Riddler - Solutions to Castles Puzzle: castle-solutions.csv
Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette
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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? |
---|---|---|---|---|---|---|---|---|---|---|---|---|
923 | 923 | 0 | 26 | 32 | 42 | 0 | 0 | 0 | 0 | 0 | 0 | I thought people would fight it out for the high value targets and end up splitting a fair number of those castles. If I could take enough of the lower (less competitive castles) I would win more points. Also, stay away from clean looking numbers. |
924 | 924 | 0 | 25 | 25 | 25 | 25 | 0 | 0 | 0 | 0 | 0 | HUNGER! |
925 | 925 | 0 | 21 | 0 | 0 | 0 | 0 | 25 | 0 | 27 | 27 | I think I need to get my minimum 28 points by trying to take 4 castles, which is the minimum it would take. There are 27 combinations of 4 that generate at least 28 pts. All of them require some combo of castle 10, 9 or 8. I chose the one that has two castles well below 8 where I think there will be less competition and concentrated my troops on 9 and 10. Bit of a punt. Can't wait to see the results! |
926 | 926 | 0 | 20 | 0 | 20 | 20 | 0 | 0 | 20 | 20 | 0 | Guesswork |
927 | 927 | 0 | 20 | 0 | 0 | 20 | 20 | 20 | 20 | 0 | 0 | I need 28 points to win, and any points past 28 are just accessory. I will send 20 troops each to the castles that will get me to that mark of 28, namely, 8 + 7 + 6 + 5 + 2 = 28. |
928 | 928 | 0 | 17 | 12 | 12 | 12 | 12 | 0 | 35 | 0 | 0 | Try to capture 28 exact points (majority) without going for castles 10 and 9 |
929 | 929 | 0 | 16 | 16 | 17 | 0 | 17 | 0 | 17 | 0 | 17 | A wild shot in a dimly lit room. Loosing any one of these forts would guarantee victory. By focusing on fewer castles, but allowing for a plan B, I feel like there is a fighting chance. To be clear, this is a guess. |
930 | 930 | 0 | 15 | 14 | 14 | 0 | 14 | 15 | 14 | 14 | 0 | Sacrifice a few castles completely to have a better chance winning against all the even splits. 3 was a hunch but considered only sacrificing 1. Then on a psychology hunch I assumed the ends and the middle would be where people did something screwy so those were the sacrificial castles. |
931 | 931 | 0 | 15 | 0 | 0 | 20 | 20 | 20 | 25 | 0 | 0 | It's a race to 28 points. I stacked my castles to focus on a path to 28. |
932 | 932 | 0 | 15 | 0 | 0 | 19 | 20 | 21 | 25 | 0 | 0 | I assume my enemy will concentrate their forces to take the most valuable positions in order to assure victory, so instead I will concede the most valuable castles to the enemy, and hope to catch them unawares by allocating all my forces to defend the lesser towers to achieve the bare minimum necessary for victory. |
933 | 933 | 0 | 15 | 0 | 0 | 18 | 20 | 22 | 25 | 0 | 0 | Need 28 to win. I put troops on 5 castles to win 28 points. I concentrated my troops on these 5 castles to win them all. I forfieted the 10 and 9 ones as I suspect these will be heavily contested. So hopefully my strategy is unique and successfull enough times. |
934 | 934 | 0 | 14 | 0 | 0 | 16 | 20 | 24 | 26 | 0 | 0 | Need to win 28 points to win the fight. I picked the fewest number of castles required to get 28 points while also trying to avoid the most obvious castles. |
935 | 935 | 0 | 12 | 0 | 0 | 20 | 21 | 21 | 26 | 0 | 0 | I chose to punt the highest 2 castles and focus only on 5 castles that would give me a majority. I tried to choose odd numbers that would be less likely to tie for these castles with high amounts of troops. |
936 | 936 | 0 | 12 | 0 | 0 | 18 | 20 | 22 | 28 | 0 | 0 | |
937 | 937 | 0 | 12 | 0 | 0 | 0 | 0 | 28 | 0 | 28 | 32 | I wanted make sure I was always ~2-3 points above a multiple of 5, since I think a lot of people will use either a multiple of 5, or add 1 extra to a multiple of 5. This is a risky strategy since I only bet in 4 rounds, and I need to win every single one of them. However, I think many strategies will be vulnerable to this one. |
938 | 938 | 0 | 11 | 1 | 1 | 21 | 21 | 22 | 23 | 0 | 0 | tried to win 28 points in way that would defeat some of the unimaginative distributions |
939 | 939 | 0 | 11 | 0 | 14 | 0 | 19 | 25 | 31 | 0 | 0 | 28 points will win any battle, so any troops deployed fighting for more are essentially wasted. I decided against chasing the top castles, as they may typically require more resource, and focused on the required 28 points on a sliding scale, aiming to take no castle within that for granted. |
940 | 940 | 0 | 11 | 0 | 0 | 21 | 21 | 21 | 26 | 0 | 0 | Need 28 to win. Decided to put all my eggs in one basket: must win 2,5,6,7,8 (unless tie with 0 at just the right spots). |
941 | 941 | 0 | 11 | 0 | 0 | 16 | 17 | 27 | 29 | 0 | 0 | |
942 | 942 | 0 | 11 | 0 | 0 | 16 | 16 | 26 | 31 | 0 | 0 | Need only 28 points, avoiding human friendly round numbers and avoiding high interest rounds. Also playing above 10 to outperform the basic 10x10 strategy. |
943 | 943 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
944 | 944 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
945 | 945 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
946 | 946 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
947 | 947 | 0 | 10 | 30 | 60 | 0 | 0 | 0 | 0 | 0 | 0 | swag |
948 | 948 | 0 | 10 | 10 | 10 | 10 | 10 | 15 | 15 | 20 | 0 | Random |
949 | 949 | 0 | 10 | 0 | 12 | 0 | 20 | 0 | 28 | 0 | 30 | Each even castle is worth more than the odd castle before it |
950 | 950 | 0 | 10 | 0 | 0 | 25 | 25 | 28 | 12 | 0 | 0 | Just hoping I get lucky, if I'm being honest, Ollie. |
951 | 951 | 0 | 10 | 0 | 0 | 20 | 20 | 25 | 25 | 0 | 0 | 28 to win! |
952 | 952 | 0 | 10 | 0 | 0 | 20 | 20 | 20 | 30 | 0 | 0 | The plan here is to give myself a chance everywhere. There are 55 available points, so 28 points are needed to win. So I divided my troops among 8, 7, 6, 5 and 2 (28 total points), with the assumption that 10 and 9 would be highly coveted, so are best avoided. |
953 | 953 | 0 | 10 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 30 | I'm "cheating" in that I am doing the opposite of my first battle plan. |
954 | 954 | 0 | 10 | 0 | 0 | 0 | 0 | 0 | 30 | 30 | 30 | My goal was to defeat the strategies I thought would be most commonly used, specifically, 10 at every castle, 25 in castles 10-7, 25 in castles 10-8 and 25 in 1. My strategy does lose to 10-8 34 33 33 however I don't think that strategy will be heavily employed as it loses to 10 at every castle. |
955 | 955 | 0 | 9 | 11 | 0 | 0 | 19 | 21 | 0 | 0 | 40 | I didn't work the math out precisely, but I first established that I only wanted to deploy troops to win 28/55 victory points to avoid spreading myself thin. Next, I gave some thought as to which Castles I felt would be least likely to have troops deployed. This is primarily guesswork, but I went with 2, 3, 6, 7, and 10. For the distribution of troops, I put more eggs in the higher values castles but didn't calculate too much beyond that. |
956 | 956 | 0 | 9 | 0 | 5 | 8 | 5 | 27 | 12 | 31 | 3 | I let a computer evolve the strategy. I started with 100 random deployments, then used a Monte Carlo algorithm to develop a deployment that would defeat as many of these as possible. I repeated this procedure until I had a new collection of 100 deployments, each one able to defeat (nearly) every deployment of the original 100. I then repeated the entire process 100 times (100 is a nice round number), each time creating a collection of 100 strategies that were all good at defeating the previous collection. I then selected from these 100 strategies the one that would win when these 100 went up against one another. |
957 | 957 | 0 | 9 | 0 | 0 | 0 | 26 | 30 | 35 | 0 | 0 | We have to keep in mind, our goal is to beat other people, not randomness. My feeling is that most of the analytical riddler minds will modify proportional distribution, giving slight edges to certain castles to try to win them by slight margins, as this seems like the optimal plan. So let's turn that on it's head, and beat a lot of people who smoothly allocate their points. There are 55 total points, so 23 total points win. There are many ways to get this with only three castles, but let's keep in mind people will tend to try to do sneaky things to steal high number castles (particularly #9, as that seems "sneaky" to ignore 10 and steal 9). My first reaction was: just win 7,8,9. Put all your points in and win those. This gives 24 and a sure win. But again, 9 seems like a very highly contested castle. So I decided instead, 6,7,8,2. Surely 2 and 6 should be more guaranteed than 9! Now just how to distribute. Well, I should mirror how others will be distributing their points here. (obviously 25 troops to each could lose me 7,8 somewhat frequently). While it seems like I MUST win all four to win, many people will likely assign 0 to some castles, so tie points may come into effect. So even losing 6 can be repaired by a tie in 10 and 3. So I aim to get 23 total points, so let's assign proportionally: {0,2/23*100, 0,0,0,6/23*100, 7/23*100, 8/23*100, 0, 0} = {0,9,0,0,0,26,30,35,0,0}. I need to win every one of these four I've chosen (unless other people elect 0 on some castles... very possible?), but I think in the long run, I've overvalued weird castles that aren't likely to be beaten in general. |
958 | 958 | 0 | 8 | 0 | 14 | 0 | 21 | 25 | 0 | 32 | 0 | Instead of comparing all options, I compared all combinations that sought to defend 4 castles and promoted the best 10 combinations to an 'a-league'. These combinations were subject to constraints: the total points being defended by at least one army was 28 or more and the armies were allotted to the castles proportional to the number of available victory points for the number of castles I decided to defend. I then did the same for all combinations that sought to defend 5 castles, 6 castles, and 7 castles, 8 castles, and 9 castles. I then ran these a-league combinations (60) against each other and found that this combination won 43 fights, tied 16 fights, and lost none. http://imgur.com/a/TUJmZ. Interestingly, this wins at most 28 points and is thus vulnerable to 0 7 0 14 0 21 25 0 32 1 and the like. I suck at game theory and I'm counting on not everyone coming up with this optimization and having one person specifically beat it. |
959 | 959 | 0 | 8 | 0 | 0 | 20 | 22 | 24 | 26 | 0 | 0 | All in on middle sized castles avoiding the high value prizes. Added Castle 2 to get over the half way point. |
960 | 960 | 0 | 8 | 0 | 0 | 18 | 21 | 25 | 28 | 0 | 0 | Put all my resources into getting 28 castle points. Hope is to just barely win. |
961 | 961 | 0 | 8 | 0 | 0 | 18 | 20 | 22 | 32 | 0 | 0 | |
962 | 962 | 0 | 8 | 0 | 0 | 16 | 22 | 25 | 29 | 0 | 0 | Castles 9 and 10 are bound to be hotbeds of WWI-style massive trench wars of wasted troops, numbering in the dozens per side. I decided to commit all of my forces to only the minimum number of castles that weren't 9 or 10, committing a troop count roughly proportional to the portion of 28 points that that castle provides, hoping to simply win those five and only those five every time, winning by a score of 28-27 very often. This strategy could massively backfire, of course, if I end up winning four out of those five castles every time, winning no battles overall, but when you're trying to be the top of the heap in a massive free-for-all...go big or go home, and be proud if you land flat on your face trying something crazy! |
963 | 963 | 0 | 8 | 0 | 0 | 15 | 20 | 26 | 31 | 0 | 0 | Figured if I punt on 10 and 9 I should win 5-8. Only need to get to 28 to win. No point going for more than that. |
964 | 964 | 0 | 7 | 10 | 14 | 18 | 21 | 0 | 30 | 0 | 0 | I submitted an answer before, but mis-added and realized my answer could not possibly win. The strategy here is to maximize my chances at getting 28, instead of maximizing the average outcome. I figure by avoiding the high castles, which most people will probably at least try to bid on, I can ensure I get the 5 lower castles that add up to 28, which is more than half of the total points. The strategies this works well against are the linear strategies (where the soldiers are distributed according to castle size), as well as a top heavy strategy, as long as I can win #8. Most people who play a top heavy strategy will accordingly weigh #10 more than #9 more than #8, so my 30 soldiers on 8 might do the trick. |
965 | 965 | 0 | 7 | 8 | 10 | 12 | 13 | 15 | 17 | 18 | 0 | I sacrificed 1 as not work it, and 10 as too expensive to fight for. Among the rest, I tried to balance value against risk, to capture the majority of points in the middle. |
966 | 966 | 0 | 7 | 0 | 14 | 0 | 21 | 25 | 0 | 33 | 0 | Ranked by troop efficiency points by expected value, all-in |
967 | 967 | 0 | 7 | 0 | 0 | 21 | 23 | 24 | 25 | 0 | 0 | It takes 28 points to win. I sacrificed five castles and over-defended five others worth exactly 28. I figured most opponents will over-defend Castles 9 and 10. |
968 | 968 | 0 | 7 | 0 | 0 | 18 | 22 | 25 | 28 | 0 | 0 | If I win email me and I'll explain. |
969 | 969 | 0 | 7 | 0 | 0 | 18 | 21 | 25 | 29 | 0 | 0 | 9 and 10 are likely to be prime targets, instead of an arms race there I'll take the likely advantage across other castles needed to win. This strategy sucks because I have only one path to victory, though. |
970 | 970 | 0 | 7 | 0 | 0 | 18 | 21 | 25 | 29 | 0 | 0 | These five castles are required to finish with one more point than the opponent. This allocation maximizes the value to point ratio (dollars per WAR in baseball?). This assumes opponents will allocate value to the castles that are conceded. If not, the point values will be split potentially adding to the margin of victory. |
971 | 971 | 0 | 7 | 0 | 0 | 16 | 16 | 26 | 31 | 2 | 2 | |
972 | 972 | 0 | 6 | 7 | 11 | 14 | 17 | 20 | 25 | 0 | 0 | There are a total of 55 points and I will need 28 to win. I don't have a specific stategy, but I am giving up 20 points by putting zeros on 1,9,10. I am guessing that most people will bet heavily on 9 and 10. I put more weights on 8 as I cannot win without castle 8. Besides that, I will win if I get 6 out of the 7 intended castle. |
973 | 973 | 0 | 6 | 0 | 12 | 0 | 23 | 26 | 0 | 33 | 0 | the maximum point in this game is 55, so to win in any 1 on 1 match up i only need to get 28 points. so focusing on specific castle(s) with total points of 28, i could distribute 100 troops in only 5 castles to guaranteed a control. this strategy can also works if i decide to put 100 troops in 4 castles e.g 1, 8, 9, 10. However majority of people tends to contest "high-value" castle(s) (castle 7, 8, 9, 10) so it would be a safer pick if i just distribute the troops in less-contested castles. |
974 | 974 | 0 | 6 | 0 | 0 | 17 | 22 | 26 | 28 | 0 | 1 | Ah, another game of trying to think one level ahead of your opponents. The Meta game is strong this week. The goal is to win small and lose big in terms of the number of troops used. So I plan on losing big on 10, but also beating those that did not deploy any troops. Also, with 55 points up for grabs, getting 28 points is the key to victory. So I will be going after 5-8 and 2, as I expect everyone to try and get either 10 or 9. Then I will be sending 0 troops to the other castles. I did think about trying to send negative soldiers but if I won, I would surely be caught. Good luck to me. |
975 | 975 | 0 | 6 | 0 | 0 | 15 | 21 | 27 | 31 | 0 | 0 | If I win the five castles I put troops at I win by one. |
976 | 976 | 0 | 5 | 11 | 17 | 5 | 11 | 11 | 34 | 3 | 3 | Assume most common strategies are to win 1,8,9,10 or 1-7 and counter. Adjust to defeat 10 per castle also. |
977 | 977 | 0 | 5 | 10 | 10 | 0 | 0 | 20 | 25 | 30 | 0 | Need 28 of 55 to win a matchup. |
978 | 978 | 0 | 5 | 7 | 13 | 19 | 26 | 0 | 30 | 0 | 0 | I'm just trying to get to 27 of the 55 points and I thought that a disproportionate number of contestants would fight it out for castles 9 and 10. But some would think like me and perhaps try only castles 1-7 or 2-7. So I added 8 and dropped 7 just in case. |
979 | 979 | 0 | 5 | 7 | 9 | 11 | 14 | 16 | 18 | 20 | 0 | Going to punt 10 and 1 and distribute my forces according to value of each castle. |
980 | 980 | 0 | 5 | 5 | 5 | 5 | 5 | 20 | 55 | 0 | 0 | You need 28 victory points to win. I figure most people will will try to win 10, 9, 8 and 1 to get the 28. I'm willing to concede 1, 10, and 9 and want to win the rest. |
981 | 981 | 0 | 5 | 5 | 5 | 5 | 5 | 20 | 35 | 20 | 0 | I figured most people would go for castle 10 to achieve the most possible points, but I believe that you would gain more by grabbing castles 7, 8, and 9. I gave the other castles a few more troops just in case I could grab a few points if those castles were left ignored. |
982 | 982 | 0 | 5 | 1 | 16 | 22 | 8 | 11 | 11 | 14 | 12 | I generated several different strategies, and also created a large number of "random" distributions of troops. This was the random distribution that had the greatest success rate against both the deployments I generated myself, and the other random distributions. I slightly edited the random distribution to improve win percentage. |
983 | 983 | 0 | 5 | 0 | 15 | 20 | 20 | 20 | 20 | 0 | 0 | |
984 | 984 | 0 | 5 | 0 | 1 | 1 | 1 | 1 | 23 | 28 | 40 | Winning castles 8,9 and 10 insures 49% of available points. Winning any other castle (other than 1) insures a victory |
985 | 985 | 0 | 5 | 0 | 0 | 16 | 21 | 27 | 31 | 0 | 0 | As 55 total points are available, 28 are needed for a victory. Castles 8, 7, 6, 5, and 2 combine for 28 points and will avoid the significant troop commitments likely required to capture castles 9 and 10. Gambling that Castle 2 will not be heavily contested does allow for additional troop allocation among castles 5-8. |
986 | 986 | 0 | 5 | 0 | 0 | 16 | 21 | 26 | 32 | 0 | 0 | I need 28 points. I get split points if my opponents also give 0 to 1, 3, 4, 9, or 20. I chose middle of the road castles to add up to 28, assigning more soldiers as value increased. Nothing overly mathematical about it. |
987 | 987 | 0 | 5 | 0 | 0 | 16 | 21 | 25 | 29 | 2 | 2 | 100 soldiers/28 points to win = 3.6 soldiers per point if none are wasted. so I focused on 8,7,6,5, and 2 castles for close to that 3.6x ratio. The goal is to win 28 and only 28 points by keying on the marginal value of an additional soldier. The one luxury is that I've allotted for 2 soldiers in castles 9 and 10 to catch others trying to slack off with 0 or 1 there. |
988 | 988 | 0 | 5 | 0 | 0 | 14 | 17 | 24 | 36 | 0 | 4 | Even though this is a zero sum game and can be solved in theory by a linear program, there are (109 choose 9) possible strategies for each player, more than 4 trillion, making the problem computationally infeasible. In addition, there is no pure strategy equilibrium. So we have to develop a heuristic based on our intuition about how we should play. I used the following rules to select a subset of strategies and then picked one at random: 1) The strategies which go after only 4 castles require two of castles 8,9 or 10. Therefore we expect that when these castles are attacked, they will be attacked with large numbers. We only go after one of these three with large numbers. We will use at least 34 soldiers for this castle. 2) A compact strategy (attack fewer castles) avoids spreading the troops to thin. We focus on strategies which only attack 5 castles. 3) A small number of soldiers should be reserved for castle 10 in the event an opponent uses a similar strategy of avoiding the high value castles. 4) The number of soldiers used for the smaller castles we go after should be roughly proportional to their value. I narrowed it down to 11 castle combinations and soldier assignments and chose the above one at random from them. |
989 | 989 | 0 | 5 | 0 | 0 | 11 | 18 | 26 | 40 | 0 | 0 | Didn't go with 10 or 9 because the initial reaction would be to go with the highest points so i started with 8 and went down to 4 given me enough points to win when I add in castle 2. |
990 | 990 | 0 | 4 | 6 | 10 | 15 | 25 | 0 | 40 | 0 | 0 | Choose the most unlikely combination to be opposed to score 28 points. |
991 | 991 | 0 | 4 | 6 | 8 | 10 | 20 | 24 | 28 | 0 | 0 | Heuristics!!! |
992 | 992 | 0 | 4 | 0 | 2 | 2 | 2 | 23 | 28 | 38 | 1 | The goal is 26 points. The easiest way is with pouring resources into three towers (10,9,7). But then there's no contingency for losing a tower. I'm planning on losing a tower but having enough safety towers to make up the difference. |
993 | 993 | 0 | 4 | 0 | 0 | 23 | 23 | 24 | 24 | 1 | 1 | Trying for exactly 28 out of 55 possible points by winning fewest contested battles (but allowing a small chance of winning 9 and/or 10, when battling people almost like me). |
994 | 994 | 0 | 4 | 0 | 0 | 15 | 21 | 26 | 34 | 0 | 0 | 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. |
995 | 995 | 0 | 3 | 6 | 13 | 0 | 4 | 20 | 27 | 26 | 1 | The best result from a quickly-bodged genetic algorithm. If I realized the deadline was EST this is what I would have submitted then. |
996 | 996 | 0 | 3 | 6 | 11 | 14 | 17 | 18 | 19 | 11 | 1 | |
997 | 997 | 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. : ) |
998 | 998 | 0 | 3 | 4 | 7 | 16 | 24 | 4 | 34 | 4 | 4 | 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! |
999 | 999 | 0 | 3 | 4 | 3 | 10 | 15 | 15 | 22 | 20 | 8 | Many simulated troops died to bring us this information. |
1000 | 1000 | 0 | 3 | 4 | 1 | 0 | 1 | 22 | 24 | 21 | 24 | 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. |
1001 | 1001 | 0 | 3 | 3 | 7 | 6 | 8 | 11 | 15 | 20 | 27 | Weighted according to the square of the value, because wasting resources at a castle I don't win is the worst outcome. Introduced some random variance (10% of the armies) so this couldn't be easily gamed with a "one more at each, way less at one" strategy. This was also distributed according to the squares of the value. 0 3 3 7 6 8 11 |
1002 | 1002 | 0 | 3 | 3 | 3 | 21 | 0 | 21 | 24 | 1 | 24 | I wanted to win 5 regions |
1003 | 1003 | 0 | 3 | 3 | 3 | 17 | 3 | 31 | 35 | 3 | 2 | Need to get to 28 points. Focus on 3 to get me to 20, then deploy a few everywhere else to pick up 8 points on poorly defended castles. |
1004 | 1004 | 0 | 3 | 3 | 3 | 3 | 20 | 20 | 20 | 25 | 3 | |
1005 | 1005 | 0 | 3 | 0 | 0 | 16 | 24 | 26 | 31 | 0 | 0 | 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. |
1006 | 1006 | 0 | 3 | 0 | 0 | 14 | 17 | 19 | 22 | 25 | 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. |
1007 | 1007 | 0 | 2 | 4 | 6 | 8 | 14 | 15 | 16 | 17 | 18 | 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. |
1008 | 1008 | 0 | 2 | 4 | 6 | 8 | 12 | 14 | 16 | 18 | 20 | Win the bigger castle over uniform strategists, while not getting blitzed too much in the smaller castles |
1009 | 1009 | 0 | 2 | 3 | 8 | 10 | 12 | 15 | 20 | 30 | 0 | Random |
1010 | 1010 | 0 | 2 | 3 | 3 | 6 | 17 | 17 | 17 | 17 | 18 | Private algorithm... |
1011 | 1011 | 0 | 2 | 2 | 11 | 20 | 2 | 2 | 2 | 28 | 31 | |
1012 | 1012 | 0 | 2 | 2 | 5 | 6 | 10 | 12 | 17 | 20 | 26 | The troop numbers are proportional to the square of each castle's value. Let's see if this works! |
1013 | 1013 | 0 | 2 | 2 | 2 | 2 | 14 | 21 | 26 | 31 | 0 | My first thought was to concentrate all of my forces on the minimum number of castles, so as to maximize my chances of winning each one. The minimum required to win the war are castles 7,8,9 and 10, which give me 34 out of the total 55 points in the game. Then I realized that everyone else would likely be doing something similar, while also probably assigning more soldiers to higher-valued castles. This however leaves all the lower-valued castles up for grabs, so it's better to completely forget about castle #10 (which would probably need the most soldiers in order to be captured) and assign just a few soldiers to castles 2-6. I went for a minimum of 2 soldiers per castle, thinking that my opponents would probably use a minimum of 1 (or 0) for castles they don't value much. |
1014 | 1014 | 0 | 2 | 0 | 9 | 4 | 1 | 20 | 0 | 28 | 36 | I generated a few hundred random teams, tested them against a few base deployments (10 in each castle, 11 in castles 2 - 10, etc) and each other, and this one appears to be the best. |
1015 | 1015 | 0 | 2 | 0 | 2 | 22 | 0 | 26 | 0 | 12 | 36 | Simple simulation among randomly generated strategies https://github.com/mattinbits/fivethirthyeight_riddler_war_game |
1016 | 1016 | 0 | 1 | 13 | 14 | 14 | 14 | 15 | 14 | 14 | 1 | Happy to lose 1, 2 and 10. Leaves 43 winnable points. Need 28. So expect to lose 9 or 8. Expect to win 3-6 which gives a solid shout! Better than an all 10 strategy! Just sneaks the almost double the value strategy |
1017 | 1017 | 0 | 1 | 11 | 2 | 11 | 3 | 3 | 23 | 5 | 41 | Determined combinations of castles that would give you 28 points, optimized for "cheapest" castle. Then developed an algorithm that distributed points to those castles in a variety of ways, as well as general approaches to the problem -- distributing points evenly, distributing points across all castles as ratios of value, etc. For each run of the script found the winner, then manually added approaches that looked like they could beat the winning combination, and did that until I couldn't improve it anymore. |
1018 | 1018 | 0 | 1 | 10 | 13 | 2 | 20 | 23 | 27 | 2 | 2 | 28 points wins a round. This attempts to find a reasonably efficient path to those 28 points 8, 7, 6, 4, 3. This avoids fights with any top heavy strategy except perhaps on the 8. A few troops on other castles is intended to capture full points on any castle zeroed out by an opponent. |
1019 | 1019 | 0 | 1 | 7 | 10 | 10 | 18 | 23 | 28 | 1 | 2 | Castle 10 and 9 are going to be bloodbath. Just putting 3 soldier to gain all the people like me who are not going to try fighting them. I can lose either 3-4-5 but not both, so similar amount in all of them. |
1020 | 1020 | 0 | 1 | 7 | 4 | 8 | 5 | 1 | 21 | 23 | 30 | I made a bunch of random strategies fight and chose the one that won. I really didn't have any idea how to pick a good strategy. |
1021 | 1021 | 0 | 1 | 6 | 8 | 15 | 2 | 19 | 21 | 26 | 2 | 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. |
1022 | 1022 | 0 | 1 | 6 | 8 | 10 | 11 | 13 | 15 | 17 | 19 | (100. / sum(np.arange(11)))*np.array(np.arange(11)) Then rounded up. |
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CREATE TABLE "riddler-castles/castle-solutions" ( "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 );