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

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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 · About: simonw/fivethirtyeight-datasette

1,321 rows sorted by Castle 9

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Suggested facets: Castle 1, Castle 2, Castle 3, Castle 4, Castle 5

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?
26 26 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.
53 53 3 6 9 14 18 22 28 0 0 0 Ignore the top ones, focus on minimum needed for majority of points
67 67 2 2 4 0 22 10 12 13 0 35 Because this is what my future self told me to pick.
98 98 1 4 6 14 18 24 33 0 0 0 Assuming more valuable castles will be more contested, negating their points advantage. 28 points wins, so it only makes sense to contest castles worth that many total. I took 1-7 (28 total pts), with troop allocations focused on the hotly contested 5,6,7 castles. I'm hoping to 'pay' for those by taking 1,2,3 cheaply.
123 123 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.
128 128 1 0 9 15 0 20 25 30 0 0  
152 152 3 5 7 2 2 15 18 20 0 28 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.
206 206 1 1 0 9 14 20 25 30 0 0 Just give up on the biggest ones, probably a waste
226 226 1 1 2 9 15 8 18 21 0 25 Mean of previous winners, then equalization of ROI on all but Castle 9 because I don't like the location of that property .
232 232 2 4 6 7 8 15 23 35 0 0 Idk, could work
249 249 1 0 9 0 0 20 20 20 0 30 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.
301 301 3 0 7 10 20 0 30 30 0 0 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)
311 311 1 1 1 5 1 10 1 20 0 60 Must win 28 points
324 324 5 7 8 10 15 25 30 0 0 0 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.
326 326 0 0 0 14 17 20 23 26 0 0 Ignored 9&10 and chose the fewest castles past that to give me more than 28 points and weighed troops by value
329 329 0 0 0 13 15 18 26 28 0 0 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-.
335 335 12 12 12 12 12 14 26 0 0 0 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
345 345 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.
351 351 0 0 4 0 11 0 30 31 0 24 I came up with about a dozen different strategies. Strategy A was an even distribution (10 per castle), B was weighted (2 for Castle 1 up to 18 for Castle 10); C was weighted to beat A-B, D could beat A-C, all the way until strategy O. After Strategy O, I couldn't make another distribution that could beat N plus the other ones I had already made. It's banking on chaos and people not wanting to overpay for Castle 10, thinking they can take Castles 6-9 for a little more points
386 386 1 0 19 1 1 21 0 23 0 34  
389 389 1 0 19 1 1 21 0 23 0 34  
391 391 0 11 0 0 16 19 22 31 0 1 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.
394 394 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
396 396 0 0 11 13 2 21 21 21 0 11 Gut feeling, picking the less selected castles by either of the previous two rounds.
400 400 8 12 13 13 13 14 0 27 0 0 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.
445 445 1 1 1 1 6 0 0 30 0 60 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.
458 458 0 0 0 0 20 50 30 0 0 0 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.
502 502 1 3 4 7 13 20 24 28 0 0 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! :)
517 517 0 10 0 0 15 25 25 25 0 0 Only deploy to certain castles to win, hope to get lucky.
523 523 0 0 0 15 15 15 25 30 0 0 Play for the middle and push for the top but don’t over commit
524 524 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.
533 533 4 7 10 14 18 22 25 0 0 0 Get 28pts by focusing on the less valuable castles
544 544 0 0 0 0 18 22 26 0 0 34 Stakeout the middle and get the top one. Didn’t waste on other castles.
555 555 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!
558 558 8 9 9 10 0 0 0 30 0 34 Try to win 1,2,3,4,8,10 to get to 28
561 561 0 4 0 0 22 22 22 30 0 0  
562 562 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.
570 570 2 0 6 0 2 0 23 36 0 31 I think people are going for 9. Trynna lock down 8 and 10 and hope 7&3 are strong enough.
585 585 4 5 7 9 11 14 17 20 0 13 surrender castle 9 completely -- exceed the average of BOTH original and May average per castle strategies for every other battle.
606 606 0 0 0 15 15 20 25 25 0 0 Focus more troops on enough points to get more than half of points.
614 614 3 6 0 14 0 22 25 30 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.
633 633 4 7 10 14 17 22 26 0 0 0 Distributed proportionally-ish on the buckets (hopefully) most likely to get to 28
648 648 0 0 0 0 0 100 0 0 0 0 All of the troops at the first castle higher than 5
649 649 2 3 4 20 23 13 4 7 0 24 Counter Strategy
667 667 0 0 8 11 0 22 28 31 0 0 Strongly attacked with the most likely castles to reach 28.
669 669 0 0 9 11 21 18 18 0 0 23 Just kinda throwing some troops like the US Govt throws money at the army
678 678 30 30 30 0 0 0 0 0 0 10 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.
679 679 2 4 7 15 18 21 0 2 0 31 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.
717 717 4 6 8 12 17 22 31 0 0 0 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)
723 723 10 10 10 10 10 25 25 0 0 0 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.
740 740 11 11 11 13 14 20 20 0 0 0 I think people will underinvest in low value castles, and invest more on high value castles than the middle range ones. So my hope is to win one through five relatively cheaply, while having a decent chance of winning 6 and 7.
747 747 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.
748 748 1 0 2 2 11 12 24 24 0 24  
771 771 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.
789 789 0 5 9 12 21 19 5 5 0 24 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.
804 804 0 0 0 20 0 10 20 30 0 20 just felt intuitively good
822 822 0 0 2 30 2 30 2 34 0 0 Three eyed raven told me
871 871 5 5 5 10 20 25 30 0 0 0 trying for a plausible counter-intuitive plan
878 878 2 4 6 6 6 21 25 30 0 0  
886 886 2 2 2 2 12 20 25 35 0 0 I didn't try for 9 or 10 and went for 5-8.
894 894 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.
904 904 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.
912 912 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.
915 915 2 5 10 10 15 15 20 23 0 0 Trumpian Electoral college: ignore NY and CA, go for TX, PA, FL
919 919 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.
920 920 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
924 924 2 4 6 12 16 18 20 22 0 0  
925 925 0 0 0 20 20 20 20 20 0 0 Why not?
951 951 0 0 4 5 17 16 25 0 0 33  
961 961 4 7 9 10 15 20 0 35 0 0 Since I figured most would go for the large numbered castles, I decided not to contest those, instead choosing to go with a more conservative strategy in which I compiled that lower numbers to form a small majority.
965 965 5 5 10 10 15 15 20 20 0 0 Slightly higher than the average for each castle from the last two games. Ignored castles 9 and 10. Adds up to 36 maximum points, well enough to win. Even if losing castles 7 and 8, can still win.
977 977 1 2 5 17 11 13 16 18 0 17 Counter positions of most successful players from last time, while exceeding averages.
988 988 0 3 6 11 13 16 0 51 0 0 Because you need to get to 28 to win so maximum chance of getting to 28
990 990 10 14 14 14 14 14 20 0 0 0 Total of 55 points. Need 28 to Win.
992 992 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.
997 997 1 9 1 1 14 19 25 30 0 0 Aim to get just 28 points
1006 1006 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.
1012 1012 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
1050 1050 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
1087 1087 2 3 5 0 0 0 15 25 0 50 Arbitrary
1116 1116 0 0 1 6 11 18 28 5 0 31 I tried to use Ken Nickerson's strategy from the first battle but with a focus on two castles that were differently successful in the first two battles. In the first one, 7&8 were the main targets by the top 5. In the next one, 9 and 10 became the big numbers to target. I need 28 points to win the battle. My goal is to take 5, 7, 6, and 10 in most matches. I get all four of those and I win. If I don't, well, hopefully I can steal the 8 (or the 4) and use dumb luck to conquer smarts.
1123 1123 2 3 5 20 30 40 0 0 0 0 I decided it was easier to capture alot of lesser castles
1145 1145 0 0 0 17 19 20 21 23 0 0 Capture the middle
1164 1164 0 2 3 3 13 13 21 20 0 25 I consulted Mars the God of War and he suggested this.
1165 1165 0 0 0 15 20 20 20 25 0 0 Figuring the enemy would over commit to the larger value castles.
1176 1176 100 0 0 0 0 0 0 0 0 0 I'm a warlord, yes, but all I really care about is myself. . . and I want a castle! If anyone stands in my way they will be sorry.
1255 1255 3 4 8 15 18 23 29 0 0 0 Only fight for enough castles to win
1257 1257 1 1 11 0 0 0 23 28 0 36 I chose 4 castles that I had to win and devoted most of my resources to them. In looking at the last winners, I didn't want to waste any resources on pricey castles I wasn't all in to win. On the other hand, if someone outbid my 3, I wanted to take the chance that they might have said nothing on 1 and 2.
1269 1269 0 0 11 14 0 21 25 29 0 0 I’ve narrowed down the gameplay to around 14 possibly optimal plays. This is one of them. There are 33 possible exactly 28points to win strategies. This one is 8-7-6-4-3. Allocated by relative castle value. Castle/28*100. Here’s the list of 9, allocate by taking castle/28*100: 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 10-6-5-4-3 8-7-6-4-3 The other 5 are semi suboptimal vs the 9 but forms the “rock,paper,scissor”: ExpectedValue: castle/55*100 EvenAcross: 10/castle Ultimate: castle/28*100+1 for castle 8,9,10 Lucky7: castle/28*100 for castles 1 to 7 Troll: 47,53 on castle 9 and 10 respectively. At least one of these strategies will do well depending on the market. And the market will shift around these strategies depending on the amount of trolldom.
1274 1274 0 15 5 0 15 20 20 25 0 0 Distributing them where I don't think people will put them so as to get at least 27.5 points
1283 1283 1 2 0 0 17 20 25 35 0 0  
1284 1284 0 1 4 10 5 15 25 10 0 30 I'm guessing (hoping) that people will still (despite the data) skew away from over-committing to castle 10 and I'm sacrificing 9 and probably 8 to win there and hoping to compensate with a lot of smaller wins.
1315 1315 4 6 9 11 16 18 0 0 0 36 Trying to reach 28 points to win and looking at past deployments. Also keep a fairly constant point per soldier ( between 2.75 and 4)
2 2 1 1 1 11 19 27 37 1 1 1 I'm going for the crumbs, hoping that most opponents bet on the valuable castles. And by betting at least 1 soldier on each I'm winning the ones that the opponent doesn't send any soldier to.
20 20 1 1 1 1 23 23 24 24 1 1 Trying to capture the mid-high castles and sacrifice the others
30 30 1 1 1 1 1 1 91 1 1 1 Banking on winning ALL the battles at Castle 7
90 90 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.
111 111 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.
115 115 1 1 1 6 7 20 27 35 1 1 I wanted to win the middle castles
166 166 3 3 3 6 6 25 25 27 1 1  

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