Riddler - Solutions to Castles Puzzle: castle-solutions-3.csv

This directory contains the data behind the submissions for castles puzzle.

Readers were asked to submit a strategy for the following “Colonel Blotto”-style game:

In a distant, war-torn land, there are 10 castles. There are two warlords: you and your archenemy. Each castle has its own strategic value for a would-be conqueror. Specifically, the castles are worth 1, 2, 3, …, 9, and 10 victory points. You and your enemy each have 100 soldiers to distribute, any way you like, to fight at any of the 10 castles. Whoever sends more soldiers to a given castle conquers that castle and wins its victory points. If you each send the same number of troops, you split the points. You don’t know what distribution of forces your enemy has chosen until the battles begin. Whoever wins the most points wins the war.

Submit a plan distributing your 100 soldiers among the 10 castles. Once I receive all your battle plans, I’ll adjudicate all the possible one-on-one matchups. Whoever wins the most wars wins the battle royale and is crowned king or queen of Riddler Nation!

The data includes all valid submissions, with solvers’ identifying information removed. The 11 columns represent the soldiers deployed to each of the 10 castles, plus a column where the reader could describe his or her strategic approach.

Correction

Please see the following commit: https://github.com/fivethirtyeight/data/commit/c3f808fda5b67aa26ea6fa663ddd4d2eb7c6187f

Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub

1,466 rows sorted by Castle 5

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Suggested facets: Castle 1, Castle 2, Castle 3

Link rowid 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?
14 4 0 0 0 0 0.0 0.0 32.0 32.0 32.0 You only need 28 to win
29 6 6 7 0 0 0.0 21.0 25.0 0.0 35.0 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.
47 1 5 10 0 0 0.0 0.0 28.0 28.0 28.0 Because I'm trying my best.
62 1 2 0 0 0 0.0 0.0 32.0 32.0 33.0 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.
68 4 0 0 0 0 0.0 0.0 32.0 32.0 32.0 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.
116 1 0 9 0 0 10.0 10.0 20.0 40.0 0.0 Adjustments to previous contest
126 1 0 0 0 0 13.0 17.0 20.0 23.0 27.0 Win big (I only want 0 troops at castle 1 but it won't let me. Hoping I dont get disqualified.)
131 1 0 0 0 0 0.0 0.0 0.0 99.0 0.0 Just Cause
141 1 0 0 0 0 0.0 0.0 99.0 0.0 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.
147 1 0 9 15 0 20.0 25.0 30.0 0.0 0.0  
183 5 1 0 0 0 0.0 0.0 32.0 31.0 31.0 I anticipate a backlash against the deployment of troops to the highest castles given the data from the last war. Because of this, committing roughly a third of my troops to each of the three largest castles should overwhelm the majority of opponents. 8 has historically been one of the most sought after castles, likely being used to deny narrow strategies like mine a victory, so i will fortify it with an extra troop. Additionally, if i win 8/9/10, only one other point is necessary, and the first castle has been historically poorly defended. I send my final troop to the second castle, because someone who has committed more than 5 troops to the first is probably less likely to have fortified the second.
202 1 4 0 0 0 0.0 27.0 0.0 34.0 34.0  
225 1 1 0 25 0 0.0 25.0 25.0 25.0 0.0  
236 1 0 0 0 0 9.0 10.0 10.0 35.0 35.0 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
241 1 0 0 0 0 0.0 0.0 22.0 37.0 40.0  
246 1 0 14 0 0 18.0 0.0 0.0 33.0 34.0 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.
249 1 0 0 12 0 12.0 25.0 25.0 25.0 0.0 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)
283 1 0 9 0 0 20.0 20.0 20.0 0.0 30.0 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.
288 1 0 0 0 0 0.0 24.0 25.0 25.0 25.0 Control the four top castles that add up to more than the rest.
315 1 0 0 9 0 15.0 0.0 35.0 40.0 0.0 Cheapest way to 28 total points. It did make me place one troop in castle one for some reason. Would rather have put that soldier at 4.
327 3 4 0 10 0 16.0 7.0 22.0 10.0 28.0 watching Game of thrones taught me to just go for it!
346 8 0 0 0 0 0.0 0.0 31.0 31.0 30.0 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.
391 2 0 0 0 0 17.0 18.0 18.0 20.0 25.0  
394 0 1 1 10 0 0.0 29.0 29.0 30.0 0.0 Exact victory points, fewest required wins, avoid 10.
396 0 0 10 0 0 20.0 28.0 32.0 5.0 5.0 Because I'm the Grandmaster.
397 5 0 0 0 0 0.0 0.0 24.0 36.0 35.0 limit losing troops, look for highest return on investment
408 0 0 0 0 0 0.0 0.0 0.0 100.0 0.0 Nash Equilibrium
424 3 2 0 0 0 0.0 0.0 25.0 35.0 36.0 I want to win 8-9-10 and either 1 or 2. Glass Cannon bby
437 0 0 1 19 0 19.0 1.0 25.0 1.0 34.0  
456 0 6 0 0 0 0.0 0.0 33.0 33.0 28.0 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.
492 5 5 0 0 0 0.0 0.0 20.0 30.0 40.0 Castles 3-7 are pretty lame
500 0 0 0 11 0 0.0 26.0 31.0 32.0 0.0 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!
502 6 0 0 0 0 0.0 0.0 32.0 31.0 31.0 If I win the 10, 9, 8 and 1, I have 28 which is just enough to win.
520 0 0 10 0 0 16.0 0.0 0.0 35.0 39.0 I started with the averages and the winners from the last 2 rounds. Then I tried to craft a few strategies: a few random ones, some crafted to specifically beat the winners, some crafted to take advantage of historically undervalued spaces between winners and averages, - with some variations on how little/much to put on some of the lighter weighted castles. Then I sat down and went for a hyper aggressive strategy that had a single path to 28 points and would defeat all of the above hahaha. And so we end up here, with a warlord who styles him/herself also as an edgelord, and possibly did not do enough to account for beating strategies that were previously losing.
521 5 0 0 0 0 0.0 0.0 30.0 30.0 35.0 I only need 28 points to win, so I'm only investing my soldiers in 4 attacks to get me the 28 - the three highest totals plus one point.
524 3 0 0 0 0 0.0 0.0 32.0 33.0 32.0 I need 28 points to win, so I'm fighting hard for those 28 points.
526 0 0 12 0 0 22.0 0.0 0.0 34.0 32.0 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.
532 2 1 0 0 0 0.0 0.0 28.0 33.0 36.0  
543 0 0 0 0 0 25.0 0.0 34.0 41.0 0.0 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.
548 0 0 0 13 0 12.0 0.0 0.0 37.0 38.0 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.
567 7 1 1 1 0 0.0 0.0 27.0 28.0 35.0 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.
568 0 9 0 0 0 0.0 0.0 32.0 32.0 27.0  
599 7 0 0 0 0 0.0 0.0 35.0 32.0 26.0 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.
600 10 0 0 0 0 0.0 0.0 30.0 30.0 30.0 People are going to overthink it. 1/8/9/10 is enough to win.
604 0 0 0 20 0 0.0 0.0 0.0 40.0 40.0 23 points to win. Overload the highest rated castles and sacrifice everything else
606 3 5 6 8 0 12.0 14.0 15.0 17.0 20.0 Scale investment to reward, but then abandon castle 5 and use the extra soldiers to try to beat other warlords scaling investment to reward
608 0 0 0 0 0 15.0 17.0 0.0 33.0 35.0  
610 5 0 0 0 0 0.0 0.0 32.0 31.0 32.0 The goal is to get 28 points. Concentrated troops at the least amount of castles to achieve that.
615 0 0 0 0 0 10.0 15.0 20.0 25.0 30.0 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.
617 8 9 9 10 0 0.0 0.0 30.0 0.0 34.0 Try to win 1,2,3,4,8,10 to get to 28
641 0 0 0 0 0 0.0 25.0 25.0 25.0 25.0 Instead of spreading out my troops, I wanted to backend my troops toward the castles with higher amount of individual points.
649 0 0 0 0 0 20.0 23.0 26.0 30.0 1.0 Grasp barely enough castles to win, plus one in 10 as a counter strategy against a mirror match.
676 1 1 1 1 0 0.0 24.0 24.0 24.0 24.0  
679 3 6 0 14 0 22.0 25.0 30.0 0.0 0.0 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.
700 5 0 0 0 0 0.0 0.0 30.0 30.0 35.0 28 points is a win, so that's all I'm going for. The Castle 1 victory is essential!
716 0 0 0 0 0 100.0 0.0 0.0 0.0 0.0 All of the troops at the first castle higher than 5
732 0 0 0 0 0 0.0 26.0 32.0 42.0 0.0 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.
739 0 0 8 11 0 22.0 28.0 31.0 0.0 0.0 Strongly attacked with the most likely castles to reach 28.
747 0 0 17 0 0 0.0 29.0 23.0 2.0 29.0 All-in on 3,7,8,10
753 30 30 30 0 0 0.0 0.0 0.0 0.0 10.0 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.
756 0 0 12 0 0 26.0 0.0 0.0 29.0 33.0 Choose just a few castles and maximize the chances of winning those.
791 0 0 0 0 0 10.0 10.0 15.0 25.0 40.0  
792 4 0 7 0 0 11.0 0.0 0.0 38.0 40.0 Focus on getting required 28 points to win by targeting top tiers to make up bulk of points, and a few lower tier castles to add in just enough points.
798 0 7 0 14 0 21.0 25.0 0.0 33.0 0.0 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.
806 0 14 0 0 0 0.0 0.0 28.0 29.0 29.0 To get more than half of the 55 total points, it requires 10+9+8+1 (28/55), thus, we should focus our soldiers most at the top three castles. The last point can come from any castle. Since it is likely that castle 7–being worth 7 points—will be paid attention to more than the castles lower than it, we should let that one fall. Since we only need one more point after assuming a win at 8-10, we should go for the lower castles. I believe, however, that many people will go after 1 strategically to get one last point, so I choose to go after 2, which tho it has more point value, might get raided less by those who are attempting a similar strategy to mjne.
810 0 7 0 0 0 0.0 25.0 0.0 32.0 36.0  
815 1 2 2 0 0 4.0 6.0 8.0 34.0 43.0 win 10/9 and two average others
826 4 0 0 0 0 0.0 0.0 30.0 32.0 34.0 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.
836 4 1 15 0 0 0.0 0.0 0.0 40.0 40.0 Only need 22.5 points to win. Figured 40 would win most of the time at 9 & 10, so I only need 3.5
840 4 0 0 0 0 0.0 0.0 41.0 31.0 24.0 Magic
848 0 5 0 0 0 0.0 0.0 35.0 30.0 30.0 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.
855 2 2 2 8 0 19.0 26.0 41.0 0.0 0.0 Avoid wasted troops at high value targets and low v; win on aggregate over sim.
861 5 0 0 0 0 0.0 0.0 35.0 30.0 30.0 28 is a win, so concentrate where you need to win, and win!
864 0 0 4 6 0 16.0 16.0 18.0 35.0 5.0  
870 1 6 0 10 0 15.0 5.0 19.0 21.0 23.0 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.
875 0 0 0 0 0 10.0 10.0 10.0 35.0 35.0 A gross misunderstanding of all logic
881 5 5 5 5 0 0.0 0.0 10.0 30.0 40.0 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.
883 6 0 0 0 0 0.0 0.0 34.0 30.0 30.0 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.
884 0 3 0 18 0 17.0 9.0 15.0 5.0 33.0 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.
890 0 0 0 20 0 10.0 20.0 30.0 0.0 20.0 just felt intuitively good
893 0 0 0 0 0 0.0 0.0 33.0 33.0 34.0 Go big or go home
900 4 0 0 0 0 0.0 0.0 33.0 33.0 30.0 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.
907 0 0 11 0 0 7.0 7.0 7.0 34.0 34.0 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.
909 0 2 7 0 0 22.0 3.0 1.0 33.0 32.0 10+9+6+3 = 28 and both 6 & 3 are not common choices in previous editions.
912 0 0 0 10 0 0.0 0.0 30.0 25.0 35.0 Just a hunch I had based on previous editions
915 0 0 0 0 0 19.0 23.0 27.0 31.0 0.0 All focused on the fewest castles needed to win, avoiding the highest and lowest valued.
924 7 0 0 0 0 0.0 0.0 31.0 31.0 31.0 28 to 27
926 5 0 0 0 0 0.0 0.0 30.0 35.0 30.0 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.
928 0 0 0 0 0 17.0 18.0 30.0 35.0 0.0  
930 2 0 6 1 0 0.0 22.0 0.0 40.0 29.0 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).
941 1 0 0 0 0 0.0 30.0 30.0 39.0 0.0 Highest % troops outside Castle 10
943 0 0 0 0 0 20.0 0.0 0.0 40.0 40.0 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.
955 0 0 0 20 0 0.0 26.0 26.0 28.0 0.0 Maximizing distribution to minimum number of castles needed to win, while avoiding expense of castle 10.
966 7 0 0 0 0 0.0 0.0 26.0 31.0 36.0 Protect the bag
985 10 0 0 0 0 0.0 0.0 15.0 25.0 50.0 Forces concentrated on minimum four castles to win
987 0 10 0 0 0 0.0 15.0 25.0 50.0 0.0 Forces concentrated on alternative 4 castles to win
1013 0 7 1 0 0 1.0 28.0 1.0 33.0 29.0 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.
1014 1 1 0 0 0 15.0 20.0 31.0 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.
1028 0 7 7 10 0 0.0 25.0 26.0 27.0 0.0 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.
1057 0 0 0 0 0 0.0 0.0 20.0 30.0 50.0 Seemed smart

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CREATE TABLE "riddler-castles/castle-solutions-3" (
"Castle 1" TEXT,
  "Castle 2" TEXT,
  "Castle 3" TEXT,
  "Castle 4" TEXT,
  "Castle 5" TEXT,
  "Castle 6" REAL,
  "Castle 7" REAL,
  "Castle 8" REAL,
  "Castle 9" REAL,
  "Castle 10" REAL,
  "Why did you choose your troop deployment?" TEXT
)
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