance to win a simple majority, and single troops at the remaining 4 gives me an auto win if my enemy leaves any empty. "
16,11,11,11,11,18,19,1,1,1,I can get 28 points out of 55 from the lower 7 castles so concentrate force there. Send a token soldier to the top castles in case someone tries a more extreme version of my strategy. Bias soldiers towards castles 6 and 7 because a 'aim at the higher castles' strategy is likely to still be interested in those. Send a few more to castle one because I could see a strategy of going for the top three castles and the lowest one.
15,14,14,14,14,14,15,0,0,0,"Target to win is 28 points. Concentrating deployment on highest-value castles means I need to capture 10, 9, 8 and 1 to reach target. Highest-value castles are likely to draw most troops by my opponent. So I am going to focus on capturing enough castles from the lowest value upwards until I hit the target, which is castles #1-7 inclusive. Divide troops equally, with the spares focused on 1 (crucial to the 10-9-8-1 strategy set out above) & 7 (because it is the highest value of my targeted castles)."
@@ -97,7 +95,6 @@ This strategy works against almost every strategies, especially the ones that ma
11,11,11,11,11,11,11,11,11,1,"Hopefully people divide equally, and this maximizes my chances against such players. If they do, I win 9 of 10, and lose castle 10"
11,11,11,11,11,11,11,11,11,1,Assume everyone else will over-allocate to castle 10. Sacrifice and make up points elsewhere.
11,11,11,11,11,11,11,11,11,1,
11,11,11,11,11,11,11,11,10,1,"Overloaded each castle except for 9 & 10. Put one in 10 incase someone else avoided it as a high risk castle, and took it from the 9 as it's a slightly higher risk castle."
11,2,11,11,11,2,12,36,2,2,"I assumed a whole bunch of people smarter than me were spending hours on the mathematically best way to deploy your troops, so I went with an opposite approach: Randomly guess which castles to deploy to, while aiming to gain 28/55 possible victory points. I chose castles 1,3,4,5,7,8 and weighted more heavily towards to castles worth more points. I chose 11 as a minimum so that I couldn't easily lose to someone who just put 10 troops in each castle, and 36 in castle 8 so that someone with the 1-8-9-10 strategy also wouldn't win. I also killed about 10 minutes at work, so I'm pretty happy."
11,1,12,1,15,1,19,19,20,1,Trying to maximize expected value knowing my opponent will be doing the same thing.
11,1,1,1,1,1,1,26,26,31,Go For 28 points
@@ -159,7 +156,6 @@ My chosen strategy (C: fully distributed) is likely to beat simple variants of A
Basically, this puzzle is much like the Riddler Express puzzle; both come down to the player's estimation of other player's strategies."
8,8,9,9,13,20,30,1,1,1,"with a total of 55 points available, i conceded the higher level castles and focused on the smaller castles to win the majority(spoiler: like how the electoral college went lol)"
8,8,8,8,8,25,30,3,1,1,I thought 7 was most important
8,2,11,12,17,2,21,21,2,2,"55 points are available, common strategies to get 28 may involve attempting to getting a few high scoring or many low scoring castles. 8,7,5,4,3,1 gets 28, with 2 soldiers minimum to each castle in case of uncontested/1 soldier chosen by an opponent, and avoids relying on the highest castles or too many castles"
8,2,4,11,8,14,13,9,14,17,"https://goo.gl/qwoylN
wrote this code to randomly generate 1000 'setups'
@@ -234,7 +230,6 @@ I plan to surrender the 10 and 9 pointer, only assigning 1 troop to each on the
5,7,5,7,12,11,15,13,13,12,"I wrote an R script to generate random arrangements of troops, and then I compared them against each other. My program ran very slowly, and this was the best arrangement of troops it came up with."
5,6,10,10,10,10,15,30,2,2,Focus on getting more low-value castles without totally ceding 9 & 10
5,6,7,8,12,13,14,15,20,0,"I sacrificed Castle 10, predicting that my opponent would heavily fortify it. Then I was able to increase the troops at all the other castles."
5,6,7,8,10,14,15,15,15,0,meh
5,6,7,8,9,11,12,13,14,15,This should perform well on average but is far from optimal.
5,6,7,8,9,11,12,13,14,15,"It seemed to me that the optimal strategy would be to take advantage of each weakness in my opponent's line, so something like 10 at each castle makes some sense, but I also wanted to weight the more valuable castles more heavily, so I started with a base of 5, and distributed the remaining 50 across the rest, weighted by castle value."
5,6,7,8,9,11,12,13,14,15,"It's a bit of a weighted average. I first deployed 1-10 soldiers based on point values, one to Castle 1, two to Castle 2, et cetera. That left 45 soldiers. I then distributed the rest evenly, sending 4 more soldiers to each castle, and then sending the last 5 to the top 5 castles. I figure some adversaries will be more top-heavy, and this way I might win some of the middle and lower castles and make it a close contest. This distribution would also beat those who went for a pure average 10-man-per-castle deployment."
@@ -262,7 +257,6 @@ I plan to surrender the 10 and 9 pointer, only assigning 1 troop to each on the
5,5,5,5,5,5,5,5,5,55,Played 20 test rounds with some friends and this one won the most frequently. Strong chance of winning 10 and at least 18 leftover points (17.5 for the tie). Prevents the 1 and 2 strategy on not desirable numbers.
5,5,0,0,0,0,0,30,30,30,You need a minimum of 4 castles. Want to try to ensure the top three and gives a good shot at lower.
5,2,1,9,4,10,6,20,21,22,"I took 10,000 random troop deployments, and found the winning deployment. I did that 10,000 times, to generate 10,000 good deployments. Then I generated a few million random deployments to test against those 10,000 good deplolyments -- and this one won all 10,000! I cannot understand why this worked, but I'll go for it."
5,1,2,3,4,10,6,7,8,9,
5,1,1,1,1,1,1,26,30,33,"OK, I figured that I need 28 points to win. Thus, taking castles 10, 9, 8, and 1 would suffice. First, I allot one soldier to each castle, should the enemy king omit any. With the remaining 90, I allotted them according to the proportional value of my target castles relative to the required 28 points, calculating this as, approximately 33 additional soldiers to C10, 30 to C9, 26 to C8, and 5 soldiers to C1. Having sent off my army, I prepare a huge victory parade that will have the largest crowds ever, no matter what the park service says."
5,1,1,1,1,1,1,26,30,33,"There are 55 total victory points in the game, therefore a player needs to get 28 points. I assume that my opponent will then choose a strategy that only sends troops to castles to achieve the minimum of 28 points and not send any troops to the other 27 points. Regardless of which strategy he chooses my strategy will beat any strategy that chooses to completely ignore castles."
5,1,1,1,1,1,1,25,29,35,"In order to win the war, I need to get more victory points than my opponent. With 55 total victory points at stake, I need 28 victory points to win. The top three castles are collectively worth 27 (8+9+10) points, so if I win those, I only need to win one more castle to win the war. The vast majority of my soldiers go to castles 8, 9, and 10 since they are the most valuable. I send five troops to castle 1 because I doubt most of my opponents will send many troops to the least valuable castle. I send one soldier to each of the remaining castles (2-7) just in case my opponent neglects to send any troops there. These six soldiers don't hurt me much in other areas. Overall, I think this strategy is the best way to win the race to 28 points. "
@@ -296,7 +290,6 @@ I also wanted to cover my bases a little by sending 1 troop to Castles 8, 9 and
4,7,10,13,16,19,22,2,3,4,"With 55 possible points, an army needs a total of 28 points to win. Thus, I can sacrifice 27 points. The quickest pathway to do so is to allow my opponent to take the castles worth 10, 9 and 8 points, for a total of 27 points. Therefore, I need to take all other castles in order to win. Thus, I split my troops along the other castles with equal force, assuming that my troops on Castle 1 is 7 times more valuable than my troops on Castle 7, 6 times more powerful than Castle 6, so on and so forth, as I will need 7 times as many troops to dedicate to Castle 7, as it is 7 times more powerful. It was then easy to distribute my troops along those lines, leaving 16 troops. After adding 1 troop to each Castle as extra defense, I added 4 to Castle 10, 3 to Castle 9, and 2 to Castle 8 in order to slightly defend against my own strategy. Knowing I had 9 extra troops, I applied the same logic to my three extra Castles, saying that Each Castle 8 soldier would be 10/8ths as strong as Castle 10. Then, I simply rounded in order to get my troop allocation to be as close as possible to those fractions. "
4,7,9,12,14,16,18,20,0,0,1-8 majority of points
4,6,8,12,16,21,33,0,0,0,The winner needs 28 points so I focused all my resources on towers tha will get me 28 points while avoiding the largest castles that most people would focus on.
4,6,8,10,12,14,17,19,4,5,"Concede the most valuable, try to pick up most of the rest."
4,6,7,9,11,13,15,17,18,0,"A basic strategy could be to deploy an average number of troops to each castle weighted by point value, in which case one would deploy 1.82 troops per point the castle was worth. Given that Castle 10 is the highest profile target, I expect my opponent to commit an above average number of troops to it. I submitted 0 troops to Castle 10 so they would waste any troops they committed to 10 over the average. Instead, I committed an above average number of troops to every other castle, distributing the average number of Castle 10 troops (18) over all the other castles (2 per castle)."
4,5,6,13,13,13,13,13,18,2,"Abandoned first castle since it would probably face strong opposition that could be better distributed elsewhere, then put one guy back to catch anyone who did what I thought to do, Then tried to put roughly equal soldiers at the rest since I'd need them all (besides the last couple that are worth very little)"
4,5,6,8,11,24,42,0,0,0,Trying to win 28-27
@@ -399,7 +392,6 @@ By the way it would be cool if you published not just the winner but the entire
3,5,7,9,11,13,15,17,19,1,
3,5,6,10,20,23,30,1,1,1,"There are 55 pts in the game -- if I have 28, the game is done (and I the winner). Thus I hope to win castles 1äóñ7 ... that results in 28 pts. I abandon castles 8, 9, 10 äóñ the sum of three totaling 27 pts äóñ assuming most players will seek the big numbers first. I do send one (unfortunate) solo man in the case the castle is indeed empty. If so, free pts for me! It is my hope I win out across the bottom 7 castles. Little room for error, but such is the case for most wars."
3,4,11,13,16,21,27,2,2,1,Scoring 1 to 7
3,4,9,10,14,6,11,6,9,18,I generated random troop distributions in numpy and ran tournaments with 25 distributions each. I did tiers of tournaments where the winners of 25 tournaments with random distributions were put in another round of tournaments and so on 4 times.
3,4,8,0,20,0,30,35,0,0,to not deploy forces to the most valuable castles where there would likely be the most competition. Place strength on mid value and low value targets to reach goal of 26
3,4,5,18,22,20,21,2,3,2,
3,4,5,6,7,8,22,22,22,1,"I expect many people to try hard for Castle 10, so no point in gunning for that. I put one there just in case some opponents abandon it entirely. 7, 8, and 9 together will get me most of the way to victory, so I put the bulk of my troops there, and then the remainder on the rest of the castles in diminishing order, to try to pick up the few extra points I would need."
@@ -444,7 +436,6 @@ I now need to fight it out at 7-9. I'm going to aim to beat the uniform distribu
3,3,3,3,3,11,16,21,34,3,
3,3,3,3,3,3,3,3,3,73,"""Clearly, I could not choose the wine in front of you.""
Many semi-optimal subsets use proportional allocations of troops. A configuration which slams troops into a single castle and sends 1 to the others beats many of those. 3 troops to almost all castles beats that variant and its 2 troop ""brother"" strategy. "
3,2,7,13,5,15,14,12,14,13,I ran simulations with various random troop deployments and this one came out on top in my limited sample.
3,2,7,12,5,18,10,12,13,18,"Excel random number generator matrix calculation. It was a terrible format for this, but fun to figure out. This combination came out as the most frequent winner in a smaller sample than I wanted to test."
3,2,2,2,2,2,2,28,29,28,"* Compete in the three most valuable castles, worth 27 points in total, and hope to win at least one more victory point by forfeit.
* Counter similar strategies by not going all-in on the top three, hedge by covering the remaining 28 points worth of castles with at least 2 soldiers."
@@ -453,7 +444,6 @@ Many semi-optimal subsets use proportional allocations of troops. A configuratio
3,1,1,11,13,15,1,21,23,11,"I'd like to pick my battles and win those by a little, and if I'm going to lose, lose by a lot. However, I figure some people will send zero troops to some castles, so I'll send one if it could result in an easy win. Otherwise, I just put an increasing number of troops on the castles I choose to fight for. Some numbers are designed to beat some common strategies like all 10's."
3,0,9,0,0,0,21,31,36,0,It doesnt waste troops on castles that I dont need to win
3,0,4,8,0,0,15,35,35,0,Abandon hopes of Castle 10 and put all the eggs in the basket of 7-9 + 4 or 3 and 1
3,0,0,11,0,0,26,27,30,0,I expected that it would allow me to win multiple battles without wasting troops on likely losses.
3,0,0,0,0,0,0,31,32,34,"To win the most wars you need to get >=28 out of 55 points the most often. Giving 30+ troops to each of Castles 8, 9 and 10 will hopefully guarantee you 27 points. Then 3 troops on Castle 1 hopefully gets you that one last point you need."
3,0,0,0,0,0,0,29,32,36,"There are 55 available points, so the winner needs 28. Castles 8, 9, and 10 provide 29%, 32%, and 36% (respectively) of the 28 points required. I allocated my troops according to their relative importance, and then put the last 3 on Castle 1 to grab my last needed point."
3,0,0,0,0,0,0,29,32,36,
@@ -510,7 +500,6 @@ I then roughly allocated the 100 soldiers eight ways proportionally -- sending 3
2,4,10,10,15,15,20,20,2,2,
2,4,9,0,0,0,15,15,25,30,"Assume low value castles may be lightly defended, so try to pick up 3 castles for a total of 15 soldiers. Send most resources to highest value castles, and basically hope the archfiend has wasted troops trying to overwhelm me at 4, 5 and 6,"
2,4,8,11,14,16,19,22,2,2,"I want to pick up free points against any strategy that is is only allocating 0 or 1 point to a castle, and I don't want to fight for the two most valuable castles"
2,4,8,10,20,25,25,0,0,0,"Figured folks would go for castles 8,9,10äóîbut 8+9+10=27, and 1+2+...+7=28. If I win the (presumably underlooked) first seven castles, I win the battle."
2,4,7,13,17,17,18,22,0,0,Trying to stack where others don't.
2,4,7,12,16,19,18,12,7,3,wild guess
2,4,7,9,11,13,19,35,0,0,Give up top two and win everything else
@@ -532,7 +521,6 @@ I then roughly allocated the 100 soldiers eight ways proportionally -- sending 3
2,4,6,8,10,12,14,16,18,10,I feel like castle 10 isn't worth it
2,4,6,8,10,12,14,16,18,10,
2,4,6,8,10,12,14,16,18,10,2 more than the Castle is worth (which only leaves half for Castle 10)
2,4,6,8,10,12,14,16,18,0,"Each point of the castle worth of 2 soldiers but the last one, since the enemy will try to conquer it by all means. "
2,4,6,8,10,10,12,14,16,18,No particular reason
2,4,6,8,9,11,14,17,29,0,Sacrificed the 10 castle as most people will over value this one. With 45 potential points then available an equal distribution of the 100 soldiers would put 2.2 soldiers x value of castle on each castle. I then overweighted the higher value castles some.
2,4,6,8,0,12,14,16,18,20,"I wanted to distribute my soldiers proportionally to each castle value. At two soldiers per castle point, I would need 110 soldiers, so I just dropped #5. Although it reduces my maximum to 52.5, that distribution has the advantage of faring well against very lopsided strategies... I'm guessing :)"
@@ -636,7 +624,6 @@ Soldiers were then assigned to castles based on the value of the castle. (99 Sol
I'm not a big mathematician but i like to try, and i appreciate your riddles :)"
2,4,5,7,9,11,13,14,16,19,"I attempted to pick values equivalent to the victories points value in making up 28 victory points. For example, winning castle 10 gives you 34.7% of the victory points needed to win a majority. The proportional percentage of this is about 18%. (I chose 19 because my math rounding got me 99 soldiers in battle.)"
2,4,5,7,9,11,13,14,16,16,Determine each castle's percentage of the total points then assigned that many units then added the remaining unit to the most valuable castle.
2,4,5,5,10,10,20,40,4,0,Really don't know
2,4,5,5,3,3,4,4,32,38,"The deployment is based on a few key principles:
@@ -665,7 +652,6 @@ Through these principles and trial and error, I found this deployment to be the
-Many people will use round numbers (10, 15, 20), so putting 1 extra point will mean a few free victories.
-The goal isn't to beat the *best* players, but to beat the *most*, and this strat should be decent against a lot of comps"
2,3,6,6,11,16,22,32,1,1,"Don't deploy any substantial troops to 9 or 10; let the others waste troops on them. Focus on 1-8; can still win if lose castle 8, so multiple win conditions. Deploy numbers like 16 and 11 to hurdle opponents who go for multiples of 5. "
2,3,5,10,10,10,10,20,10,10,I figure most people will go heavy on the top two.
2,3,5,8,13,21,13,21,13,1,Attempt to pick a different strategy than most people
2,3,5,8,12,17,23,30,0,0,
2,3,5,7,10,11,13,14,16,19,"Based on points and number of soldiers, you want about 1.8*points value at each castle. I then rounded to the closest whole number."
@@ -734,7 +720,6 @@ My strategy is less about winning individual battles with other distributions an
2,2,2,20,2,2,22,22,24,2,"Trying to win castles 9, 8, 7, and 4 to score more than half the points. Also trying to poach castles where my opponent put 1 or 0 soldiers."
2,2,2,16,17,18,19,20,2,2,"we need 27.5 points to get a victory. overloading the top two castles only nets 19 points and i feel like an emphasis will be to get the highest castles. I'm overloading the middle 8,7,6,5,4. that's 30 points for a victory. the 2 soldiers at the remaing 5 castles are to win castles left with 0 or 1 soldiers and to not completely concede the other 5 castles."
2,2,2,16,2,19,2,15,25,15,"Given that Blotto games are notoriously difficult, I assumed people would not play Nash Equilibrium strategies (this may be a terrible assumption, but I also didn't want to solve for Nash Equilibrium in a different variation of a Blotto game from what I'm used to). With 55 VP total, you need 28 to win. I figured a number of people would try that by going low (1-7), or high (1, 8-10). I thought people would think going high is the obvious choice, and go low. So I mostly went high, but put large allocations on a few small ones other than 1 (since that is needed for both low an high)."
2,2,2,15,17,18,19,20,2,2,"Assuming people would go for the highest value castles the most I started with castle 8, assuming I'd win sometimes, then incremented down, removing one from each lower castle because of the lower priority. Then I dumped 2 into each other castle to catch anyone who tried a similar strategy, assuming they'd only leave 1 to go for the split."
2,2,2,15,16,17,25,5,6,10,Hybridization. Aggressively pursuing lower castle chunks against basic high castle value strategy while leaving medium low numbers to feast on remains of overly clever NYT readership.
2,2,2,14,16,18,20,22,2,2,"Trying yo win all from 4 to 8, which is enough to win the war. Also, trying to win ""free"" castles. "
2,2,2,12,15,18,21,24,2,2,"I decided to try to claim a set of middle value castles that are worth over 100 points, allocating 3 soldiers per point for those castles. The remaining soldiers are distributed 2 each in the remaining castles, in case there are any unguarded easy captures."
@@ -796,21 +781,18 @@ Thank you for the interesting challenge - more of these crowd-sourced submission
2,2,2,2,3,3,4,30,50,2,Hunch.
2,2,2,2,3,2,18,28,39,2,Seeing if I can get some big points and share in some others.
2,2,2,2,2,42,2,2,2,42,"Focus on 2 castles, disrupt others, capture uncontested castles"
2,2,2,2,2,27,33,24,2,2,"I wanted to be able to pick up cheap points by beating anyone who leaves a castle un-attacked or with just one attacker. I figured lots of people might concentrate on winning castles 9 and 10, so I concentrated my forces on three smaller castles that add up to more than 19 points. Varied my troop numbers at the castles 6-8 in case of opponents divining them evenly."
2,2,2,2,2,26,2,2,2,58,"Get easy points, take castles 10 and 6. Relies on opponent leaving a bunch blank or sending 1s"
2,2,2,2,2,22,22,22,24,0,Conceded 10 points hoping to get some of the lower castles in exchange.
2,2,2,2,2,22,22,22,22,2,(i may have mis-typed the first entry... stupid mobile phone. sorry!)
2,2,2,2,2,22,22,22,22,2,"I figured the 10 castle would be highly sought after, so i punted there. I tried to overpower the next 4 castles, as winning those will give me victory. I also put 2 in every other castle, with the idea that some people will punt castles completely, others will put 1 troop in some castles, I will beat the people in those castles which will cover me if they go super heavy in one of my 4 big castles."
2,2,2,2,2,22,22,22,22,2,Revised my last one where I didn't use all of my troops. Math is hard.
2,2,2,2,2,18,18,18,18,18,Top Five (for robustness instead of top 4) and the rest to counter snipes
2,2,2,2,2,17,17,17,20,2,"Fighting a meta of 1s, then dodging a fight for 10"
2,2,2,2,2,14,16,18,20,22,2 men to defeat everyone who just sent 1. then hope to get lucky with the larger ones.
2,2,2,2,2,12,21,21,22,14,
2,2,2,2,2,11,11,10,38,20,
2,2,2,2,2,9,18,25,28,10,"It seemed prudent to concentrate forces. I did 2 troops to the lower yield castles, just in case lots of people concede those with 0-1 troops (although the case can be made, others used my reasoning as well, which would dictate 3 troops, and on and on). But, I chose 2. Castle 10 is the jewel and people may send a bulk of troops there or either concede it. I don't want to waste troops against players that want it at all costs, but I didn't want to just give up on it either. If a player sends just token forces there, I like my odds with 10 troops. and if not, then I'm glad to let them expend lots of troops against my 10. My thought was to really concentrate forces, and do so at the castles towards the upper half of the castles, with castle 10 being the exception. I need 28 points. My goal is to take a high percentage of the 7-9 castles and hope for a few others. and if the opponent has overwhelmed me at 1 or 2 of those, then I hope my ""beat token troop deployments"" strategy works at enough of the other castles to succeed. Look forward to seeing the data!"
2,2,2,2,2,8,14,28,38,2,Many people will overload on 10 or put 0 or 1 in some castles. I hope to abuse that.
2,2,2,2,2,2,26,29,31,2,Targeting castles 9/8/7. Will try to take any other castles that others allocate 0 or 1 soldiers to with 2 solders.
2,2,2,2,2,2,22,22,22,2,"Because I've run a blotto tournament at my office (and before that, at grad school w/ my students) each summer for the past 10 years, and this strat tends to do well against first-timers. (So maybe not so well against readers of your column but oh wells!)"
2,2,2,2,2,2,20,33,33,2,"Basically I'm sacrificing castle 10 to improve my odds with 7,8 and 9, then hoping the 2 soldiers I send to the other castles is enough to get me 4 more points.
I compared 33 different combinations against each other. This was the best performer overall, and second best when I pitted my top 10 against one another.
@@ -831,7 +813,6 @@ It was interesting to see how many of my most ""clever"" ideas would often lose
2,2,2,2,2,2,2,2,82,2,Guarantee a big number and hopefully pick up some smaller ones where others leave them as zero.
2,2,2,2,2,2,2,2,42,42,"I think most people will try to get to 28 as efficiently as possible, which requires winning at least four castles with your allotted 100 soldiers. I am banking on overpowering the 10 and the 9 from those strategies and picking up uncontested (or lightly contested) castles to make up the final 9 points. This configuration will beat any configuration that tries to distribute its soldiers evenly (or relatively evenly) between only 4 castles, which I hope many people will do. "
2,2,2,2,2,2,2,2,2,82,Put 2 for everything just to beat everyone who sends one troop just in case someone sends none. Then bet all my marbles on the big guns at castle 10!
2,2,2,2,2,2,2,2,2,2,"Send two to every castle. For each castle, one of the troops stays & attempts to capture, while the other retreats back & reports to me how many troops the opponent sent. With the additional information, I'll have the advantage on how to deploy the 90 troops for a counter attack. Lose the battle, win the war. "
2,2,2,1,2,7,19,19,9,37,"Wrote a genetic algorithm because I thought it would be cute, and let it run for a while. It doesn't converge because it's easy to generate a child that can beat its parents, so to pick a final submission I looked at the best deployment from a few generations and chose the one that appealed to me."
2,1,16,15,16,16,13,19,1,1,"The race to 29 so to speak, if you can guarantee your own total, cede the more valuable castles."
2,1,6,6,7,11,16,21,23,7,"Concede 10 to focus on 9,8,7,6. Avoid round numbers and bid slightly above them. Bid 2 on 1 since most will probably bid 1 or 0 on it"
@@ -1024,7 +1005,6 @@ Therefore I chose a strategy where deployments to each castle were approximately
1,2,4,6,9,11,13,15,18,21,average of 1.81.. soldiers per point with some weighting to the higher point castles away from lower point castles.
1,2,3,18,17,16,15,14,4,10,I figured that most people would stack their top castles. I also wanted to pick something that would beat an even 10 across. Getting 5 Wins and a Tie is easier than 6 wins.
1,2,3,6,9,10,13,16,18,22,"Again, I used a simulation of between 1000 and 2000 players, some attempting to play optimally, some attempting to play randomly, and some a hybrid of the two. I found that, the more optimal players, the more the optimal distribution steadily increased from 1 to 10. The distribution I chose is a compromise between many simulation parameters."
1,2,3,5,8,12,10,15,18,25,I have faith that I can win submitting only 99 soldiers.
1,2,3,5,7,11,15,19,23,14,"Tested strategies against random generated values in a monte carlo. Exponentially weighted distribution worked best. From here, I took points from castle 10 to add 1 to 1,2,3,4,5 and 2 to and 6,7,8,9. The logic in it is that I expect many people to arrive at the exponentially weighted distribution, and I only need to win 6, 7, 8, and 9 to beat them. "
1,2,3,5,7,10,14,16,21,21,"I started with deploying troops in proportion to the marginal value of winning that battle. For Castle k bid the closest integer to 20k/11. That maximizes the expected number of points but doesn't necessarily maximize my winning percentage. So I simulated the bidding strategies of others 10,000 times from a beta distribution and noticed that small adjustments to my original deployment could lead to improved results."
1,2,3,5,7,9,15,17,19,22,Chaos
@@ -1051,7 +1031,6 @@ I'm hoping that this will generally dominate the strategy of ""30 or more to Cas
1,2,2,2,20,20,2,25,25,1,
1,2,2,2,16,21,0,26,29,1,"Prioritizing castles 5, 6, 8, and 9 concentrates my forces on securing exactly the 28 minimum points required to win, while avoiding wasting forces on a massive arms race at Castle 10 and, to a lesser extent, Castle 7. Leaving 1 or 2 soldiers at most of the other Castles allows for some flexibility, since I can afford to lose 1 or 2 of my prioritized castles if the opponent ignores some of the other castles."
1,2,2,2,11,15,30,2,2,33,"I figured that some people would focus on castles 7-10, because you can win with just them, and that others would focus on 1-7, because they also give enough points to win. The people who aim for 7-10 will be beaten by my strategy because they will most likely lose 7 and 10, or at least be tied. People who aim for 1-7 will almost certainly lose 7, and perhaps tie for 6. People who put 10 in every castle will lose 5, 6, 7, and 10, which makes me get 28. People who allocate their soldiers like 1-3-5-7-9-11-13-15-17-19 will also lose 5, 6, 7, and 10."
1,2,2,2,7,9,18,27,30,0,"By avoiding the 10 value - I both nearly guarantee the next 17 points for myself, and can view any investment my opponent makes to the 10 value a wasted effort (or lost soldiers) and giving me a numerical advantage for the remaining points. They may actually only get 10 total."
1,2,2,2,5,15,16,23,32,2,I made the game and played around with it on http://www.solidmecha.com/game/CastleCalc/
1,2,2,2,2,29,30,30,1,1,"I think if I can secure 6, 7, 8 plus some of 1-5 I will beat out those who go all in on 8, 9, 10."
1,2,2,2,2,5,11,15,24,36,Loading up on the top makes the most sense.
@@ -1096,17 +1075,14 @@ Ignoring some castles to focus on others requires winning at least four castles,
I chose this strategy to defeat four-castle focused strategies that rely on winning castle 9 yet remain strong against hybrid weighted-focus strategies designed to beat an even distribution."
1,1,3,5,12,15,20,18,15,10,"I wrote a little bit of JS to help me test some configurations - although I wish I could do more testing, this one did the best out of all my trials"
1,1,3,4,10,20,20,20,20,1,Tried to predict some common strategies and tried to give myself the best odds to win the most matchups.
1,1,3,3,4,10,25,30,15,4,"Attempt at guaranteed victory at higher than average but not too high values in hopes opponents would go all in on high value, and I could get more blue chippers for a higher total number. Put low numbers on other targets just in case opponents went even lower for some ""luck"" victories."
1,1,3,3,3,9,25,25,30,0,Punting 10 figuring everyone goes after it. Went after a bit of everything else.
1,1,2,12,21,12,21,26,2,2,"Preventing potential major strategies (e.g. Capture top 4 numbers with 25 each, match expected value of soliders to castles.) Also 2 soldiers for 10 and 9 attempts to steal these castles from people who dont make an attempt on them or try to steal with only 1. Covering numbers like 8,7 and 5 because they are in a majority of sets that would lead to a win. Appologies for brevity and typos, on a cell phone on a plane hurdeling down the runaway."
1,1,2,12,5,21,2,24,2,30,Some guesswork and pseudo-statistical modelling on how to reach 28...
1,1,2,11,5,7,19,11,22,21,"I randomly assigned troop deployment values for 100 warlords, simulated the choose 4950 battles, and then chose the deployment strategy that won the most wars."
1,1,2,11,5,7,9,11,22,21,"I randomly assigned troop deployment for 100 warlords, simulated the 4950 wars, and then chose the deployment that won the most of their 100 match ups. Note, I am re-entering my answer out of concern that I miss-typed my original answer (it may have added up to 110)."
1,1,2,10,12,15,25,30,2,2,"Winning the game requires 28 points. This means that even winning castles 8, 9 and 10 is not enough to guarantee victory. I want to maximize my potential avenues to win by concentrating on castles 4 through 8. If I win all three, I have 30 points and guaranteed to win. The biggest weakness is giving my opponent an easy path to 9 and 10, but by spreading out my attack I have more options. "
1,1,2,10,1,15,12,19,21,18,This is the top random dog after very many iterations. I don't think there's a stable choice. Some randomness has to prevail.
1,1,2,6,12,18,24,30,3,3,I focused troops on castles 4-8 as winning all of those is sufficient to win. I then scattered a few troops elsewhere in case my opponent had not sent any or very few troops to those castles.
1,1,2,5,10,1,20,20,20,20,"Go for an even distribution between the top 4 castles on the assumption that a lot of people will more heavily weight towards the top and decrease gradually as the castle value decreases, skip 6 as it's the last in the 'upper tier' of castles, and scatter some troops around the lower values to try to pick them up."
1,1,2,5,7,9,11,16,21,26,I just winged it
1,1,2,5,7,8,10,14,22,30,Gut
1,1,2,4,14,21,27,27,2,1,"Assuming some will split evenly and others load up high, I am trying to make sure also possible castles that remain unguarded can be one, but focus on higher side below most highly picked choices and those of little value."
1,1,2,4,6,10,16,25,34,1,"Start with Fibonacci numbers which goemetrically increases soldiers per castle. Don't give up any castle without a fight, so at least 1 soldier for each. Reduce Castle 10 to 1 soldier hoping to enphasizing middle-to-higher-numbered castles. Distribute the other 11 soldiers to those castles, so starting with Castle 4, add 1, 1, 2, 3, and 4."
@@ -1178,7 +1154,6 @@ I'm sure those who had more time probably tested their solutions against this ty
1,1,1,10,10,1,20,25,30,1,I wanted to put at least one soldier on every castle to try to win some without much resource allocation to them or at least split them with anyone else having the same idea. I put more soldiers on castles that I thought would give me the best chance to get to the key 28 points required for victory. Also I love the idea of the community interaction in the riddler this week!
1,1,1,9,11,13,18,20,25,1,
1,1,1,7,15,15,15,15,15,15,"I didnt really have a plan, but thought that I should evenly focus my troops on the higher level ones to get a better chance and put a single troop on the low ones in cas the enemy put 0"
1,1,1,7,15,15,15,15,10,10,I was looking to spread over my unites in as much of the middle numbers as possible.
1,1,1,7,12,14,16,21,27,0,"by sacrificing 10 I am hoping the enemy sends the bulk of their army to that castle and I can outright win the rest of the castles, I did not care about the lower castles but sent 1 to each just in case the enemy also did not care about the lesser castles"
1,1,1,7,11,15,20,21,22,1,"sacrifice #10, but load up on 5-9, knowing that 9 + any 3 of the other 4 will win it for you. also, putting 1 on 1, 2, 3, 10 just in case those were totally neglected by my enemy "
1,1,1,7,10,12,14,16,18,20,"Biased towards the more valuable castles, but not ignoring the high end. Mostly ignoring the bottom 3, but one troop just in case."
@@ -1222,9 +1197,6 @@ This leaves me very vulnerable to very basic strategies (e.g. 10 soldiers per ca
1,1,1,1,24,24,1,23,23,1,I can't spend anymore time on this stupid castle game. I need to get back to work. This is the count I had in my Excel sheet when I decided I'd spent too much time on this.
1,1,1,1,23,23,1,24,24,1,Decided to play electoral college with this and focus on the 4 numbers that would get me half. I put 1 everywhere else to thwart other people doing the same thing
1,1,1,1,23,23,1,24,24,1,"I didn't have any great ideas. But you need 28 points to win - might as well go for exactly 28. I think a lot of people will load up on 10. After that, just guesswork. Putting at least 1 on each castle is a cheap investment. "
1,1,1,1,23,23,1,23,24,1,"The goal is to get get 1 point more than half the points available (28). Therefore, it is mostly a waste of resources to allocate troops to getting additional points, an advantage to concentrate resources only on the castles you need to win.
The minimum number of forts needed to get this point total is 4. I need to guess which set of 4 castles is the least likely for the majority of players to concentrate their forces on. Castle 10 is an obvious ""honeypot"", so I'll avoid concentrating there. Castle 7 is the overlap between the needed ""high castles"" (7-10) and ""low castles"" (1-7). A good combination is then perhaps 9, 8, 6, and 5 (total 28). I will mostly concede all the other castles, but since some people may totally concede a castle if they are concentrating forces as well, I will leave at least 1 troop at every castle. Since I can't divide 93 evenly between 4 castles, I will give an additional troop at castle 9 since it's most valuable."
1,1,1,1,21,21,1,26,26,1,"winning 5, 6, 8, 9 wins"
1,1,1,1,20,21,1,26,27,1,"Punted on the 10, concentrated troops to get 28 points (minimum to win), deployed 1 troop to remaining castles just in case."
1,1,1,1,20,21,1,26,27,1,Fill all with at least one - hopefully easy points - and take an unconventional path to 28 that didn't use the 10.
@@ -1244,9 +1216,6 @@ roughly leave rest of troops (94) proportionally on those particular 4 castles"
1,1,1,1,17,17,1,26,34,1,"Primary strategy is to win 4 numbers to get to 28. I chose 9,8,6,5. Psychologically I assume people will go crazy to win 10 so I avoided 10. I set my armies to beat almost all simple strategies using other sets of 4 numbers (4 25's or 3 33's + 1 or even split from 1-7). I lose to 25 armies on 10, 7, 6 ,5 but you can't win them all. The spread out singles are key to beating people that leave castles undefended, allowing me to lose 9,8,6,or5 and still win. Analyzing strategies might be a fun topic for a follow up column . . . "
1,1,1,1,16,25,2,26,26,1,
1,1,1,1,16,24,25,28,1,2,"Firstly, I need to make sure to send 1 to each castle to pick up any freebies. 9 and 10 are the obvious castles, so I'm hoping my opponent overcommits. I spread the rest around the remaining high points in descending order because I suspect that is what my opponents will do, although hopefully with fewer remaining soldiers after those allocated to 9 and 10."
1,1,1,1,16,20,1,27,30,1,"Put 1 soldier in each castle in case an opponent doesn't put any, to get an ""easy victory.""
Pick castles representing a bare majority of points, and focus all remaining resources there. Don't pick 10, or a string of numbers, as those seem too obvious. Focus forces proportional to value.
"
1,1,1,1,16,19,1,28,31,1,"Victory requires 28 points, which requires a minimum of 4 castles. The sum of any castle and the 3 above it exceeds 28 points beginning at castle 6 (6,7,8,9), and then by 2 points. High value castles will be more competitive than low, so dropping castle 7 in favor of 5 places as many castles as possible as far down the list as possible. Weighting troop commitment by point value yields 18,21,29,32 for castles 5,6,8,9. In this case all castles are must win, one victory condition. Risking castles by diverting 6 troops (2 each from 5,6 and 1 from 8,9) picks up any remaining castle where no troops were committed by the opponent, laying claim to any of the remaining 27 points that might compensate for a tie or loss in the big 4. If the enemy also sends a token troop to every castle I still gain 13.5 points, within half a point of compensating for the total loss of any two of my must-win castles except for both 8 and 9. The solution is not rigorously tested, but it provides ubiquitous coverage while focusing maximum troop strength on the easiest targets necessary."
1,1,1,1,15,19,23,1,1,37,"If you want to win, you must acquire 28 or more points. This requires that you should spend approximately 3.57 units per point that you wish to acquire. Regardless of choice, each castle should have at least 1 unit assigned so to capture castles that the other player does not find interesting for their win strategy.
@@ -1302,7 +1271,6 @@ I always send at least one soldier to ensure I don't split points with any castl
1,1,1,1,6,11,16,26,36,1,"I abandoned castle 10 in hopes of saving troops where the other team might send a larger force. Focused more troops on castles 6-9, since those are more valuable, but saved at least 1 troop for the low value castles and castle 10 in case the other team also sent no one there."
1,1,1,1,6,11,16,21,21,21,"Send at least 1 solider per castle; use ""1/6"" ending numbers on the assumption that many players will round to 0/5; send majority of armies to the highest-valued castles."
1,1,1,1,6,11,12,33,34,0,"Think of this as bidding at a silent auction instead of troop deployment. The value of Castle 10 is high enough that there will be lots of bids - leaving me a very small chance of winning it. So I put my resources elsewhere. The idea in general is to invest just enough to win each castle except Castle 10, but no more than necessary."
1,1,1,1,3,30,30,30,1,1,"People will prioritize castle 9 and 10 to get 19 points, but if I win 8, 7, and 6, I will get 21 points."
1,1,1,1,3,30,30,30,0,3,Gut feeling
1,1,1,1,2,4,6,12,24,48,
1,1,1,1,2,2,7,11,23,51,"A game can be modeled in normal form. After solving the toy problems of (2,1), (2,2), (3,2), (2,3) where (troops, castles). One only wins in the upper triangle of the matrix. Using iterated domination can only reduce the real game space a bit. If one assumes there is a positive probability of the opponent playing all of the non-strictly dominated strategies, then a best-response is to mix over the available strategies with probability of winning as the mixing probabilities. I used a RNG, random module in python, to draw a deployment of troops in the set of feasible solutions. Then transitioned using pairwise castle changes until it was satisfactorily burned in ensuring that a positive number of troops were allocated to every castle. "
@@ -1368,7 +1336,6 @@ Fun puzzle; thanks for offering it!"
1,1,1,1,1,1,1,29,30,34,"Need 28 points to win so try to get 10, 9, 8 and then hope to split/win one other castle "
1,1,1,1,1,1,1,28,31,34,"This is a second submission, so please disqualify this one if only one submission is allowed. I wanted to see how ""dominate the blue states"" faired, so I proportionately distributed to castles 8,9,10 and then removed 7 (2,2,3) to distribute 1 per castles 1-7."
1,1,1,1,1,1,1,21,31,41,A bunch of 1s on lower castles to win points from the presumably many people who submit zeros. Then heavy deployment to the top three castles.
1,1,1,1,1,1,1,1,1,1,"Opponent can't focus on all of the castles, so I'm spreading out to try to win more volume. The low ones aren't valuable but I'm more likely to win those outright."
1,1,1,1,1,0,11,17,26,41,Heavy on big castles
1,1,1,1,0,15,21,0,28,32,"Each point is worth about 2 soldiers. But like gerrymandering, you want to win a lot of castles by a slim margin and lose a few castles by a large margin. So I didn't compete for castles 8 and 5 and hope to use those soldiers to win the other big castles by a little."
1,1,1,1,0,0,0,48,0,48,"28pts wins. I hope my opponent won't play for castles 1, 2, 3, and 4, and so I put one soldier each there, splitting the remainder between castles 8 and 10 to make exactly 28. Cool idea, BTW!"
@@ -1533,9 +1500,6 @@ After many campaigns, I had a lot of rock/paper/scissors where one of my strateg
0,1,3,3,11,18,25,33,3,3,"Went in heavily for 8,7,6, and 5 while keeping some forces at 10,9,4, and 3 in case opponents put a weak force there. This alignment won head-to-head the most often against a lot of other strategies that I considered. Any possibility that you are able to publish the complete head-to-head records of all participants? Thanks, this was a fun one (and the first time I've formally entered!)."
0,1,3,3,6,10,20,19,1,37,Lots of computer simulations... then an itsy-bitsy tweak to guarantee I'd beat my own answer.
0,1,3,1,11,12,12,19,22,19,I don't have a good explanation for this.
0,1,2,11,11,13,26,2,31,2,"My first thought was to come up with a combination of numbers that meets or just exceeds 28, focus on those, and ignore the rest. I suspect many other people are thinking this too. I realized that if I'm too focused on getting the minimum necessary to win, I can be undone if someone spikes one castle I'd counted on. I also didn't want to have a ""backup plan"" though because that only makes my main plan weaker. So my main plan now is to defeat my first main plan, I think I'll win against virtually everyone whose strategy is to win exactly 4 or 5 castles including 7 or 9 (which I figured would be easier to spike than 8 or 10).
I also sent small brigades to some castles I'm not counting on because the risk-to-reward ratio is so good."
0,1,2,7,11,15,19,21,22,2,"Value difference between 9 and 10 not that much, and assumed most people would focus on 10, so shifted resources away. Still wanted a few soldiers in most castles in case people consolidated too much. Ran some crude tests to see how this distribution compared to others like a even, proportional, and various versions of my strategy."
0,1,2,4,7,9,13,17,21,26,"i wanted to slightly beat what i thought the popular solutions would be:
2, 4, 5, 7, 9, 11, 13, 15, 16, 18 (a proportional solution)
@@ -1596,7 +1560,6 @@ On 1 through 5, I'd rather send a 1 force than nothing, I expect those 5 soldier
Follow Me!"
0,1,1,1,1,1,1,15,38,41,
0,1,0,1,2,2,1,1,1,1,idk
0,1,0,1,0,1,0,1,0,96,Maximize my chances of winning castle 10 while hedging in the event I lose castle 10 that I get other castles to sufficiently win the game.
0,1,0,0,19,22,26,30,0,2,"I found the average number of troops at each castle necessary to win ""proportional points"" =(Castle Number/28)*100. At each of my ""key castles"" (5 through 8) I put more troops than expected to win those number of points. I guessed people would overvalue higher numbers (i.e. 9 and 10) so I started my firewall at 8. If I win 8 through 5 I will likely tie at some lower castles and get to a win at 28 points. I threw two troops at 10 to pick up against people who abandoned 10 entirely (my own strategy taken to the extreme.) I also threw one troop at 2 - which can allow a clean win if I pick up 8,7,6,5 and 2."
0,0,30,26,20,0,14,10,0,0,"I tried to target 28 points in places that are not as likely to be contested, allocating more troops to the more contested locations."
@@ -1678,9 +1641,6 @@ The remainder of the troops are concentrated on trying to win castle 3, rather t
This strategy is robust against another strategy which leaves a lot of the smaller castles undefended. Even if it lost castle 9 or castle 10 to such an opponent, it would still win because of the split points at the castles ignored by both sides.
It would lose to a strategy which attempted to win castle 1 rather than castle 3 but it has an advantage over the latter strategy in that it would beat the ""obvious"" strategy of putting 10 troops on each castle, while the latter strategy would not."
0,0,9,9,9,15,25,30,0,0,"Decided that castles 3-8 were a pretty solid sum of points. 1 and 2 were skipped because they weren't that many points...9 and 10 were skipped because they were more likely to be contested. Incremented the value of troops somewhat haphazardly based on how I thought it should be, because damnit I'm the warlord and can do what I want. I also intentionally kept 3 troops at home because I will need protection when all of my troops die in this bloody war and I need to flee the land.
I tried to look into game theory formulas to figure out the optimal strat but didn't find anything too helpful. Interested in what other people do. "
0,0,9,3,6,5,19,26,29,3,"I tried to ""grow"" a solution using a genetic algorithm. Turns out that's not the best strategy, since the function you're optimizing depends on the population of solutions you're testing. Still, it was a fun thing to try and even kind of stabilized on a set of strategies (everything ignored 1-2 to some extent and either went hard on 10 or just sent a few there)."
0,0,9,1,1,16,1,1,34,37,"I'm shooting to win castles 3, 6, 9, and 10 for a total of 28 points. I'm also putting one soldier at 4, 5, 7, and 8 in case there are easy points to pick up there in case I loose one of my preferred castles."
0,0,8,12,15,18,21,24,1,1,"By ignoring castles 1 and 2, and only investing 1 troop in castles 9 and 10, i am effectively conceding approximately 2/5 of the points with the strategy of sending overwhelming forces to the remaining castles with 3/5 of the points. I have invested 1 troop in castles 9 and 10 in order to counter a similar strategy - ignoring the highest value castles - and potentially splitting or winning points a large number of point with only 2% of my troops invested. No maths/game theory involved "
@@ -1700,7 +1660,6 @@ Tall builds will be more likely to involve the higher numbers (8,9,10) than the
0,0,8,9,10,14,27,32,0,0,"Just need 28 to win. Tossed out 9 and 10 hopping to win the rest, need just 2 out of 3 from the 3:4:5 group. Tried to put more on 8 and 7 to protect against 10:9:8:1 and 10:9:7:2 strategies."
0,0,7,9,11,12,13,8,20,20,Not a damn clue.
0,0,6,16,21,26,31,0,0,0,"(10+9+8) < (7+6+5+4+3+2+1), so the top three castles are negligible if I can win the bottom seven castles. Since winning the 6th castle once is the same as winning all three of the 1st, 2nd, and 3rd castles, it makes the most sense to load up troops in the middle four castles. Also assuming people naturally group numbers into multiples of five, I used a distribution of (multiples of 5)+1."
0,0,6,14,0,20,26,32,0,0,I chose what I thought the path of least resistance to 28 points was and put more on the higher ones.
0,0,6,11,18,27,38,0,0,0,I did (C-1)^2 + 2 for 2< C < 8
0,0,6,11,0,22,27,32,0,2,"I need 28 points to beat any opponent. I figure most strategies out there will be of several forms: (1) get all the high point castles, so 10-9-8 plus something small; (2) skip the 10 and try to get something like 9-8-7-4 or 9-8-6-5; (3) get all the small castles, 7-6-5-4-3-2-1, and (4) some general ""what-is-each-castle-worth?"" strategy that has a declining point value for each castle. To triangulate against them, I went with a very specific 8-7-6-4-3 strategy to try to get to exactly 28. I also assume some human bias toward numbers ending in 0 or 5, so my numbers are 1 or 2 above those values. Finally, I put 2 points in castle 10 to cover against those putting 0 or 1 in there. Note that winning castle 10 would cover against losses three different ways: 8 or 7-3 or 6-4. I don't expect to win, but I'm hoping that I'll place pretty high with this strategy, with an outside shot at winning."
0,0,6,10,1,22,28,31,1,1,"Attempt to get 28, and only 28 points."
@@ -1763,7 +1722,6 @@ Thank you so much for creating and adjudicating this game!
0,0,0,33,33,22,3,3,3,3,Most people will start high to low is my guess so I put 0s there to not compete where I can't win. A % of people will not compete at all for the 7 to 10 spots if they load up toward other castles early on. And the 3-6 spots should include less of peoples weights - my play is less of a stats based play and more of a sociology play
0,0,0,25,25,25,25,0,0,0,"I figured there would be lots of different strategies tried on this problem, thus the first couple of obvious ones (send 100 troops to castle 10, send 10 troops to each one of the castles) would likely be used. For some reason (call it a hunch on human nature) I figure there will be a more likely event that people will place a number of troops either in castles 1-3 or 8-10, but I feel like the odds are lower that they will place troops in the middle 4 castles 4-7. I also felt like there would be a better shot at winning castles if I ""didn't get greedy"" and go for either a large number of castles, or castles with the highest point value. So, here goes nothing!"
0,0,0,25,0,0,25,25,25,0,4+9+7+8=28 which is the least amount needed to win the war.
0,0,0,25,0,0,24,25,25,0,"10*11/2 = 55 points in the game, score of 28 wins, need at least 4 castles, so 4 castles it is, avoid the bing guns (e.g the 10+9+8+1 combo) since vegas addicted people will front-load the 10, the only other 4 castles combo without repeat is 9+8+7+4, even spread of ressources between castles since they are all equally important in this strategy. "
0,0,0,24,0,0,25,25,26,0,I tried to ensure victory at the minimum number of castles that would give me the minimum number of points to win.
0,0,0,21,0,0,26,26,27,0,"There are 55 victory points, so we need to win 28 to win the war. No three castles provide enough victory points by themselves, so my strategy is to concentrate on four castles that are cumulatively just enough to win the war, avoiding the most attractive castle #10, and concentrate all my troops there to maximize odds of winning these castles. Castles 4, 7, 8, and 9 work. (Another similar choice would have been castles 5, 6, 8, and 9.) I distributed the 100 armies across these castles with slightly more on the more valuable castles rather than evenly."
0,0,0,20,20,20,20,20,0,0,complete guess
@@ -1843,11 +1801,6 @@ I have done no computer simulations - this is all in my head - but as far as I c
It will defeat every fully proportionate strategy and every non-proportionate strategy in which the emphasis is on overloading castle 10.
It will also defeat a flat strategy, in which 10 troops are allocated to each castle, or 25 troops are allocated to each of four different castles."
0,0,0,11,0,0,23,28,33,0,"It's impossible to win with only three castles -- even if we take the best three castles we'll have fewer than half the points. But it's possible to win with only four castles.
The optimal strategy is one which guarantees 28 or more points as often as possible. With the four castle strategy, we must win Castle #9 or #10 or we can't reach 28 points. I chose Castle #9 which would be less contested than #10. This surprisingly leaves only two options: [9, 8, 7, 4] or [9, 8, 6, 5].
Between the two, [9, 8, 7, 4] just seemed a little more consistent to me. I think a reasonable player might commit 15 or more soldiers to Castles #5 and #6, so it might be more of a guessing game. But 11 soldiers will almost certainly win Castle #4."
0,0,0,11,0,0,22,22,22,23,"There are 55 victory points available, so I need 28 to win. The smallest number of castles I can do this with are Castles 10, 9, 8 and any one of the others. In order to have a margin of error, I decide to target Castle 7 additionally and out of the ""any ones"", I target Castle 4. This way, I need three out of the four large ones plus Castle 4. I reckon Castle 4 will not be targeted so often, so I only go with 11 soldiers there, allowing me to beat an ""evenly distributed"" strategy. The large castles get 22 soldiers, beating any ""target only the largest five evenly"" strategy and even those that assign 21 soldiers to beat these. That leaves one odd soldier, who I send to the largest castle. "
0,0,0,10,20,20,50,0,0,0,Trying to win the mid castles
0,0,0,10,20,20,25,25,0,0,Mostly Random with emphasis on numbers between 5-8.
@@ -1867,7 +1820,6 @@ Between the two, [9, 8, 7, 4] just seemed a little more consistent to me. I thin
0,0,0,10,15,20,25,30,0,0,Ignore the top and bottom focus on the middle
0,0,0,10,13,20,26,31,0,0,I assume most will attempt to aim for the top only. I'll take the center-top instead.
0,0,0,10,10,20,20,40,0,0,Everyone is going to put lots of soldiers on the top castles. So I give them the 19 points hoping to get a lot of points from the five I defend.
0,0,0,10,10,10,20,30,0,0,"Didn't want to compete in upper end, or lower end, and figured had a better shot at winning the middle"
0,0,0,10,10,10,10,15,20,25,Take the positions that earn the most - abandon the weak ones.
0,0,0,10,0,21,0,21,0,48,"Bet on fewer castles and ignore the one immediately below it, keeping in mind to bet on enough castles to get over half the available points."
0,0,0,10,0,0,30,30,30,0,"If I usually overwhelm the opponents on 4, 7, 8, and 9, I'll get 28 points, which is enough to win the war."
@@ -1910,8 +1862,6 @@ My submission was the best after 10 rounds of this. I'm sure more rounds would g
Finally, the messy details about how I made random weakly increasing deployments. I generated 10 random independent samplings of the Unif(0,1) distribution. I then scaled them all so as they summed to 100, rounded each of them down to the nearest integer, and added whatever I needed to the last sample to make them sum to 100. Then, I sorted them, assigning the lowest integer to the least valuable castle, etc."
0,0,0,1,1,1,12,12,33,40,"Base strategy of 37,33,11,11,1 for castles 10 through 6 with 7 spare soldiers for flexible deployment. Then into thinking about what others would play to 'optimise' final distribution."
0,0,0,1,1,1,2,1,3,1,"I took a computational approach. First, generate a population of random strategies, then pit them against each other. Save the top 50% of the strategies by win % and propagate them to the next round. Repeat for 10,000 rounds.
An interesting property of this game is that strategies are non-transitive in head-to-head matches. Additionally, the best strategy depends on the distribution of the strategies in the competition pool. The computational approach that I took assumes a competition pool of 1/2 ""good-ish"" strategies and 1/2 random strategies. Here's hopin'! Code at https://github.com/cjbayesian/riddlerfivethirtyeight/blob/master/Riddler%20Classic%20Battle%20Royale.ipynb"
0,0,0,0,50,50,0,0,0,0,"Figured someone would send 100 to 10, so the easiest way to get to 11 castles was splitting between 5 and 6."
0,0,0,0,25,25,25,0,0,25,"You only need 28 points to win - and intuitively any troop you spend on a castle you lose is wasted, as is any troop you spend on points beyond your 28th point. So is any troop you spend on a particular castle you win beyond what you needed to beat your opponent. Targeting castles 5,6,7,10 adds up to exactly 28 points if you win all 4, so if you can win those 4 without overspending on any of them you played well. I played with other combinations of castles but in simulations they didn't win as frequently. I also looked at other ratios of castles but an even split won out in the end. In a bloody melee with 100000 randomly chosen bots playing against every other bot (using a few different strategies to choose troop allocation but mostly dice-rolling), this simple approach won 97.9% of the time - the highest rate. I then filtered those bots to only those that won 80+% of the time (3905 bots reached that threshold), and re-ran the competition. Playing against this high-talent pool (surely the closest analog to the Riddler contestants...), this approach still came out on top, winning 98.7% of the time."
0,0,0,0,25,25,0,25,25,0,"Note that at least 4 castles are needed to win. In general, I'd expect people to place more troops at higher-value castles. I've gone for 4 castles which have enough total value to win, but which should hopefully have be the easiest to win (I expect people to put most troops at higher value castles, so I've not just gone for 10, 9, 8, 7)."
@@ -1997,7 +1947,6 @@ We want to either just win a castle, or lose by a lot (so the opponent ""wasted"
0,0,0,0,3,5,16,22,27,27,"I wrote some Python scripts to generate random deployments, and compared them against sorted versions, as well as against balanced versions, and I played several rounds where the best ones went on ... not sure if this makes sense as a strategy but it was fun"
0,0,0,0,1,17,19,20,21,22,Emphasized larger castles.
0,0,0,0,1,10,16,20,24,29,Ran a lot of simulated tournaments and picked a top choice from those.
0,0,0,0,1,2,3,2,0,2,"I ran an evolutionary algorithm for a couple hours, and this beat more strategies than any other."
0,0,0,0,0,100,0,0,0,0,"Any selection higher than 6, if a tie, will result in, at most, 5 pts, therefore 6 will win. "
0,0,0,0,0,33,33,34,0,0,Spooky magic
0,0,0,0,0,29,0,34,37,0,"55 points total. 23 points to win. In order to get 23 points, you need to win at least 3 castles. choose 3 and go ham to win them."
@@ -2062,4 +2011,4 @@ I then picked a deployment similar to my final answer and ran it head-to-head ag
0,0,0,0,0,0,0,0,100,0,I figure many will put all 100 in #10 and thus have lots of ties
0,0,0,0,0,0,0,0,25,75,Because you told me to
0,0,0,0,0,0,0,0,0,100,Go big or go home.
0,0,0,0,0,0,0,0,0,100,YOLO
0,0,0,0,0,0,0,0,0,100,YOLO
1 Castle 1 Castle 2 Castle 3 Castle 4 Castle 5 Castle 6 Castle 7 Castle 8 Castle 9 Castle 10 Why did you choose your troop deployment?
10 23 21 1 18 1 15 1 13 1 11 2 9 2 6 23 4 23 2 23 1 The ones and twos are mostly to pick up any undefended castles, while I hope to grab the highest castles to get me over 27.5. Have to admit I don't know much game theory, so it's mostly just a guess. On average 1.81 soldiers per point, with some slight weighting to the top castles and unweighting the lower castles.
11 21 18 0 15 0 13 0 11 0 9 0 6 0 4 26 2 26 1 27 On average 1.81 soldiers per point, with some slight weighting to the top castles and unweighting the lower castles. If you were to win castles 10, 9, 8, and 1 each time, you would win every matchup. I put all of my soldiers on those castles, with a few extra on the more valuable castles to beat out anyone with the same strategy
12 21 20 0 12 0 13 0 13 0 14 0 14 0 14 26 0 26 0 27 0 If you were to win castles 10, 9, 8, and 1 each time, you would win every matchup. I put all of my soldiers on those castles, with a few extra on the more valuable castles to beat out anyone with the same strategy Get to 28 by conquering the smallest towers
20 12 13 13 14 14 14 0 0 0 Get to 28 by conquering the smallest towers
13 20 0 0 0 0 0 0 25 25 30 it put high power making it easy to win the castles with troops.
14 19 17 15 13 11 9 7 5 3 1 ?
15 19 1 1 1 1 1 1 25 25 25 need 28 to win
27 15 14 0 14 0 14 0 14 0 14 0 15 0 15 17 0 26 0 42 0 Submission #5. I guess I have the second most confidence in this (of my 6 submissions). Defending just enough points/castles to win and dividing them unequally in (probably vain) hopes that I can win. To win a war I need 28 victory points (round up half of the total number of available points). Figure most people are going to try to target the high value targets (8,9,10) which together make 27 points. So if I can capture the rest, I win.
28 14 14 14 14 14 15 15 0 0 0 To win a war I need 28 victory points (round up half of the total number of available points). Figure most people are going to try to target the high value targets (8,9,10) which together make 27 points. So if I can capture the rest, I win. With limited math skills, my basic thinking is that in this 1v1 scenario I just need 28 points to be victorious since the total number of points is 55. 1+2, +7 = 28, where 8+9+10 = 27. So I'm able to capture the first 7 castles while leaving my opponent to deploy most of his troops on the higher value castles (because who wouldn't normally want the highest value castle?) then I have the highest chance of succeeding and capturing 28 points. Hope I won. PS I see that double half-zip.
29 14 14 14 14 14 15 15 0 0 0 With limited math skills, my basic thinking is that in this 1v1 scenario I just need 28 points to be victorious since the total number of points is 55. 1+2, +7 = 28, where 8+9+10 = 27. So I'm able to capture the first 7 castles while leaving my opponent to deploy most of his troops on the higher value castles (because who wouldn't normally want the highest value castle?) then I have the highest chance of succeeding and capturing 28 points. Hope I won. PS I see that double half-zip. You need 28 points (a majority of 55) to win. I am guessing that it will be easier to do that if I focus all of my troops on 1-7 and none on 8 through 10, because I think the majority of people will overvalue those.
14 14 14 14 14 15 15 0 0 0 You need 28 points (a majority of 55) to win. I am guessing that it will be easier to do that if I focus all of my troops on 1-7 and none on 8 through 10, because I think the majority of people will overvalue those.
30 14 14 14 14 14 14 16 0 0 0 There are 55 points total, and I need 28 to win. Most people will concentrate on the higher numbers.
31 14 5 6 8 10 12 14 10 10 11 Long story short, a ton of meta-gaming. I'm an avid gamer, so analyzing strategies that are in 'meta' is something I do often. I developed 6 (really 3 archetypes) solid strategies, which would each win in a random environment. The 'uber meta' strategy that won against every strong, solid strategy whilst still being able to win an 'average' game against randoms was this one, developed out of my "Empty Castle" strategy. I know this may sound pretentious, but if I win, I would very much like to show you my "strategy notes". They're too complicated to describe in words, but pictures could give you a better idea. Cheers!
32 13 13 13 14 14 15 15 1 1 1 Need 28 points to win = win castles 1 through 7. Spread troops close to evenly among those castles and put 1 troop each on 8-10 in case opponent is using similar strategy.
95 10 10 8 7 8 5 13 7 8 7 20 16 30 11 1 13 1 14 1 set.seed(154) poo <- sample(1:10, 100, replace = T) table(poo) There are a maximum of 55 Points available, so 28 is a Winning score. My strategy is to win the first 7 castles to get 28 points, hoping my opponents over commit solders to the last 3 castles. I have also overcommitted to castle 1 as Castle 1,8,9,10 is a winning strategy same applies to castle 4 as 4,7,8,9 is a winning combination.
96 10 8 1 8 1 13 1 8 1 20 1 30 1 1 27 1 28 1 29 There are a maximum of 55 Points available, so 28 is a Winning score. My strategy is to win the first 7 castles to get 28 points, hoping my opponents over commit solders to the last 3 castles. I have also overcommitted to castle 1 as Castle 1,8,9,10 is a winning strategy same applies to castle 4 as 4,7,8,9 is a winning combination. The plan is to get to the 28 points needed with as few castles as possible while also leaving a guard against other strategies that assign zero soldiers to some castles.
97 10 1 0 1 0 1 0 1 0 1 0 1 0 27 30 28 30 29 30 The plan is to get to the 28 points needed with as few castles as possible while also leaving a guard against other strategies that assign zero soldiers to some castles. If I win castles 1,8,9,10 I will receive 28 points and my opponent will only receive 27. This is the least number of castles that I need to win in order to beat my opponent. Assuming that I need to win all 4 to have a chance and that my opponent will put very little into winning a single point from castle 1, I will only deploy 10 soldiers. Winning castle 1 is a lynchpin though and I need to win it or my theory fails. All other castles are very important to me and I am able to put 30 soldiers in castles 8, 9, and 10 because castles 2-7 mean nothing to me. I can lose them all and still win if I win 1,8,9,10.
10 0 0 0 0 0 0 30 30 30 If I win castles 1,8,9,10 I will receive 28 points and my opponent will only receive 27. This is the least number of castles that I need to win in order to beat my opponent. Assuming that I need to win all 4 to have a chance and that my opponent will put very little into winning a single point from castle 1, I will only deploy 10 soldiers. Winning castle 1 is a lynchpin though and I need to win it or my theory fails. All other castles are very important to me and I am able to put 30 soldiers in castles 8, 9, and 10 because castles 2-7 mean nothing to me. I can lose them all and still win if I win 1,8,9,10.
98 10 0 0 0 0 0 0 30 30 30 Load up the soldiers on the minimum castles needed to win
99 10 0 0 0 0 0 0 30 30 30 Tried to choose the fewest number of castles (and in the case of #1' the least likely to be attacked) to attack that would give me a majority of the points.
100 10 0 0 0 0 0 0 30 30 30 Deploying hopefully overwhelming force at castles 8 through 10, and a token force to capture 1. It doesn't allow any room for failure, but hopefully will be strong enough at the one point to ensure victory.
156 5 12 10 17 20 13 10 13 5 11 5 13 20 5 10 4 5 7 10 monte carlo simulation of 100,000 placements. Expecting to crush people who put 0 a lot or overdo #10
157 5 10 20 10 10 15 5 15 5 20 20 25 10 0 5 0 10 0 Expecting to crush people who put 0 a lot or overdo #10 Assuming most people will try to take at least one of the high-value castles, I send disproportionately high numbers to the lower value castles in an attempt to sweep all 7, and win the war 28-27
158 5 10 9 10 15 15 14 15 16 20 16 25 17 0 0 0 8 Assuming most people will try to take at least one of the high-value castles, I send disproportionately high numbers to the lower value castles in an attempt to sweep all 7, and win the war 28-27 Winning all the castles from 1 through 7 gives you a victory no matter if you win or lose the remaining three castles. So using that I weighed my army heavily on the lower portion figuring most people's gut instinct would be to distribute their troops with powers relative to the VP for a castle. I gambled on people giving up on the lower castles so taking those for free points and putting a good number of troops in the middle range where I expected the most resistance to the strategy.
5 9 15 14 16 16 17 0 0 8 Winning all the castles from 1 through 7 gives you a victory no matter if you win or lose the remaining three castles. So using that I weighed my army heavily on the lower portion figuring most people's gut instinct would be to distribute their troops with powers relative to the VP for a castle. I gambled on people giving up on the lower castles so taking those for free points and putting a good number of troops in the middle range where I expected the most resistance to the strategy.
159 5 9 12 14 16 19 22 1 1 1 I need to win 28 points- there is no prize for winning all the points. So- rather than go after Castle 9/10 which will be heavily contested, I'll aim for capturing 1 through 7 to earn 28 points. I shouldn't completely neglect the higher castles- if they're undefended I might as well capture them (because they must've stationed their troops elsewhere!)
160 5 8 12 15 18 22 5 5 5 5 This beats the vast majority of strategies that do the following: focus attention on a subset of castles totaling >=28 points, assigning soldiers proportional to points for castles in the subset, and zero elsewhere.
161 5 8 8 10 13 16 37 1 1 1 There's two main strategies: 7 8 9 10, and 1 2 3 4 5 6 7. Castle seven is, then, the most important castle. My strategy seeks to prey upon the first strategy, with a miser's troop in each expensive castle, to try to prey upon the second strategy.
230 4 7 6 9 7 12 9 14 11 16 13 18 15 20 17 0 18 0 1-8 majority of points A basic strategy could be to deploy an average number of troops to each castle weighted by point value, in which case one would deploy 1.82 troops per point the castle was worth. Given that Castle 10 is the highest profile target, I expect my opponent to commit an above average number of troops to it. I submitted 0 troops to Castle 10 so they would waste any troops they committed to 10 over the average. Instead, I committed an above average number of troops to every other castle, distributing the average number of Castle 10 troops (18) over all the other castles (2 per castle).
231 4 6 5 8 6 12 13 16 13 21 13 33 13 0 13 0 18 0 2 The winner needs 28 points so I focused all my resources on towers tha will get me 28 points while avoiding the largest castles that most people would focus on. Abandoned first castle since it would probably face strong opposition that could be better distributed elsewhere, then put one guy back to catch anyone who did what I thought to do, Then tried to put roughly equal soldiers at the rest since I'd need them all (besides the last couple that are worth very little)
232 4 6 5 8 6 10 8 12 11 14 24 17 42 19 0 4 0 5 0 Concede the most valuable, try to pick up most of the rest. Trying to win 28-27
4 6 7 9 11 13 15 17 18 0 A basic strategy could be to deploy an average number of troops to each castle weighted by point value, in which case one would deploy 1.82 troops per point the castle was worth. Given that Castle 10 is the highest profile target, I expect my opponent to commit an above average number of troops to it. I submitted 0 troops to Castle 10 so they would waste any troops they committed to 10 over the average. Instead, I committed an above average number of troops to every other castle, distributing the average number of Castle 10 troops (18) over all the other castles (2 per castle).
233 4 5 6 13 7 13 8 13 18 13 22 13 26 18 2 2 Abandoned first castle since it would probably face strong opposition that could be better distributed elsewhere, then put one guy back to catch anyone who did what I thought to do, Then tried to put roughly equal soldiers at the rest since I'd need them all (besides the last couple that are worth very little) Thought most people would go after high value targets and I prefer a quantity over quality approach. Sent a few troops at top castles to counter a similar technique.
234 4 5 6 8 7 11 8 24 10 42 13 0 19 0 28 0 Trying to win 28-27 By trying to determine the optimal strategy, then countering that strategy. And likely failing
235 4 5 6 2 7 19 8 18 18 19 22 3 26 4 2 3 2 23 Thought most people would go after high value targets and I prefer a quantity over quality approach. Sent a few troops at top castles to counter a similar technique. I tested randomly generated deployments against others, and the winners advanced to the next round vs. a newly generated random. the one with the most wins is the submission. I tried to test the winner against all possible deployments, but O^2... it ran all weekend and still hasn't finished haha.
257 4 0 0 0 0 0 0 32 28 32 32 36 I decided to go all in on a single strategy instead of hedging. You need to conquer a minimum on 4 four castles to win. I am putting all my soldiers into those four castles, so I want at least one of them to be uncontested to free up soldiers for other castles. There is only one such group of four that includes the least contested castle. That is (1, 8, 9, 10). I put the minimum force towards 1 that I thought could gain me victory relatively often. I want to maximize my victory points, that is, with the least number of soldiers. The higher the castle, the more troops needed to secure a victory point. To win, I need more than half of the total victory points, which is 55 (to win, I need 28). To achieve this, I selected the fewest castles that will allow me to get 28 victory points, that is: castles 10, 9, 8 and 1 (10+9+8+1=28). So I need to distribute 100 soldiers in these 4 castles and let opponent take all other castles. I weighted the victory points to win vs the amount of soldiers, ie castle 10= 10/28*100=35.7, or 36 , castle 9= 9/28*100=32.1 or 32, castle 8= 8/28*100=28.57, or 29-1. and castle 1 is 1/28*100= 3.57 =4. I assumed castle 1 would be uncontested, but ensured at least its value of 4.
258 4 0 0 0 0 0 0 29 28 32 35 36 To choose a strategy, I have thought about two axes. The first one is the tendency of players to use balanced strategies such as x y x yäó_ with x+y =20 as a response to the simplest strategy of 10 10 10 äó_ the second one is to concentrate troops on castles with 28 as value sum (the number needed to win a battle). Each castle i with a number of troops proportional to its value i.e. 100i/28. Using these two hypotheses, castles with highest values would have fewer troops than their values required (using the first axe). The best strategy would be then (using the second axe) to use a set a castle with sum values 28 and with the highest values possible. We end up then with using Castle 10,9,8 and 1 (sum is 28). Proportional allocation would be 36,32,28 and 4 (sum is 100).
259 4 3 0 11 0 11 0 11 0 11 0 21 0 26 28 2 32 2 36 2 I want to maximize my victory points, that is, with the least number of soldiers. The higher the castle, the more troops needed to secure a victory point. To win, I need more than half of the total victory points, which is 55 (to win, I need 28). To achieve this, I selected the fewest castles that will allow me to get 28 victory points, that is: castles 10, 9, 8 and 1 (10+9+8+1=28). So I need to distribute 100 soldiers in these 4 castles and let opponent take all other castles. I weighted the victory points to win vs the amount of soldiers, ie castle 10= 10/28*100=35.7, or 36 , castle 9= 9/28*100=32.1 or 32, castle 8= 8/28*100=28.57, or 29-1. and castle 1 is 1/28*100= 3.57 =4. I assumed castle 1 would be uncontested, but ensured at least its value of 4. I need to win 28 points to win a war, If someone evenly distributes I beat them. Most other scenarios I win.
4 0 0 0 0 0 0 28 32 36 To choose a strategy, I have thought about two axes. The first one is the tendency of players to use balanced strategies such as x y x yäó_ with x+y =20 as a response to the simplest strategy of 10 10 10 äó_ the second one is to concentrate troops on castles with 28 as value sum (the number needed to win a battle). Each castle i with a number of troops proportional to its value i.e. 100i/28. Using these two hypotheses, castles with highest values would have fewer troops than their values required (using the first axe). The best strategy would be then (using the second axe) to use a set a castle with sum values 28 and with the highest values possible. We end up then with using Castle 10,9,8 and 1 (sum is 28). Proportional allocation would be 36,32,28 and 4 (sum is 100).
260 3 11 9 11 14 11 14 11 10 21 3 26 16 2 14 2 16 2 1 I need to win 28 points to win a war, If someone evenly distributes I beat them. Most other scenarios I win. I wanted a quick programming challenge so I put together a small python notebook to create 200,000 different deployments, ran all the match ups, and spit out a winning deployment. I ran the program five times to get five different deployments, matched them all up against each other and picked the one that had the highest average number of points. Not sexy, but it was fun.
261 3 9 7 14 11 14 10 18 3 21 16 26 14 0 16 0 1 0 I wanted a quick programming challenge so I put together a small python notebook to create 200,000 different deployments, ran all the match ups, and spit out a winning deployment. I ran the program five times to get five different deployments, matched them all up against each other and picked the one that had the highest average number of points. Not sexy, but it was fun. Point weighted distribution of troops for the lowest 7 ranked castles (which constitute the majority of the points in the game).
262 3 7 11 14 18 0 21 0 26 0 0 29 0 0 36 Point weighted distribution of troops for the lowest 7 ranked castles (which constitute the majority of the points in the game). I've no real knowledge of game theory so I'd imagine mine is extremely primitive but it was based on the idea of attempting to win exactly enough points to have a majority and not contest the other towers. Obviously there are a variety of combinations that come to the 28 points needed. I then calculated how many troops should go to each tower proportionally based on the value of the tower relative to the target value of 28. As for which of the many combinations adding up to 28 I selected? Well I stook my finger in the air and picked (10, 8, 4, 3, 2, 1), as I felt it had a nice balance of covering the Highest value tower, but also covering a decent spread of other towers.
290 3 5 7 11 9 14 11 17 13 20 15 23 17 0 20 0 I predict people will over-deploy on the biggest castles. Thus I can save these troops and use them to win all the other castles. I added a bonus troop to castles 7 and 8 in case someone thinks like I do. Concede castle 10 in hopes that opponents will deploy large troops there.
291 3 5 7 9 11 13 15 17 20 19 0 1 Concede castle 10 in hopes that opponents will deploy large troops there. Punt on Castle 10, try to take the rest.
292 3 5 7 9 11 13 15 17 19 1 Punt on Castle 10, try to take the rest. I thought about splitting my troops roughly equally according to the castles' value. Then I decided to sacrifice Castle 10, which I expect most people to fight over, and get a bit of a boost everywhere else. But I left 1 soldier at Castle 10 in case some people send none there. By the way it would be cool if you published not just the winner but the entire ranking table so we could all see how we did.
3 5 7 9 11 13 15 17 19 1 I thought about splitting my troops roughly equally according to the castles' value. Then I decided to sacrifice Castle 10, which I expect most people to fight over, and get a bit of a boost everywhere else. But I left 1 soldier at Castle 10 in case some people send none there. By the way it would be cool if you published not just the winner but the entire ranking table so we could all see how we did.
293 3 5 7 9 11 13 15 17 19 1 x 2 +1
294 3 5 7 9 11 13 15 17 19 1 Intuition as a game designer - trying to stay 2 steps ahead. Also, liked the pattern.
295 3 5 7 9 11 13 15 17 19 1
392 2 4 6 8 10 12 10 14 12 20 14 24 16 0 18 A small perturbation of troops proportional to reward, forfeiting the largest castle in favour of the next two largest. No particular reason
393 2 4 6 8 10 9 12 11 14 16 17 18 29 10 0 I feel like castle 10 isn't worth it Sacrificed the 10 castle as most people will over value this one. With 45 potential points then available an equal distribution of the 100 soldiers would put 2.2 soldiers x value of castle on each castle. I then overweighted the higher value castles some.
394 2 4 6 8 10 0 12 14 16 18 10 20 I wanted to distribute my soldiers proportionally to each castle value. At two soldiers per castle point, I would need 110 soldiers, so I just dropped #5. Although it reduces my maximum to 52.5, that distribution has the advantage of faring well against very lopsided strategies... I'm guessing :)
2 4 6 8 10 12 14 16 18 10 2 more than the Castle is worth (which only leaves half for Castle 10)
395 2 4 6 5 8 7 10 11 12 13 14 17 16 19 18 20 0 2 Each point of the castle worth of 2 soldiers but the last one, since the enemy will try to conquer it by all means. Essentially abandon 10 because it will be largely overshot (win if opponent places 0 or 1 though). From there, place troops according to castle points with some extras on 7-8-9. Will handly beat someone with weighted distribution or too many on 10 which I anticipate will be the most common placements.
396 2 4 6 5 8 7 10 9 10 15 12 17 14 20 16 21 18 0 No particular reason I loaded my forces to the mid range castles, figuring that naive opponents would overload castle 10.
397 2 4 6 5 8 7 9 11 14 13 17 15 29 16 0 18 Sacrificed the 10 castle as most people will over value this one. With 45 potential points then available an equal distribution of the 100 soldiers would put 2.2 soldiers x value of castle on each castle. I then overweighted the higher value castles some. Closest to the fractional value of each castle.
436 2 4 5 4 7 8 9 11 10 13 12 14 15 16 17 19 Soldiers divided by the available points = (100/55) 1.81 Soldiers were then assigned to castles based on the value of the castle. (99 Soldiers) (One extra soldier was applied to Castle 10. In case someone chooses the same strategy, then you split the points, so it is not worth applying it to any other than the most valuable one.) I'm not a big mathematician but i like to try, and i appreciate your riddles :) Not knowing how my fellow Riddler readers will attack this problem, I went for the optimal strategy against a random distribution. The ideal ratio of troops each to point is 1.8181... . I believe my distribution comes as close as possible to achieving that, as measured by the average of castle-by-castle ratios. We'll see how it goes!
437 2 4 5 4 7 4 9 4 11 10 13 18 14 20 16 22 19 12 I attempted to pick values equivalent to the victories points value in making up 28 victory points. For example, winning castle 10 gives you 34.7% of the victory points needed to win a majority. The proportional percentage of this is about 18%. (I chose 19 because my math rounding got me 99 soldiers in battle.) I've played this before! In the past I've seen that 4 is usually enough to contest the lower castles, while committing too much to castle 10 is often a mistake, especially among groups still new to the game.
438 2 4 5 2 7 3 9 14 11 21 13 1 14 30 16 21 16 2 Determine each castle's percentage of the total points then assigned that many units then added the remaining unit to the most valuable castle. The best result from a somewhat improved algorithm. The old code is at http://pastebin.com/zT2PifR4, while the new code is at http://pastebin.com/Q3UYquxr.
2 4 5 5 10 10 20 40 4 0 Really don't know
439 2 4 3 5 11 5 2 3 15 3 18 4 21 4 1 32 26 38 1 The deployment is based on a few key principles: 1. Have a set minimum number of troops for each castle It pays to leave a few troops in each castle, even the lower valued ones. If an opponent leaves a castle empty (and it is likely that a decent chunk of opponents will do so in order to focus on higher-valued castles) then you can gain substantial points for a very small cost. The minimum is largely trial and error; I ended up with 3 as this was a good compromise between saving troops for larger castles and not getting easily defeated. I did not apply this minimum to Castle 1 as it would not be economic to do so - Castle 1 is worth so little that deploying more than 2 troops to it can quickly become a waste. 2. Fight hard for Castles 9 and 10 This should seem obvious, but if you can win both of these it makes your work a lot easier. On the other hand, if an opponent manages to beat you in these then they have barely any troops left, and thanks to your minimum you have a good chance of winning most of the rest. 2. Pay more attention to Castles 1-4 then 5-6 You can win Castles 1-4 fairly cheaply and get an easy 10 points. If you also win Castles 9 and 10 then you have easily won the war. On the other hand, if an opponent also focuses on 1-4, then the minimum should give you at least a few points in the middle. Combine with #2 and you have a decent shot. 3. Don't try to remain undefeated No deployment is undefeatable. My deployment, for instance, loses to putting 10 soldiers in each castle, and also to the deployment 1,3,5,7,9,11,13,15,17,19 (in Castles 1-10 respectively) which could be considered the "mean" deployment. Other submitters are unlikely to go with these deployments as they are overall quite weak - they are more likely to go with stronger options which nonetheless have vulnerabilities. One likely mistake is to heavily weight 3 Castles instead of 2 - you will not be able to put enough soldiers in each to beat a strong Castle 9 or 10, effectively wasting a larger amount of soldiers while also leaving less for the smaller castles. Remember, any path to victory requires at least 4 castles. Through these principles and trial and error, I found this deployment to be the most successful, beating 22 other hypothetical deployments. I wanted a slightly random option that would defeat obvious choices like an even distribution (10 to each of 10 castles). Or going for all the top castles (25 each on 10, 9, 8, x) which I would prevent by winning castle 9. I was initially going to go for all of the lower castles, (7 and below) but that would lose whenever someone spent big on 10, 9, 8, and a random one. My goal here is to win castle 9 almost always, 7 almost always, and usually 6, 5, and 3 without conceding any other castles. Winning these castles would provide 30 points and a win. Losing one of them could be made up if someone sent zero soldiers to castles to some of the other castles. If someone else tried a similar strategy while sending 0 to any castle (especially 8 or 10), that would be a victory for me and a large bonus.
440 2 4 3 4 8 8 2 9 2 10 0 12 17 15 26 17 38 19 2 Not knowing how my fellow Riddler readers will attack this problem, I went for the optimal strategy against a random distribution. The ideal ratio of troops each to point is 1.8181... . I believe my distribution comes as close as possible to achieving that, as measured by the average of castle-by-castle ratios. We'll see how it goes! I'm ceding ten because others will deploy a lot of troops there--hopefully many will be wasted. Trying to get the next three plus Castle 3 which would just barely be a win. Also hoping to sneak in on some places where the enemy might have put in 0 or 1.
441 2 4 3 4 7 4 9 4 13 10 18 18 20 20 24 22 2 12 2 I've played this before! In the past I've seen that 4 is usually enough to contest the lower castles, while committing too much to castle 10 is often a mistake, especially among groups still new to the game. We decided to sacrifice the 9/10, hope that most people will waste too many armies there and we could win the rest.
444 2 3 8 6 2 6 2 11 0 16 17 22 26 32 38 1 2 1 I'm ceding ten because others will deploy a lot of troops there--hopefully many will be wasted. Trying to get the next three plus Castle 3 which would just barely be a win. Also hoping to sneak in on some places where the enemy might have put in 0 or 1. Don't deploy any substantial troops to 9 or 10; let the others waste troops on them. Focus on 1-8; can still win if lose castle 8, so multiple win conditions. Deploy numbers like 16 and 11 to hurdle opponents who go for multiples of 5.
445 2 3 7 5 9 8 13 18 21 20 13 24 21 2 13 2 1 We decided to sacrifice the 9/10, hope that most people will waste too many armies there and we could win the rest. Attempt to pick a different strategy than most people
446 2 3 7 5 9 8 11 12 13 17 15 23 18 30 21 0 1 0 Sacrifice 10 and load up on the rest..look at soldiers per point and give about equal resources per that metric
2 3 6 11 16 26 33 1 1 1 -Worth leaving 1 point at every castle, in case opponent leaves 0 -People will waste troops on high point castles -Many people will use round numbers (10, 15, 20), so putting 1 extra point will mean a few free victories. -The goal isn't to beat the *best* players, but to beat the *most*, and this strat should be decent against a lot of comps
447 2 3 6 5 6 7 11 10 16 11 22 13 32 14 1 16 1 19 Don't deploy any substantial troops to 9 or 10; let the others waste troops on them. Focus on 1-8; can still win if lose castle 8, so multiple win conditions. Deploy numbers like 16 and 11 to hurdle opponents who go for multiples of 5. Based on points and number of soldiers, you want about 1.8*points value at each castle. I then rounded to the closest whole number.
448 2 3 5 10 7 10 9 10 15 10 17 20 19 10 21 10 2 I figure most people will go heavy on the top two. Started with distributing by value. 10/55= 18.2% so should have 18 soldiers. Then I figured others will use this strategy so I should take advantage of it. I also wanted to take advantage of those who put too much value on castle 10, but also take advantage of anyone who sends only one soldier.
449 2 3 5 8 7 13 9 21 11 13 21 15 13 17 1 18 Attempt to pick a different strategy than most people Figured out the total number of points, and allocated troops based upon each Castle's portion.
500 2 2 2 22 16 2 17 2 18 22 19 22 20 22 2 2 I identified the minimum number of castles to reach 28 points (4), and placed the maximum number of troops I could while still being able to place 2 everywhere else. I chose 2 everywhere else so that I could win others if someone else decided to put 0 or 1 there, which would make up for losing some of the others. we need 27.5 points to get a victory. overloading the top two castles only nets 19 points and i feel like an emphasis will be to get the highest castles. I'm overloading the middle 8,7,6,5,4. that's 30 points for a victory. the 2 soldiers at the remaing 5 castles are to win castles left with 0 or 1 soldiers and to not completely concede the other 5 castles.
501 2 2 2 21 16 5 2 3 19 21 2 21 15 21 25 2 15 There needs to be a focus on at least four of the castles in order to enough points to win (28). Castle 10 is the most likely to draw large numbers of troops due to its high value, so attacking 9, 8, and 7 will hopefully guarantee some values. The rest of the castles attracted low numbers in the case of an opponent simply not sending any troops or only sending one to pick up any uncontested castles. Given that Blotto games are notoriously difficult, I assumed people would not play Nash Equilibrium strategies (this may be a terrible assumption, but I also didn't want to solve for Nash Equilibrium in a different variation of a Blotto game from what I'm used to). With 55 VP total, you need 28 to win. I figured a number of people would try that by going low (1-7), or high (1, 8-10). I thought people would think going high is the obvious choice, and go low. So I mostly went high, but put large allocations on a few small ones other than 1 (since that is needed for both low an high).
502 2 2 2 21 15 2 16 29 17 2 25 2 5 2 6 36 10 focus on 3 castles, disrupt other strategies, capture uncontested castles Hybridization. Aggressively pursuing lower castle chunks against basic high castle value strategy while leaving medium low numbers to feast on remains of overly clever NYT readership.
2 2 2 20 2 2 22 22 24 2 Trying to win castles 9, 8, 7, and 4 to score more than half the points. Also trying to poach castles where my opponent put 1 or 0 soldiers.
503 2 2 2 16 14 17 16 18 19 20 20 22 2 2 we need 27.5 points to get a victory. overloading the top two castles only nets 19 points and i feel like an emphasis will be to get the highest castles. I'm overloading the middle 8,7,6,5,4. that's 30 points for a victory. the 2 soldiers at the remaing 5 castles are to win castles left with 0 or 1 soldiers and to not completely concede the other 5 castles. Trying yo win all from 4 to 8, which is enough to win the war. Also, trying to win "free" castles.
504 2 2 2 16 12 2 15 19 18 2 21 15 24 25 2 15 2 Given that Blotto games are notoriously difficult, I assumed people would not play Nash Equilibrium strategies (this may be a terrible assumption, but I also didn't want to solve for Nash Equilibrium in a different variation of a Blotto game from what I'm used to). With 55 VP total, you need 28 to win. I figured a number of people would try that by going low (1-7), or high (1, 8-10). I thought people would think going high is the obvious choice, and go low. So I mostly went high, but put large allocations on a few small ones other than 1 (since that is needed for both low an high). I decided to try to claim a set of middle value castles that are worth over 100 points, allocating 3 soldiers per point for those castles. The remaining soldiers are distributed 2 each in the remaining castles, in case there are any unguarded easy captures.
505 2 2 2 15 12 17 15 18 19 21 20 24 2 2 Assuming people would go for the highest value castles the most I started with castle 8, assuming I'd win sometimes, then incremented down, removing one from each lower castle because of the lower priority. Then I dumped 2 into each other castle to catch anyone who tried a similar strategy, assuming they'd only leave 1 to go for the split. At least 2 everywhere to win castles against people who leave castles empty/one token soldier. Focus on mid-high numbers as enough points on offer to get to 28. Do not want to waste a sizeable amount of troop on 9 and 10 has other armies could really focus on winning points there
521 2 2 2 6 3 8 5 16 6 16 9 16 14 16 22 16 35 I wanted to distribute them somewhat evenly towards the higher numbers Picked some Fibonacci like numbers
522 2 2 2 6 3 8 4 12 6 14 11 16 14 20 22 18 34 Modeled chance of winning each castle as an exponential distribution in the number of soldiers used, and then iterated through different possible means (generally increasing as the point value increased, though not always, especially at either end of the scale). Iterated through possible strategies and chose the most successful ones for various values of the means, then cross-tested them for robustness. Achieved about an 80% win rate with this one in my simulations. I noticed that the sum of the first 9 Fibonacci numbers was 88, so if I placed 1 troop in castle 1 and started the sequence on castle 2, I would have enough troops left over to place an additional troop in each castle. This left me with 1 remaining troop for castle 7, as placing 9 troops seems quite inefficient in a game where you expect a lot of 10s. Looking over my answer, it felt a little crazy spending 35 troops on castle 10, so I bumped it down to 34 and placed that remaining troop again in castle 7 so I could beat the 10s instead of tie.
523 2 2 2 5 3 5 3 26 10 26 18 26 19 3 20 3 21 Never leaving any blank but counting on the middles. Emphasis on winning highest value castles
2 2 2 4 10 12 14 16 18 20 trying to win 4 of the highest 6
524 2 2 2 3 2 5 22 6 22 9 22 14 2 22 2 35 22 Picked some Fibonacci like numbers I never put 0 or 1 soldier in a castle because I suspect that several opposing armies will often put 0 or 1 soldier, and I want to be able to win those. For some reason, I feel like folks will focus a lot of their troops on castles 8 and 9, so I mostly want to concede those castle, (except I want to win it if the opponents are also conceding the castle). I also kinda feel like there's not much difference between 13 to 19, but 20, 21, and 22 armies are each more likely to win.
525 2 2 2 3 2 4 21 6 21 11 21 14 21 22 4 34 4 I noticed that the sum of the first 9 Fibonacci numbers was 88, so if I placed 1 troop in castle 1 and started the sequence on castle 2, I would have enough troops left over to place an additional troop in each castle. This left me with 1 remaining troop for castle 7, as placing 9 troops seems quite inefficient in a game where you expect a lot of 10s. Looking over my answer, it felt a little crazy spending 35 troops on castle 10, so I bumped it down to 34 and placed that remaining troop again in castle 7 so I could beat the 10s instead of tie. Minimal focus on the very high (people more likely to devote large amounts of troops to capture the most valuable castles) allows me to heavily attack the middle ones. Capturing 9 and 10 is worth 19 points, but 5-8 is 26. Putting 4 towards 9 and 10 lets me potentially capture them from other people attempting to metagame similarly to me.
526 2 2 2 3 2 3 18 10 20 18 2 19 22 20 28 21 2 Emphasis on winning highest value castles Reduce wasted troops contesting some castles, but still trying to edge out others using the same strategy. Also, making sure to commit heavily to enough castles to get to 28 points
624 1 5 4 1 5 5 1 15 5 15 1 15 5 15 38 25 38 0 I let each soldier choose for himself No sense fighting over castle 10. Concentrate forces on 9, which is worth almost as much, and the other higher-value castles. A few points to lower-valued castles in case someone concentrated more heavily on the higher-valued ones.
625 1 5 4 1 2 1 2 17 3 21 12 24 14 28 16 1 26 1 20 Attempt to secure 28 points needed to win while exploiting opponents assigning 0s. First I picked several intuitive submissions: all 10s, 100 at Castle 10, and "1, 3, 5, ... 19", among others. Then I ran a script to pick a deployment that generally performs well against all of them.
626 1 4 9 1 3 11 16 1 19 21 7 1 10 26 12 1 19 33 This game, at this scale, is not solvable through theory alone. In a simpler, 3-battlefield case this problem is essentially solved, but with 10 battlefields and 100 soldiers the scale is too large. I decided the best course of action would be to optimize over the win/loss rate of a strategy against a set of random possible opposing strategies. So I booted up R and ran a simulated annealing algorithm to create a strategy that seemed to win a lot. That failed horribly because the set of all opposing strategies is enormous. So instead of trying out random opposing sets, I tried to create a smaller set of "plausible" opposing strategies (repeated or nearly-repeated values in 3-10 slots making up the bulk of the allocation, with random allocation to all other slots). I found a strategy that was robust to my changing various parameters of my "plausible strategy" set, and decided to submit that (win rate in my simulator is about 87% across plausible-strategy perturbations). I don't know if I picked a good plausible strategy set, but that's why I'm submitting my answer! I did check to make sure it beats "all 10's" and "11's and 9's," which I suspect will be really common. I don't beat (0,0,0,0,0,0,25,25,25,25), but that's a risk I'm going to take. I brainstormed a lot of different strategies and played them off against one another. This one (focusing on the even towers) came out on top. I tried to look at different ways to get to 28 points, with perhaps some wiggle room. The obvious is just to aim for the high numbers. Towers 8-10 leave you one point short, so you can try to take the #7 or drop all the way to trying to sneak the #1. You can try to abandon the high numbers and just take #1-7. I thought of some sneaky in between answers, like taking towers #4-8. Generally the top heavy strategies worked well. Any strategy that focused more troops on the bigger towers did better than those that divvied out the troops equally. This final strategy of focusing on the even towers ended up winning the mini battle-royale. I suppose the point is to win the 10, while conceding the 9, win the 8 , while conceding the seven, and so on, netting just enough points to win with a little room to spare. I made sure to get at least one troop to each tower to sneak wins against folks who focus too heavily. I massaged some of the totals to keep them above any product of 5 (11, 21, 26...). I figured 33 was good up top, since most folks won't commit more than 1/3 of their army to any one tower.
1 4 7 9 15 17 2 19 26 0 Every strategy can be beaten if known in advance. It's not possible to guess what other people will do, but I've dropped out of competing for castle 10, while trying to ensure I win castle 9 as well as 8, 6 and 5 totalling a winning 28 points. I've spread some remaining troops around the lower numbers in order to hopefully pick up enough points if I lose one of the castles in my primary strategy.
627 1 4 6 1 12 3 15 11 15 17 21 10 24 21 1 1 31 Give up on the two highest where opponents will mostly focus their troops. Focus instead on capturing mid-high value castles. Wrote a script to generate a bunch of strategies and play them in a big round robin + elimination tournament.
628 1 4 6 1 8 1 12 18 14 21 16 26 18 26 20 1 1 Most people will put some of their troops on the biggest point castle, 10, leaving less for the rest. So I give away castle 10 and divide out the rest according to the castle's worth proportionately. The extras I have I use to gain a slight advantage to higher point castles. I cover castle 10 with 1 troop in case someone else has the same logic as me. I'm pretty certain this game isn't solveable and I'm far too lazy to model scenarios so I just played a few practice rounds with "friends" and submitted the most successful one.
629 1 4 6 1 8 1 10 1 12 1 14 1 16 30 18 30 11 30 Most people will load up the high value so i give away the top spot unless they are spread evenly to try to ensure the next group can be won
652 1 3 5 7 9 11 13 15 17 19 Made the % of troops near % of points available rounding down. Put extra troops on biggest one evenly spread. I used each castle's Shapely-Shubik power index to distribute troops.
653 1 3 5 7 9 11 13 15 17 19 proportionally to the Banzhaf power index basically deployed 1.8 per castle point rounded down
654 1 3 5 7 9 11 13 15 17 19 Strict linear distribution, using 100 as the total, and trying to maximize Castle 10 without losing all the other ones. Started at 1 troop for Castle 1, then kept adding until I filled all of the 100 spots. Interestingly, my naive solution was to just use an arithmetic sequence starting at 1 with an increment of 2. My long winded solution below comes out as almost the exact same result, so I just went with the naive one. After much back and forth, I gave up on trying to predict others' strategies and assigned soldiers solely based on my perceived relative importance of the castles for victory. I used the following python script to determine relative importance of castles. (I ignored ties in my analysis to keep it simple) from collections import defaultdict from itertools import combinations from math import ceil # constants SOLDIERS = 100 CASTLES = 10 total_points = sum(range(CASTLES + 1)) victory_points = ceil(total_points / 2) # 1024 (2 ** 10) combinations of conquering 10 castles combs = [] for x in range(11): combs.extend(list(combinations(range(1, CASTLES + 1), x))) # Half the combinations have enough points for victory winning_combs = [comb for comb in combs if sum(comb) >= victory_points] # Weigh importance of castle by inverse of total castles needed. # Only count a castle if victory depended on it. weighted_score = defaultdict(float) for comb in winning_combs: total = sum(comb) weight = 1 / len(comb) for val in comb: if total - val < victory_points: weighted_score[val] += weight # Assign soldiers proportional to weighted score normalizer = sum(weighted_score.values()) / SOLDIERS soldier_proportions = {k: v / normalizer for k, v in weighted_score.items()}
1 3 5 7 9 11 13 15 17 19 A simple pattern.
655 1 3 5 7 9 11 13 15 17 19 I felt like they should be distributed mostly proportionally to the amount of points up for grabs, and so 2p-1=s fit that idea.
656 1 3 5 7 9 11 13 15 17 19 I decided to choose soldiers proportional to the values of each victory point. Roughly proportional to the value of each castle
657 1 3 5 7 9 11 13 15 17 19 I used each castle's Shapely-Shubik power index to distribute troops. linear progressions sound good
720 1 2 1 2 15 1 17 16 1 22 21 26 21 27 21 1 2 1 Overthought and undermathed Pick 5 castles to hold most troops that sufficient to win if I get them all. 1 instead of 0 in others to pick up easy wins if somebody puts 0. Avoid 9 and 10 as the most valuable, where many people will put many troops.
721 1 2 1 2 13 1 1 16 23 21 23 21 23 24 23 1 1 Winning towers 6-9 will yield a point value of 30 points out of the possible 55 which would win. In order to divide them I sent one to the other remaining towers which left me with 94 troops for four towers. 94/4= 23.5 so 23 troops per tower. The remaining two troops were placed on tower 2 & 3 in case of a tie. This is a game to 28, avoiding the most obvious big wins, and going for the middle ones should optimize my wins in the middle. Avoiding multiples of 10 and 5 should reduce ties. Keeping one in each castle will pick those up for people who completely ignore those
722 1 1 29 13 24 1 19 1 1 12 15 11 31 1 1 35 I wrote a script to compare a bunch of what I though were reasonable strategies, and this one performed the second best compared to that set of plans (the best strategy used 0's instead of 1's on the non-priority castles, but I figured this one was probably more robust against crazy strategies other people might use that have a bunch of 0's). You can find my script here: https://github.com/jakewalker56/ml-lab/blob/master/visualization/riddler_castles.R I rolled a 10-sided die to choose which castles to focus on - until I got a set that got me 28 points (the minimum to win) in the minimum number of castles (4). These castles would be my focus where almost all my troops would go. This exploits strategies that try to win all or almost all the castles. Putting at least 1 in all castles is attempting to exploit strategies that don't send any troops to certain castles (I initially tried a strategy where I was exploiting this by putting at least 2 in all castles, but it seemed this didn't leave enough for the ones I was focusing on). I divided my remaining 94 soldiers into the castles I was targeting by proportion of points they were worth. I made a few adjustments to that in order to try to exploit strategies which divided proportionally (and to avoid similar exploitation myself). This is also to try to make up for the loss of 6 soldiers to my previous point. I'm sure this loses to computer-simulation-designed strategies, but I think it will do well against a large range of 30-minutes-of-thinking strategies.
1 1 19 1 12 19 19 26 1 1 Aiming to grab a "non-optimal" >28 using numbers that add to 30 (wasting soldiers) and splitting extras for ties and a change to grab undefended castles. Boosted chance on 8 to stop losing to a 25/25/25/25 split on the top half. Took the extra soldiers from 5 since it doesn't feature in many easy 28 additions
723 1 1 17 11 18 12 1 19 20 24 21 29 1 1 I didn't want to put too many resources into the highest values, assuming others will put plenty of resources into them. By ceding those, I have more soldiers left for the others. Similarly, I assume some people will have this thought and put lots into the lowest values, or think both of those things and focus in the center. My distribution avoids the bottom (1 and 2), the top (9 and 10), and the very middle (5). The castles I have put resources into total exactly 28 points, which is exactly the amount necessary to win. If I do take all five of those, then I have no need for any other castles. I then sent 95 of my soldiers to these five, weighted ever so slightly to the higher value ones. This leaves me five left to send, one each, to the other five castles, so that if others leave any castles empty I can grab the points almost for free, potentially saving me if I lose or tie one of the five Iäó»m focusing on. Derp. I submitted the opposite order 2 minutes ago (along with my explanation) because I used a different naming convention in my code.
724 1 1 16 11 16 11 16 1 1 21 16 26 1 26 16 1 16 1 I'm trying to win castles 3,4,5,7,9,10. If I win any five of the six, I'll win. Target smallest, lowest 5-castle win.
725 1 1 16 11 16 11 16 1 1 11 16 11 1 26 16 1 16 26 I'm trying to win castles 3,4,5,7,9,10. If I win any five of the six, I'll win.
781 1 1 1 17 14 18 15 19 16 20 25 21 25 1 1 The goal here is to claim 30 points, and give up the remaining 25. I feel like many people will try to claim the 10 and 9 castles (with them being the most valuable targets), so I'm focusing on castles 4-8. I did place one soldier on a suicide mission to each of the remaining castles, just in case someone decided to completely abandon a castle I can claim a free VP or two. I tried pick a strategy that could counter strategies such as uniform deployment and top end (7,8,9,10) deployment. I focused on the middle castles, but left at least one troop everywhere to get free castles in case others leave them open.
782 1 1 1 16 14 1 14 1 14 26 14 26 14 26 14 1 13 This essentially an electoral college problem - a race to 28 points. Mostly ignore 10 (California) so opponent's expected high deployment there is an inefficient use of resources. However, use 1 in every castle in case it is ignored. I choose 9, 8, 7 and 4 as my path to 28. I also went with 26 instead of 25 in 9, 8, and 7 to counter someone trying to do the same strategy with an even split of 25 in each castle. 4 gets less troops because its not really a critical path to winning, especially if I pick up some other small ones which were ignored. maximize chance to win 7, concede 3
783 1 1 1 15 14 20 1 20 1 20 24 20 27 1 30 1 0 Sacrifice the top 2 to give a better chance at holding the next 5 highest which would be enough to guarantee victory. Also, put at least 1 in every Castle in case opponent doesn't bother defending. Voodoo
1 1 1 15 20 20 20 20 1 1 Reasoning was psychological, with expected opponent preference for either near-exclusive focus on valuable castles or an even spread. This distribution is designed to defeat both approaches. At least 1 point in each punishes exclusive focus anywhere, while grabbing all mid-value castles will beat the top two, or three if you get all the low-value ones as well.
784 1 1 1 15 14 18 1 1 27 18 1 26 34 36 1 Put just over (castle VP number)/(28 points needed to win) at four locations totaling 25 VP with expectations of getting the remaining 3 VP from tying or winning another castle where the opponent has not placed troops Safety Case
785 1 1 1 15 13 17 16 19 21 22 23 25 1 1 55 possible points to be won, figure winning 30 points gets a win against most opponents. Let the opponent have the high point castles (9+10) to try and guarantee 30 points from the middle castles. At least 1 soldier at each castle in case the opponent has any zeroes Basically, give up 1,2,3,9, and 10 to anyone willing to fight over them (but not for free - punishing anyone who focuses too hard on specific castles) while committing more to the centre castles 4 to 8. If 4 to 8 are won, the majority of the points are won.
786 1 1 1 15 13 15 16 15 18 16 22 16 0 10 28 10 0 Grab the middle and hope for the best I wanted to only go for 28 of the 55 points, but I hedged my bets by bidding 1 for the low values, hoping that I might win easy points.
787 1 1 1 15 12 1 17 1 18 26 20 25 26 28 2 1 2 I only need 28 points to win. Thus, I can spread my troops out over 4 castles (10, 9, 8, 1 or 9, 8, 7, 4). I chose the second option as I believe I am more likely to lose the 10 castles. Secondly, I want to win all the vacant castles by the other player. Thus, I can win even if I fail to secure all the castles I plan. My distribution was mainly based on a pro rata points spread with the exception, that if an opposing player distributed his/her castles pro rata over castles 1-7, I would still secure both and win. Tried to decisively win in the 4,5,6,7,8 range (if all wins, will definitely win), while devoting minimal resources to 1,2,3 and 9/10 but enough to take them if minimal support from other team.
788 1 1 1 14 12 16 15 19 22 23 24 26 1 1 Essentially abandoning the high point castles allows for many troops in castles required for majority. Duck the 9 and 10 but try and dominate enough to get victory.
789 1 1 1 14 12 15 14 16 25 17 25 18 1 19 1 I tried pick a strategy that could counter strategies such as uniform deployment and top end (7,8,9,10) deployment. I focused on the middle castles, but left at least one troop everywhere to get free castles in case others leave them open. Sacrifice 10 (most likely contested) and low scoring castles, with token soldier in case someone did what I do but leaves 0. Stack all middle tier castles with increasing quantities slightly proportionate to benefit.
1 1 1 14 14 14 14 14 14 13 maximize chance to win 7, concede 3
790 1 1 1 14 12 1 12 1 9 24 1 27 1 30 31 0 31 Voodoo It was not nearly as systematic as I would have liked to have time for. But I designed a similar adjudication tool as you describe you'd use in excel. Started with testing a strategy of comparing single troop deviations from an initial point-value weighting. This led to the realization that I'd have too many iterations to test this searching for the local maximum to fit in m excel. Knew that you just needed a winning coalition, not to represent on each castle (left one soldier on each to cut from cheaters, with slightly similar strategies, though thinking I maybe should've put two in each). Focused bulk of troops on 9 & 10 (my plan pretty much needs those to win, and realized I'd just need to pick up two of 4, 5, or 6, so put some troops there. I'm sure those who had more time probably tested their solutions against this type, but it's what I got.
791 1 1 1 14 12 1 1 18 20 26 25 36 37 1 Safety Case Focus on getting 28 points and sacrificing the 10 point castle.
792 1 1 1 13 11 16 14 19 18 22 21 25 1 1 31 1 Basically, give up 1,2,3,9, and 10 to anyone willing to fight over them (but not for free - punishing anyone who focuses too hard on specific castles) while committing more to the centre castles 4 to 8. If 4 to 8 are won, the majority of the points are won. I didn't want to focus on the big point value castles because people are going to waste a lot of soldiers on those unnecessarily. I went for the middle range ones, with a decent amount of soldiers on the 9 castle so that I could win one big one. I put 1's in 1, 2, 3, 8, and 10 just in case someone is foolish enough to not send any soldiers to a castle. Against both a uniform strategy (10 on all castles) and a weighted average strategy, (weight each castle according to its point value, then send a proportional amount of soldiers to that castle), my strategy wins 31 to 24.
793 1 1 1 13 11 16 1 18 1 22 27 0 28 28 0 1 I wanted to only go for 28 of the 55 points, but I hedged my bets by bidding 1 for the low values, hoping that I might win easy points. Picked a simple route to 28 and defended it without leaving any uncontested.
794 1 1 1 12 11 17 1 18 1 20 21 26 21 2 21 2 21 Tried to decisively win in the 4,5,6,7,8 range (if all wins, will definitely win), while devoting minimal resources to 1,2,3 and 9/10 but enough to take them if minimal support from other team.
795 1 1 1 12 10 15 14 19 18 23 24 26 20 1 10 1 Duck the 9 and 10 but try and dominate enough to get victory. I am guessing a lot of people will overvalue castle 10 and to a lesser extent 9, so I am all but seceding those castles. I am hoping to win a majority of the middle ground by placing a disproportionate amount of troops there, and placing 1 troop everywhere else to beat others who are trying the same strategy as I am.
1 1 1 12 14 16 17 18 19 1 Sacrifice 10 (most likely contested) and low scoring castles, with token soldier in case someone did what I do but leaves 0. Stack all middle tier castles with increasing quantities slightly proportionate to benefit.
796 1 1 1 12 10 12 10 9 1 1 20 1 25 31 30 31 1 It was not nearly as systematic as I would have liked to have time for. But I designed a similar adjudication tool as you describe you'd use in excel. Started with testing a strategy of comparing single troop deviations from an initial point-value weighting. This led to the realization that I'd have too many iterations to test this searching for the local maximum to fit in m excel. Knew that you just needed a winning coalition, not to represent on each castle (left one soldier on each to cut from cheaters, with slightly similar strategies, though thinking I maybe should've put two in each). Focused bulk of troops on 9 & 10 (my plan pretty much needs those to win, and realized I'd just need to pick up two of 4, 5, or 6, so put some troops there. I'm sure those who had more time probably tested their solutions against this type, but it's what I got. I wanted to put at least one soldier on every castle to try to win some without much resource allocation to them or at least split them with anyone else having the same idea. I put more soldiers on castles that I thought would give me the best chance to get to the key 28 points required for victory. Also I love the idea of the community interaction in the riddler this week!
797 1 1 1 12 9 1 11 1 13 20 18 25 20 37 25 1 Focus on getting 28 points and sacrificing the 10 point castle.
798 1 1 1 11 7 14 15 18 15 21 15 1 15 31 15 1 15 I didn't want to focus on the big point value castles because people are going to waste a lot of soldiers on those unnecessarily. I went for the middle range ones, with a decent amount of soldiers on the 9 castle so that I could win one big one. I put 1's in 1, 2, 3, 8, and 10 just in case someone is foolish enough to not send any soldiers to a castle. Against both a uniform strategy (10 on all castles) and a weighted average strategy, (weight each castle according to its point value, then send a proportional amount of soldiers to that castle), my strategy wins 31 to 24. I didnt really have a plan, but thought that I should evenly focus my troops on the higher level ones to get a better chance and put a single troop on the low ones in cas the enemy put 0
813 1 1 1 5 2 11 10 16 12 28 16 29 17 3 19 5 21 Because my buddy Tony showed me his plan and this one beat it. Minimum of 1 to each to win any low hanging fruits -- then emphasize higher value castles
814 1 1 1 5 2 7 3 11 6 15 9 17 14 19 24 23 39 Intuition, whim, and some very amateur gamesmanship. Mimics Fibonacci series. I approximated the percentages for the first ten numbers in the sequence to give higher strengths to higher value castles.
815 1 1 1 5 2 5 3 10 5 1 20 25 21 1 22 50 24 It won the most random matchups I saw Try to win 7,8,9,10, and any other unchallenged castles.
1 1 1 4 1 1 25 30 35 1 Linderman said go for it!
816 1 1 1 3 2 6 3 11 5 18 10 23 20 22 21 14 36 Poisson distribution around SQRT(10), with at least one troop per castle Fibonacci sequence with modifications. Aiming for 28 total points. Playing against a few different strategies. In a simple top 5 get 20 strategy, this wins the bottom castles plus 10 for the win. In an even spread, this gets 34 and wins.
817 1 1 1 3 2 3 2 19 12 20 14 20 17 31 24 1 26 Assumed highest troop concentration would be castle 10 -- want to try and win castles 6-9 I wanted to earn points if someone didn't put any troops at a castle, so I put minimal troops at the first five. Then I just tiered up the troop level at the rate the points go up. I may not win, but I'm confident I can go above .500
818 1 1 1 3 2 1 2 23 11 23 13 23 1 23 1 45 I worked with a few assumptions- You must get to 28. To do this you have to win outright a minimum of 4 towers. (10,9,8, and 1) It is always better to try for every tower with at least one troop. There is also never going to be a perfect strategy which beats all other strategies. The best way to win will be by countering the most common strategies. The higher value towers are worth the most, but getting two lower towers will more often than not, net more value- 10 is equal or worth more than 1/2 of the tower value combinations, 9 is worth less than 1/2 of the combined pairings and so on. I based my selection loosely around the Fibonacci sequence (very loosely) and then chose 8 as a tower to essentially pass on so that I could maybe out guess some of the strategies which simply tried to win the higher towers. Here's hoping, To Battle!
1005 0 4 3 0 3 0 3 15 3 21 20 26 20 34 20 0 25 0 3 I first noted that I only needed 28 points to win the war. I then started finding all of the combinations of castles that add up to 28. I liked 2, 5, 6, 7, 8 the most because I felt that I was making my opponents waste troops on castles 9 and 10. I thought this would leave the middle castles open for my taking, while hopefully leaving just enough behind to secure castle 2.
1006 0 3 6 0 13 0 0 16 4 24 20 26 27 31 26 0 1 0 The best result from a quickly-bodged genetic algorithm. If I realized the deadline was EST this is what I would have submitted then. Not sure if we are allowed to choose 0 for any but I figured all you need is to take castle 5,6,7,8 and then 2 and you're there.
1007 0 3 6 0 11 0 14 17 18 19 19 22 11 25 1 0 I am conceding castle 10 completely, since I expect others will attack it heavily. I am also conceding castles 1, 3, and 4 based on their low point value. I did defend castle 2, since sending troops there means I could lose one of the six castles I sent soldiers to and still have the most points in the battle. Then, I distributed my 100 troops among castles 2, 5, 6, 7, 8, and 9 weighted on the points available, rounding up all fractions for castles 5, 6, 7, 8, and 9, which leaves only 3 left for castle 2.
0 3 5 1 2 14 12 28 1 34 I ran a series of simulations, using a sort of fuzzy genetic algorithm. I started with thousands of random sets, saw what succeeded, and began to apply mutations to the successful sets. Through many hundreds of mutations, certain strategies started to emerge. None appeared drastically stronger than the others. So I chose one of the stronger mutations and am curious to see how it does. : )
1008 0 3 2 4 7 6 16 8 24 14 4 15 34 16 4 17 4 18 The idea is to win forts by small amounts and to lose by big amounts. Am thinking most people will heavily attack castles 9 and 10 which I hope to lose by big amounts, while I hope to win castles 2, 3, 4, 5, 6, and 8 for a 28 to 27 victory! I wrote C++ code to randomly assign soldiers several million times, then tweaked the best result a bit to get marginal improvement and make the values flow better.
1009 0 3 2 4 3 6 10 8 15 12 15 14 22 16 20 18 8 20 Many simulated troops died to bring us this information. Win the bigger castle over uniform strategists, while not getting blitzed too much in the smaller castles
1010 0 3 2 4 3 1 8 0 10 1 12 22 15 24 20 21 30 24 0 Need to win at least 28 points to win a battle. A reasonable strategy should be to exceed the expected number of soldiers at each castle if they were evenly distributed according to points such that you gain at least 28 points (e.g. try to win castles 10, 9, 6, 3). In practice, I used a genetic "like" algorithm to randomly evolve a population of 1000 strategies that competed against each other and took the best performing strategy out of that population after 1000 generations. The algorithm used elitism where the top 10% of strategies were carried over from one generation to the next. The top 40% of strategies were each randomly modified by shifting a few soldiers around (15 on average). The final 50% of the population at each generation was a set of random new strategies. Random
1031 0 1 6 3 8 3 15 6 2 10 19 20 21 19 26 1 2 37 Step 1. Allocate troops proportional to value +6. (160 total) Step 2. Surrender castle 10 and 6 to avoid bloodshed in favor of fortifying other castles. Leave 2 troops in 10 and 6 just in case. (123 total) Step 3. Reduce forces in castle 1-4 to comply with 100 force total. Step 4. Randomly reallocate to counter human tendencies. Lots of computer simulations... then an itsy-bitsy tweak to guarantee I'd beat my own answer.
1032 0 1 6 3 8 1 10 11 11 12 13 12 15 19 17 22 19 (100. / sum(np.arange(11)))*np.array(np.arange(11)) Then rounded up. I don't have a good explanation for this.
1033 0 1 6 2 8 7 10 11 11 15 13 19 15 21 17 22 19 2 There are 55 total victory points. On average, each point will be secured by 100/55 of a soldier. Trying to allocate that number of soldiers to each point gives an approximate number of soldiers to allocate for each castle. I took the ceiling of each number to ensure that I sent at least enough soldiers to capture the castles based on their worth. Rounding allowed exactly 100 soldiers to be allocated to each castle, but on average, I would be losing the 10 and 9 castle to be able to win the 1 and 2 castle. Not a good trade-off. As a result, I had 5 extra soldiers allocated. I simply took them away from the lowest valued castles (2 from castle #1 and 3 from castle #2) until I had gone back down to 100 soldiers. The most tempting soldier to redeploy is at castle #5 since I think I need 9.09 soldiers and have allocated a full 10. That is a lot of wasted soldier, but is worth securing castle #5 over getting a small chance at castle #1 or #2. Value difference between 9 and 10 not that much, and assumed most people would focus on 10, so shifted resources away. Still wanted a few soldiers in most castles in case people consolidated too much. Ran some crude tests to see how this distribution compared to others like a even, proportional, and various versions of my strategy.
0 1 5 5 5 0 21 21 21 21
1034 0 1 4 2 5 4 6 7 9 14 13 14 17 22 21 25 26 Ran lots of Python simulations. Winning strategies tended to have about a quarter of the troops at Castle 10. i wanted to slightly beat what i thought the popular solutions would be: 2, 4, 5, 7, 9, 11, 13, 15, 16, 18 (a proportional solution) 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 (a naive solution) and 20, 20, 20, 20, 20, 0, 0, 0, 0, 0 (concentrating on bigger towers) i decided to make my armies proportional to the squares of victory points. these are roughly in agreement with the power index with these voters.
1035 0 1 3 2 6 4 9 7 13 9 17 13 22 17 28 21 1 26 Firstly, I decide not to seriously contest castle number 10. As it's a high value target it can be expected that many people will throw a lot of soldiers at it, and without contesting it I'll have more soldiers left over to have a better shot at claiming the other castles. Now I want to assign troops to the remaining castles, but ensure that I assign more troops to the more valuable ones. I square the value of each remaining castle (so castle 3 is worth 9, castle 9 is worth 81, for a total of 285 points) I then assign troops to each castle with a weighting proportional to this squared value (so castle 9 gets 81/285*100 soldiers, or 28) Due to rounding errors there's one soldier left over after this process, I place him in the 10th castle just in case my opponent has also decided not to contest it. Proportional to x^2
1036 0 1 3 2 6 4 1 7 23 9 2 13 27 16 35 21 2 27 Gameplan: Win 28 victory points through capturing castles. Objective: Conquer the kingdom. The total value of the castles is 55. The total victory points needed to win is 28, assuming no ties. The first thing to do is to establish the minimum number of ways to reach the winning number, given some assumptions and assessing potential strategies. I had to be careful that my strategy could not lose to an even distribution, and I assumed that everyone else would take the same precautions. Now, I wouldn't have to worry about other strategys that would lose to 10 troops at each castle, 20 trooops at 5 castles, etc. What I did need to worry about were more developed strategies like a bell distribution and whether or not people would put more than a third of their troops on one castle to secure a victory. Initially, I believed that giving up free castles was a poor strategy, so I started with the idea that a troop must be sent to each castle. That most players would send most of their troops to castle #10 was an assumption I kept. Assessing the average of winning #8 and #9 was as good as winning #7 and #10, I decided to lose the a few battles, and win the war. After many campaigns, I had a lot of rock/paper/scissors where one of my strategies would lose to one that didn't follow assumptions, but that one would lose to a more deliberate bell-curve or even spread. I decided to remove the requirement of challenging each castle, and kept optimizing, while ensuring they were safe from easily preventable defeats. Weighted the soldiers by the sum of the squares to increasing weight of the more valuable castles
1075 0 0 15 11 0 15 0 20 30 26 35 28 0 0 There are 55 points to win, I need 28. I don't need to win every round, just the majority so if I deploy to win exactly 28 points in some of the less likeable castles, I should win more often then not. Goal is to get 28/55 points and no more. Anticipating what other peoples' common strategies might be, I selected a combination of castles and troop deployments designed with an attempt to win exactly 28 points in a typical one-on-one match-up.
1076 0 0 15 11 0 14 0 15 21 0 25 0 29 35 0 35 0 It beat my previous strategy Find the total points (55) then minimum winning total (28). Determine which combinations of castles yields 28 points (15 total combinations). Find the percentage each castle would make up a victory condition. Add each percentage of a combination and remove any combination above 100% leaving 6 combinations. Find each castle's percentage of total points then remove any combinations above 50% leaving four combinations (10-8-6-4, 10-9-6-3, 8-7-6-4-3, and 10-9-4-3-2). Went with gut in decision of 8-7-6-4-3 combination due to belief that majority of people will go after 10 and 9. Used percentages from winning total calculations as number of units in each castle.
1077 0 0 14 11 16 14 20 0 20 16 24 14 29 0 1 0 1 The higher numbers are likely to draw more troops from one's opponent, thus making them harder to win. The lower numbers are easier to win, but provide less value per troop. It seems making a play for the middle values offers the highest likely return on troop investment. Since 28/55 is needed to win, the 33 points offered by the middle six numbers would be sufficient to win. You need 28 points to win so only play for them, I went for the mid values as I more people would go all out for the high values.
0 0 14 15 0 15 15 39 1 1 The most general strategy for defeating "random" deployments is to pick a set of castles representing a majority of points. Most obvious would be the high-point castles, and in fact if you look at the 27 combinations of four castles that add up to 28 points or more, each of the top three castles are required for at least 17 of the 27. So, we expect most strategies to rely on two or more of the top three castles plus two others (25,0,25,0,25,0,25,0,0,0). The available approaches to beat these baseline strategies are: 1) Claim two of those three with overwhelming strength and pick two more with sufficient strength to pick them up against token support (0,37,37,0,13,13,0,0,0,) 2) Figure that almost everyone wants to use either the 9-point castle or the 10-point castle and overload that, then spread the rest fairly widely expecting to pick up the holes in the opponent's broken strategy (1,51,8,8,8,8,8,8,0,0) 3) Execute the strategy more or less directly, trying to claim three of the top four with strength, then choosing a fourth castle to claim with less than overwhelming support. (1,26,26,26,1,17,1,1,1,0) 4) Pick a strategy that requires winning five castles that do not include the top two. (1,1,41,14,14,1,14,14,0,0) Of these, the third seems the weakest--the others break it. Counterintuitively, the fourth strategy is the most successful. Going hard after the 8-point castle leaves enough points to pick four others against token support that other strategies can afford after preparing to win one of the top two castles. The disadvantage is that it fails against even support Variations include how many troops to send as tokens to the other castles, hoping to pick up all of the points from an undefended castle.
1078 0 0 13 11 13 1 0 20 22 23 25 26 29 2 0 2 0 The numbers I need to hit to win a given battle is 28. I decided to try to get it by getting 3, 4, 6, 7, and 8. I distributed most of my soldiers proportionately among these numbers. I'm hoping a lot of people will put too much stock in the top two numbers and I will have a better chance at winning these. However, putting all of my troops in these numbers would make the others winnable with a single troop. Ultimately, I decided to forfeit 1 and 2 so that I would have a distribution that would beat someone who put 10 in each or 11 in the top 9 or 12 in the top 8. Heavily stacked castles summing to 28.
1079 0 0 12 11 16 12 20 14 24 16 28 2 0 2 0 41 0 2 Since the sum of 1-10 is 55, it's really a race to 28 points. I figured most people will try to evenly distribute their answers, sacrificing the guarantee of winning a 9 or 10, in order to ensure they *could* win something. I figured I should stack all my marbles to try and guarantee winning 4-5 castles equalling 28 points, which would do well against a balanced distribution. I figured 3-7 was the best way to do this, because people will still weight their answers towards the higher numbers, so 3-7 is a nice sneaky way to ensure I get all of them (if I put 28 on the 10 square, there is a good chance someone with a more even distribution could still beat me on that one). With a sum of 55, a score of 27 wins, and the top 3 castles sum 27, so the easiest path to victory would be to win all of the top 3, and any path to victory includes one of them. I assume most people will try hardest to win the top three, but that no one is likely to go over 40 for castle 9 (though they might for 10), so with a deployment of 41 I can take castle 9 in most matchups. Then I want to win the magic 27 at the lowest-scoring castles possible, to maximize my chance of victory, which means aiming to win 6, 5, 4, 3. This is where I put the majority of my troops, more in the higher-ranking castles. If I don't win these five (9,6,5,4,3), winning one or two will do nothing for me, so they get none. I do want to have some minimal presence in case opponents totally and completely ignore 10, 8, or 7, though in going after any of the 5 I'm targeting, so 2 will beat anyone who leaves just 1 or 0 in those three spots.
1080 0 0 12 11 16 12 11 0 0 16 14 30 0 31 47 0 0 I wanted a strategy that would defeat the following strategies: (1) Maximize points -- give castle N 100N/55 soldiers (2) Greedy "maximize chance of getting 28 points" -- putting 100N/28 soldiers in castles 10, 9, 8, and 1 (3) Basic implementation of my strategy -- 100N/28 soldiers in castles 9, 7, 5, 3, and 2 Versus a strategy that puts soldiers in every castle, like (1) above, my strategy can only get 28 points max. That means I need to have at least 1+ceil(100N/55) soldiers in every castle I try to claim. Against (2), I need to make sure I win at least 1 of the castles they contest. I decided to contest castle 9, so I'll put my spare troops there. Against (3), I'll need to win castles adding up to at least 15. I'll probably win 9 with all my spare troops there, so I need to pick more castles that add up to 6 or more and give them extra soldiers. I put 1+ceil(100N/28) troops in castles 3 and 4, leaving 1+ceil(100N/55) in castles 5 and 7. Final results: Castle 3: 1+ceil(100*3/28) = 12 soldiers Castle 4: 1+ceil(100*4/28) = 16 soldiers Castle 5: 1+ceil(100*5/55) = 11 soldiers Castle 7: 1+ceil(100*5/55) = 14 soldiers Castle 9: the other 47 soldiers Let's see how it goes! Cede 9 and 10, concentrate power on 6,7,8 with remaining forces allocated to ensure a point victory is possible
1081 0 0 12 11 13 11 0 11 22 21 25 21 28 21 0 0 4 Who cares. It's probably wrong :) I know that I have to win every castle that I put troops in. I just thought about the different configurations that people might choose and I'm hoping that I win against more than anyone else My thought was that most people would go for the highest totals so I would take advantage by going for the middle numbers 3-8. I also figured many people would pick multiples of 5 so going one above would be good. Additionally I had 4 troops left and figured enough people might forgot the 10 in thoughts other people would use their troops their so I put my last four on the 10.
0 0 12 13 0 20 25 30 0 0 Picked castles that, if I won, would give me one more point than those points attributed to castles I lost.
1082 0 0 12 11 0 11 0 11 23 11 1 11 1 0 29 34 34 11 Please send me results if and when available. Much appreciated. Beats some of the simpler strategies, and is beaten only by strategies with more obvious flaws.
1083 0 0 11 15 11 0 1 20 16 26 28 33 0 1 0 1 Goal is to get 28/55 points and no more. Anticipating what other peoples' common strategies might be, I selected a combination of castles and troop deployments designed with an attempt to win exactly 28 points in a typical one-on-one match-up. Basically picked a strategy that I thought would beat most simple solutions that people would think of immediately, beat some more complex well thought out strategies, and beat basically no strategies of people with programming to run every possible combination that identifies which solution wins most frequently against other strategies. This particular warlord has no such modern technology, plus my war-manager has instructed me to get back to work...
1084 0 0 11 14 11 0 21 25 26 29 31 0 0 Find the total points (55) then minimum winning total (28). Determine which combinations of castles yields 28 points (15 total combinations). Find the percentage each castle would make up a victory condition. Add each percentage of a combination and remove any combination above 100% leaving 6 combinations. Find each castle's percentage of total points then remove any combinations above 50% leaving four combinations (10-8-6-4, 10-9-6-3, 8-7-6-4-3, and 10-9-4-3-2). Went with gut in decision of 8-7-6-4-3 combination due to belief that majority of people will go after 10 and 9. Used percentages from winning total calculations as number of units in each castle. I need 28 points to win. I m gonna put everything in castle 8 7 6 4 and 3. I need to win all of them though (can't tie).
1085 0 0 11 14 11 0 20 21 24 26 29 31 1 0 1 0 You need 28 points to win so only play for them, I went for the mid values as I more people would go all out for the high values. If I "forfeit" some battles, I can focus my forces on the battles I choose to take. I can feasibly win with four battles if I take castle 9 and forfeit 10, but I could instead to forfeit 9 & 10 and win with five castles total: 8, 7, 6, 4, 3 (one might also replace "...4, 3" with "...5, 2"). To win with 6 castles, forfeiting castle 6: Castles 8, 7, 5, 4, 3, 1. Another option is to forfeit castle 7 as well, again winning the war with 6 castles: Castles 8, 6, 5, 4, 3, 2. Lastly, if I wanted to win with 7, I'd need to win all the castles from 1 to 7. These are somewhat minimalist answers, as I tried to forfeit the highest-valued castles possible. I chose to go with castles 8, 7, 6, 4, and 3, but I tried to avoid multiples of 5, since I suspected them as likely answers from other submitters, and ties on castles 6, 7, or 8 should result as a loss for my battle plan. 0 on 10, 0 on 9, 31 on 8, 26 on 7, 21 on 6, 0 on 5, 11 on 4, 11 on 3, 0 on 2, 0 on 1.
0 0 11 13 0 22 25 29 0 0 Heavily stacked castles summing to 28.
1086 0 0 11 12 0 14 16 18 2 23 2 34 41 0 2 0 With a sum of 55, a score of 27 wins, and the top 3 castles sum 27, so the easiest path to victory would be to win all of the top 3, and any path to victory includes one of them. I assume most people will try hardest to win the top three, but that no one is likely to go over 40 for castle 9 (though they might for 10), so with a deployment of 41 I can take castle 9 in most matchups. Then I want to win the magic 27 at the lowest-scoring castles possible, to maximize my chance of victory, which means aiming to win 6, 5, 4, 3. This is where I put the majority of my troops, more in the higher-ranking castles. If I don't win these five (9,6,5,4,3), winning one or two will do nothing for me, so they get none. I do want to have some minimal presence in case opponents totally and completely ignore 10, 8, or 7, though in going after any of the 5 I'm targeting, so 2 will beat anyone who leaves just 1 or 0 in those three spots. I'm only trying to win 3,5,6,7, & 8
1087 0 0 11 12 0 0 16 0 30 26 31 27 0 0 36 Cede 9 and 10, concentrate power on 6,7,8 with remaining forces allocated to ensure a point victory is possible This approach goes all-in on winning just enough points to win. It is very vulnerable to "random" distributions, which only need to win one of the castles I actually allocate troops to, but puts enough troops in the "target" castles that I should be able to win them most of the time.
1088 0 0 11 10 11 20 11 30 21 40 21 0 21 0 0 4 0 My thought was that most people would go for the highest totals so I would take advantage by going for the middle numbers 3-8. I also figured many people would pick multiples of 5 so going one above would be good. Additionally I had 4 troops left and figured enough people might forgot the 10 in thoughts other people would use their troops their so I put my last four on the 10. Went for middle of the road, figuring most would deploy larger troops at the higher values
1154 0 0 0 25 18 25 19 25 20 25 21 0 22 0 0 I figured there would be lots of different strategies tried on this problem, thus the first couple of obvious ones (send 100 troops to castle 10, send 10 troops to each one of the castles) would likely be used. For some reason (call it a hunch on human nature) I figure there will be a more likely event that people will place a number of troops either in castles 1-3 or 8-10, but I feel like the odds are lower that they will place troops in the middle 4 castles 4-7. I also felt like there would be a better shot at winning castles if I "didn't get greedy" and go for either a large number of castles, or castles with the highest point value. So, here goes nothing! I focus on 5 middle castles that allow me to just win more than half the points
1155 0 0 0 25 17 0 0 25 17 25 33 25 33 0 4+9+7+8=28 which is the least amount needed to win the war. Minimize castles. 9 & 8 are most important. 10 will probably be overvalued.
1156 0 0 0 25 16 0 1 0 1 24 21 25 26 25 35 0 10*11/2 = 55 points in the game, score of 28 wins, need at least 4 castles, so 4 castles it is, avoid the bing guns (e.g the 10+9+8+1 combo) since vegas addicted people will front-load the 10, the only other 4 castles combo without repeat is 9+8+7+4, even spread of ressources between castles since they are all equally important in this strategy. Goal to capture 7 thru 9 (because 10 will be contested) at which point I only need 4 more for 28
0 0 0 24 0 0 25 25 26 0 I tried to ensure victory at the minimum number of castles that would give me the minimum number of points to win.
1157 0 0 0 21 15 0 25 0 30 26 30 26 0 27 0 0 There are 55 victory points, so we need to win 28 to win the war. No three castles provide enough victory points by themselves, so my strategy is to concentrate on four castles that are cumulatively just enough to win the war, avoiding the most attractive castle #10, and concentrate all my troops there to maximize odds of winning these castles. Castles 4, 7, 8, and 9 work. (Another similar choice would have been castles 5, 6, 8, and 9.) I distributed the 100 armies across these castles with slightly more on the more valuable castles rather than evenly. Collect mid-range castle with high concentration of troops.
1158 0 0 0 20 15 20 20 21 20 21 20 23 0 0 complete guess Guesswork
1159 0 0 0 20 15 20 18 20 0 20 0 20 0 0 32 0 35 Submission #2. I'm not convinced this will be successful either. I abandoned the low AND high end value castles in favor of equally dividing them amongst the middle tier of castles (that would still give me a winning score). Used the minimum number of castles to get to 28 points, and then allocated for the highest average win probability.
1197 0 0 0 12 11 0 0 20 29 34 29 34 31 0 Wanted to focus my efforts on the easiest way to get to 28, but not focusing on 10 (which will probably have most of the opponent's soldiers). Taking a risk to let the other 6 castles fall. I looked at different ways to get 28 points and thought that committing to 3 big numbers hard and one small number that makes the total 28 could be a good strategy. I debated between 9,8,7,4 and 10,9,8,1 and in the end decided skipping out on the 10 fight is probably worthwhile. 11 on the 4 beats the 10 across the board plan and the 29 on 7 beats the even split across the lower 7 numbers plan.
1198 0 0 0 12 11 0 0 20 26 30 31 38 32 0 Don't waste any soldiers. Get to 27.5 points. There are 55 pts to get, any path to 28+ requires at minimum 4 castles (10+9+8 is still not enough). I am letting go of #10, which I expect to waste a lot of soldiers without being more useful in the 4-castles path to victory. All desired castles should have more than 10, to beat the equal spread in every castle. I expect big castles to often go for over 25 (4*25 path to victory). However, I am betting I can get my fourth castle (#4) much cheaper (between 11-25, thus saving soldiers to secure 9+8+7). I expect to lose some matchups (especially ties), but to do well overall. But then again, strategical thinking against an unknown crowd is harder than tactical games or strategical games against known opponents. If everybody sees the 4 castles path and nobody goes for wide spread, I might be crushed every time since I have no back-up.
1199 0 0 0 12 11 0 0 16 26 34 30 38 33 0 I chose to focus on 4 castles, because that is the fewest number of castles that would provide a majority of the 55 points available. I figured that the most obvious way to focus on 4 castles would be to go for 10,9,8,1; the alternative, which I expected fewer people to focus on, is 9,8,7,4. I placed the bulk on 9 & 8, seeing those as the most important, in order to defeat someone who was focusing on the 10,9,8,1 strategy. I then left just enough on both 7 and 4 to defend against anyone who happened to do an even 10 distribution on all castles, as well as anyone who did a variation of a proportional distribution (~1.8 soldiers per victory point). Put one extra soldier (than allocation by normal victory point value) at castles 7, 8, and 9, then put remainder at castle 4, so that if all 4 castles won, the total would be 28 out of 55 points. Hopefully, I can win all castles 7, 8,and 9 much of the time, and castle 4 also some of the time.
0 0 0 11 21 0 0 0 31 37 The total number of points available is 55. So, in order to win, I must get at least 28 points. Rather than spreading my troops out, I decided to put all my eggs in one basket and attempt to receive the minimum number of points. I figured that most people would stay away from numbers 10 and 9, since those are too obvious. Taking the contrarian approach, I decided to invest heavily in these two castles. This gives me 19 points, so I must add a further 9 points to my total. The easiest way to do this was simply choose castles 4 and 5 (I wanted to stay away from castles 6, 7, 8 as I figured these would be very popular.) I invested my remaining troops there. This gives me a total of 28 points, just enough to win. Additionally, when assigning troop values, I tried to have the ones digit of my troops 1 and 6, so I would beat simple multiples of fives.
0 0 0 11 13 17 21 38 0 0 Submission #6. I have the most faith in this, my final submission. Since I have little faith in this one as well, however, I think I would properly be considered a "pessimistic general". Anyway, I chose to only defend the middle value castles and to divide my forces unevenly rather than equally. I know there are lots of other options than the three choices (with two variations each) that I chose but they seem like a good set of choices to me! Thanks for the fun riddler!? (I'd love to know how many submissions you received and where each of mine fell in the rankings but I'm sure that's WAY more work than you're prepared to put into this. Take care!
0 0 0 11 12 13 14 15 17 18 Tried to weight the higher point castles more, but distribute troops. Ignored the low value castles.
1200 0 0 0 11 11 0 0 26 26 30 26 33 0 I thought about strategies I thought large number of people would pick and chose a strategy that would perform well against those strategies. As per my e-mail to Oliver, I have previously submitted an entry but I would like to change it to the above. My thinking has not changed all that much. I still think that a proportionate strategy is best but that it is also a good idea to aim for enough points to win, rather than all of the points. I also think that a strategy needs to be robust against similar strategies and to defeat all obvious strategies. My concern, however, is that an opponent who anticipates the popularity of a proportionate strategy could exploit this by making their strategy slightly less proportionate, for example by overloading castle 10 at the expense of one of the other castles. This would defeat a proportionate strategy which targeted the same castles. The best way to counter this is to not target castle 10 at all, and to let those smart alecs waste their resources. Therefore, my strategy is now an almost-proportionate 28 point strategy, focusing on castles 4, 7, 8, 9. It is only non-proportionate to the extent that it takes 3 troops away from castle 4, and adds one to each of castles 7, 8 and 9. I have done no computer simulations - this is all in my head - but as far as I can see, it will do very well against almost every opponent. It will defeat every fully proportionate strategy and every non-proportionate strategy in which the emphasis is on overloading castle 10. It will also defeat a flat strategy, in which 10 troops are allocated to each castle, or 25 troops are allocated to each of four different castles.
1201 0 0 0 11 2 0 2 0 17 22 34 22 34 22 0 23 Surrender the 10er, but get 7, 8, 9 and 4 for 28 - enough to win. I need 11 on 4 to beat a 10 x 10 strategy; I need 34 on 8 and 9 to beat a 34-33-33 strategy. I initially had 21 on 7, but I hedged my bets just in case I run across a copycat strategy. (7 on 21 loses to a 25-25-25-25 strategy anyway, for example!) I could very very well fall in the first round, but I can also see this strategy work well. There are 55 victory points available, so I need 28 to win. The smallest number of castles I can do this with are Castles 10, 9, 8 and any one of the others. In order to have a margin of error, I decide to target Castle 7 additionally and out of the "any ones", I target Castle 4. This way, I need three out of the four large ones plus Castle 4. I reckon Castle 4 will not be targeted so often, so I only go with 11 soldiers there, allowing me to beat an "evenly distributed" strategy. The large castles get 22 soldiers, beating any "target only the largest five evenly" strategy and even those that assign 21 soldiers to beat these. That leaves one odd soldier, who I send to the largest castle.
1202 0 0 0 11 10 1 20 1 20 24 50 26 0 36 0 1 0 Hopefully the opponent sends several troops to 10. By sacrificing 10, I can concentrate on 7,8, and 9. Winning those will put me 4 points away from clinching. I also sent 1 to several castles I was going to leave blank just in case my opponent was also going to send 0. Then I get a very cheap win at those castles. Trying to win the mid castles
1216 0 0 0 10 15 0 20 0 25 30 30 0 30 0 Only need 28 points to win and high point castles are most valuable, but don't compete for the highest value castles; they are likely too expensive to win. If I usually overwhelm the opponents on 4, 7, 8, and 9, I'll get 28 points, which is enough to win the war.
1217 0 0 0 10 15 0 20 0 25 30 0 35 0 The lowest castles arent worth enough points to commit troops, and the highest castles are likely to be overvalued by my enemies. If i win these middle castles my 30 points will win the war. I expect 2 general deployments: 1) Equal deployment, or downmarket. Trying to win as many castles as possible. These folks will have either equal, or concentration on the lower castles. I beat them at the higher castles, and tie on at least one of 4 and 10. 2) Upward mobility. These folks gamble on capturing 8, 9 and 10. 10 would then have the highest concentration. So, I hope to win most of 7, 8, 9 and 4, plus tie on any other lower castles that they left empty.
1218 0 0 0 10 15 0 20 0 25 20 30 34 0 35 0 1 Ignore the top and bottom focus on the middle The maximum possible points is 55, so more than 27.5 are required to win. So the strategy should be to try to get enough castles to guarantee at least that many points, and not waste troops on trying to get more. There are of course a variety of ways to do this - e.g. holiding castles 1 through 7, or 4 through 8, or 19, 9, 8 plus at least one other one. Since at least 4 castles are required, I figured I would go for a strategy that requires 4 but NOT castle #10, which I imagine people on average will try to defend heavily. So I opted for 9, 8, 7, and 4. I am putting 1 person in castle 10 so that I can win a tie if someone else uses a strategy that doesn't involve castle 10 and happens to win over one of my other castles. I figure that even in the 8-9-10 concentration strategy, people are unlikely to use more than one third of their troops in a castle, particularly those less than 10, which is why I stuff 35 and 34 in 9 * 8. 7 is probably most vunerable, but if someone is using a strategy that involves castle 7 then they are likely diluting troops and chances are they have less than that there. Castle 4 is essentially a random small castle, so if someone is diluting troops to put there, I figure 10 (100 total/10 castles) is a fair number here.
0 0 0 10 13 20 26 31 0 0 I assume most will attempt to aim for the top only. I'll take the center-top instead.
0 0 0 10 10 20 20 40 0 0 Everyone is going to put lots of soldiers on the top castles. So I give them the 19 points hoping to get a lot of points from the five I defend.
0 0 0 10 10 10 20 30 0 0 Didn't want to compete in upper end, or lower end, and figured had a better shot at winning the middle
1219 0 0 0 10 10 0 10 0 10 20 15 30 20 40 25 0 Take the positions that earn the most - abandon the weak ones. I figure most people will want the 10 points at castle 10 and will be willing to spend close to half their budget on it. My strategy is to get exactly the number of points needed to win (28) so I'm going to load up on the minimum amount of battles that I need to win in order to get those points. Sending no one to 10 ensures I'll have more to use against my opponent at the next three battles.
1220 0 0 0 10 9 0 14 21 19 0 24 21 34 0 48 0 Bet on fewer castles and ignore the one immediately below it, keeping in mind to bet on enough castles to get over half the available points. Using the lowest possible combination to achieve over 28 points and deploying troops proportionally to the value of the points available.
1221 0 0 0 10 9 0 11 0 12 30 14 30 16 30 18 0 20 If I usually overwhelm the opponents on 4, 7, 8, and 9, I'll get 28 points, which is enough to win the war. Total number of points available is 55. 100 soldiers / 55 points = 1.81 I picked: 1.81 * pt value of castle + 1 (rounded up) for the 7 most valuable castles 0 for the 3 castles with the least points.
1271 0 0 0 0 17 16 21 0 1 29 28 33 32 0 2 This is a go for broke strategy attempting to secure a 28-27 victory by taking only 4 castles. Each contested castle receives a number of armies proportional to its value, with the extra 2 units sent to the highest value castles rather than based on simple rounding. 4 castles are highly contested castles picked to add up to 28 points. Troop deployment numbers for these castles are near the 3.57 troop/point ratio that is the maximum number of troops that be deployed to win a point and still win the battle. Chose not to contest lowest 4 point castles at all and put very small amounts in castle 7 and 10 to potentially "steal" the points if uncontested or only contested with 1 troop.
1272 0 0 0 0 17 16 21 0 26 31 36 32 0 Same as before, different case. I assume there will be 2 common strategies. Strategy A is to send to each castle soldiers proportional to the amount of points available at the castle, if not a bit skewed toward the higher castles. Something like 24-19-16-13-10-7-5-3-2-1. Strategy B is going all in on just 28 points worth of castles. Something like 40 on Castle 10, 28 on Castle 8, 19 on Castle 6, and 13 on Castle 4. There is little room for error with Strategy B, as losing just 1 of your targets guarantees a loss, but the big advantage here is that all soldiers are warring at the required castles and none are wasted. I need to figure out a way to beat both of these strategies consistently ---- if I can, I figure I will win enough wars against these two to ignore any other strategies (strategies geared to beat these 2, strategies geared to beat mine, or other "optimal if both are playing completely logically" strategies I cannot come up with.) My first idea is to concede Castle 10, giving me more soldiers to play with in the rest of the 9 castles and hopefully proving to be a key advantage going forward. If I was to then proportion my soldiers out similar to Strategy A, but just on the back 9, I would clean up house against Strategy A. However, this will usually doom me against Strategy B. There are so many alterations of Strategy B: 10+9+8+1, 10+9+7+2, 10+9+6+3...39 different ones by my count. Moreover, each castle shows up in 19 to 20 of these different strategies. So I am going to make an assumption that most people who choose Strategy B will choose a 4-castle strategy as that contains the least room for error. The 4-castle strategies are as follows: 10+9+8+1 10+9+7+2 10+9+6+3 10+9+5+4 10+8+7+3 10+8+6+4 10+7+6+5 9+8+7+4 9+8+6+5 10 shows up 7 times, 9 shows up 6, 8 shows up 5, 7 - 4, 6 - 4, 5 - 3, 4 - 3, 3 - 2, 2 - 1, 1 - 1. Still wanting to avoid the assumed-to-be-hotly-contested 10 castle, and noting that all but one contain either a 9 or an 8, I am going to choose my own 4-castle, 28-point strategy that is front-loaded on 9 and 8: 9 + 8 + 6 + 5. Lastly, I chose my distribution of soldiers using a Price is Right-esque strategy, going just over multiples of 5 to hopefully avoid tying with the most common answers. Using complete guesswork, I assume most of these 4-castle strategies will use something like a 40-30-20-10 split, so I put 9 and 8 just over 30 and let 6 and 5 have the rest: 9 - 32 8 - 31 6 - 21 5 - 16
1273 0 0 0 0 17 16 19 17 20 0 21 29 22 38 1 0 Ten's not worth blowing all your troops for. Hopefully they wasted too much on ten to match us for 5-9 Picked the smallest group of castles which if all are won gives victory (four castles). Split them to allow for victories in smaller castles (5 and 6) and give up 10 point castle as a hopeful over extension on the enemies behalf. Then split troups, favoring higher point castles.
0 0 0 0 17 17 17 17 16 16 I assume most people will send more troops to the first castles, and I only need 6 castles to win so If I deploy as many troops as possible to the last 6 and forfeit the first 4 castles I will hopefully dominate the last 6 while opponents waste soldiers on castles I didn't attempt to win in the first place.
1274 0 0 0 0 17 16 17 16 17 0 17 0 17 49 17 Optimizer. I played around in Excel with an evolutionary alogrithm, although I'm still not sure it's optimized.
1275 0 0 0 0 16 15 21 20 1 0 29 30 32 35 1 0 Focus on minimum number of castles four. Focus on the least valued of those. 9,8,6,5 proportionally. Then adding a little bit back for possible 10,7. Little tricky because not working against random troop assignments but working against visitors of 538.
1276 0 0 0 0 16 15 21 19 1 0 28 30 32 36 2 0 4 castles are highly contested castles picked to add up to 28 points. Troop deployment numbers for these castles are near the 3.57 troop/point ratio that is the maximum number of troops that be deployed to win a point and still win the battle. Chose not to contest lowest 4 point castles at all and put very small amounts in castle 7 and 10 to potentially "steal" the points if uncontested or only contested with 1 troop. The easiest way to get to 28 points (the lowest winning score) is to deploy at castles 1, 8, 9, 10. I assume that most puzzlers will figure this out, and so designed a strategy that effectively wins against the "obvious" strategy.
1336 0 0 0 0 0 10 0 20 25 30 25 39 25 1 25 You need 28 points to the war. The fewest castles this can be achieved in is 4, but I can go for #6 instead of #10 and still meet the goal. I'm hoping others overvalue castle 10 and I'm able to win 6-9 for 30 points. If they ignore 10 and contest one of the others integral to my plan I have 1 soldier at 10 to avoid splitting those points defend the top scoring castles
1337 0 0 0 0 0 10 0 15 25 20 25 25 30 25 the biggest numbers are the most important x Submission #3. A variation on my first submission. Here, however, I gave an equal number to each of the castles I defended.
1338 0 0 0 0 0 6 0 16 25 21 25 26 25 31 25 I anticipated a couple strategies (10 all, proportional distribution, 25 on the top 4, 30-25-20-15-10, etc.) and I tried to come up with a simple strategy that would beat them. I anticipated that many players would use multiples of 5, so I used number that had a remainder of 1 when divided by five to get a slight edge over them. The top four castles are more valuable than the descending 6 combined
0 0 0 0 0 1 12 12 34 41 Base strategy of 37,33,11,11,1 form castles 10 to 6 with remaining 7 soldiers distributed to give 'optimal' result.
1339 0 0 0 0 0 0 100 22 0 24 0 26 0 28 Win at least one of the higher value castles I gave up on the smallest three - and then tried to optimally place the others. Not much math involved, honestly.
1340 0 0 0 0 0 0 25 21 25 24 25 26 25 29 you need the last four to win Against a random opponent, assigning soldiers in proportion to the value of each castle is a winning strategy. Unfortunately it loses to anyone who focuses troops on a smaller number of castles. Since it is impossible to win without at least one of the four strongest castles, I sent a number of troops proportional to value to each of the four strongest castles, totally neglecting the smallest castles. (I got lazy when trying to calculate the Nash Equilibrium and stopped here.)
1341 0 0 0 0 0 0 25 20 25 24 25 26 25 30 defend the top scoring castles Started with a points weighted distribution of troops and created successively better strategies by shifting troops from lower ranked castles to higher ranked castles.
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