riddler-castles/castle-solutions

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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?
1 100 0 0 0 0 0 0 0 0 0 because, I am number one!
5 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.
6 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).
7 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.
8 25 0 0 0 0 0 0 25 25 25 Since there are 55 available points, I only need to win 27.5 or more points to win any given battle. By maximizing my soldiers in the four castles that are worth 28 points combined, I maximize my chances of beating more evenly distributed enemies.
11 21 0 0 0 0 0 0 26 26 27 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
13 20 0 0 0 0 0 0 25 25 30 it put high power making it easy to win the castles with troops.
27 15 0 0 0 0 0 0 17 26 42 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.
38 13 0 0 0 0 0 0 29 29 29 Seeing as there are only 55 total points available, you only need 28 victory points to win. The "easiest" way to do this (in terms of total number of castles won) is Castles 1, 8, 9 and 10. I then split the number of soldiers such that the ratio of soldiers at castles 8 to 9 to 10 is 1:1:1 and the number of soldiers at castle 1 is greater than 10. This strategy will beat anyone who splits evenly between the 10 castles, and (I'm hoping) will beat a decent number of people who go for the same four castles. An example strategy this would lose to is is someone split all 100 of their troops between e.g. Castles 9 & 10. I decided not to employ a similar strategy since I think more people will try something similar to mine rather than something somewhat counter-intuitive like betting all their troops on only two castles (although this isn't really based on any evidence).
39 13 0 0 0 0 0 0 29 29 29 Focus all troops on the fewest number of castles that would win the minimum 28 points necessary to win.
80 11 0 0 2 3 3 3 26 26 26 The easiest way to win is to win {1, 8, 9, 10} for 28 v 27. The strategy needs to counter: [*] Strategy who tries to win {7,8,9,10} and goes all-25: This means that {8,9,10} must have at least 26 soldiers. [*] Strategy who splits 10 soldier to all: This means that {1} must have at least 26 soldiers. This means we have 1 : 11 8 : 26 9 : 26 10 : 26 remaining 11 soldiers The only enemy for this strategy would be strategy who goes kamikaze and play for {9,10} and goes split-50. The remaining 11 soldiers is split for {4,5,6,7} to make up for the 19 points loss from the kamikaze play.
81 11 0 0 0 0 0 0 29 29 31  
99 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.
100 10 0 0 0 0 0 0 30 30 30 Load up the soldiers on the minimum castles needed to win
101 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.
102 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.
121 7 11 0 14 16 0 23 0 29 0 I want a winning coalition of 28.
131 7 0 0 0 0 0 0 31 31 31 28 or bust.
132 7 0 0 0 0 0 0 31 31 31 There are 55 points total to be won between the 2 warlords if all castles are fought for, so whoever gets 28 or more wins in that case. In that case there are 14 ways to get at least 28 points, by winning one of the following specific groups of castles: {10,9,8,7}, {10,9,8,6}, {10,9,8,5}, {10,9,8,4}, {10,9,8,3}, {10,9,8,2}, {10,9,8,1}, {9,8,7,6}, {9,8,7,5}, {9,8,7,4}, {8,7,6,5,4}, {8,7,6,5,3}, {8,7,6,5,2}, {7,6,5,4,3,2,1}. I would like to try to win the fewest number of castles yielding at least 28 points and including a castle that fewer warlords would desire if possible so I can win it with a light deployment and concentrate in the others. From the above, it appears that a 4-castle group of {10,9,8,1} satisfies that, so those are my targets and I have concentrated the soldiers in the higher values castles as desired.
133 7 0 0 0 0 0 0 31 31 31 Well i was in the armed forces for about 27 years soooooo i think i know what I'm talking about pfffff
134 7 0 0 0 0 0 0 23 30 40 There are a total of 55 victory points available, so 28 are needed to win each war. Winning is not necessarily about getting the most victory points -- it's about getting to 28 victory points as often as possible. Thus I dumped almost of my troops in the 8,9, and 10 victory point castles, since winning those three is a total of 27 victory points. Unfortunately, I needed one more victory point, so I put 7 in the 1 victory point castle, hoping that it would be virtually ignored by most people. If one were to distribute troops to castles proportional to their victory points, only (1*(100/55))= 1.818 (which rounds to 2) would be sent there, so I hoped 7 would be enough to take care of that.
156 6 0 0 0 0 0 0 26 27 41  
201 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.
207 5 1 0 11 14 13 14 11 17 14 Simulation! I created 10,000 possible deployment strategies. For each one, I generated a scalar, u, from Uniform(0.1, 10). Then, generate a set of probabilities, theta, from Dirichlet((sqrt(u), sqrt(u), ..., sqrt(u))). Finally, generate the troop deployment from Multinomial(100, theta). Then, I paired off all possible deployment strategies and found the one that won the most. The top few seemed pretty similar, but might as well go with the best of the best, even if it's probable that a slight change will beat this particular one.
210 5 0 0 0 14 21 25 1 32 2 Focus on five castles to reach 28 points. Try to disrupt strategies going after low or high castle numbers. Capture uncontested high-value castles.
211 5 0 0 0 0 0 0 27 31 37 The three most-valuable castles are worth 27 total, and the 7 least-valuable are worth 28. So making a strong claim to 27 points and a weak claim to the 28th point seems like a good distribution. The vulnerabilities can be exposed, though, by a distribution that weights castles 2-7 as moderately important, and emphasizes a strong attack on one castle in the 8-10 range. I just have to count on my 8-10 range being fortified enough and few enough other people being crazy enough to send 5 soldiers to a castle worth 1 point.
212 5 0 0 0 0 0 0 25 30 40 Only need 28 total pts to win the battle
258 4 0 0 0 1 1 1 30 31 32 Heavy value on 10,9,8, and 1 as you would only have to win those 4 castles to win any battle.
259 4 0 0 0 0 0 0 32 32 32 Since I needed to win just over 50% of the possible 55 points I put all my men into the 4 castles that would earn 28 points and conceded the rest to my enemies. I figured this would allow me to concentrate my forces on castles that would guarantee me a victory if I was able to capture them. I know this is a risky (foolish?) strategy because I'm giving my enemies 27 points and failure to capture my 4 target castles would guarantee defeat. I'll be interested to see how my gamble/this game plays out. "Once more unto the breach"
260 4 0 0 0 0 0 0 32 32 32 All in, just like in Poker - I bet you can tell I lose a lot of money :(
261 4 0 0 0 0 0 0 32 32 32 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.
262 4 0 0 0 0 0 0 29 32 35  
263 4 0 0 0 0 0 0 28 32 36 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.
264 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).
275 3 7 0 14 0 21 26 29 0 0 The strategy in blotto games is always an attempt to win each castle that you win by as few soldiers as possible, while losing the castles you lose by as many as possible, in such a way as to get more than half of the available points (here the target is 28 points). I decided to chose the castles adding up to 28 points that I thought the fewest people would put significant resources in to securing, and roughly allocate my 100 armies to those castles proportionally to their point values, giving up completely on the other castles.
311 3 4 0 0 1 0 2 0 7 83 I ran a few simulations in MatLab, starting with warlords who randomly assigned their soldiers and then using the most successful warlords of each previous generation to bias the assignments of the next. This is a rough average of some of the winning strategies after a few hundred rounds.
343 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.
344 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.
345 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.
346 3 0 0 0 0 0 0 29 32 36  
347 3 0 0 0 0 0 0 29 32 36 28 wins, proportional to castle value
348 3 0 0 0 0 0 0 29 31 37 There are 55 points available on the board, so only 28 are needed to win, assuming no ties. I could incorporate ties in my strategy, but I'm an engineer, not a mathematician, it's late on a Friday afternoon, and I'm kind of tired. 28 points can be achieved through winning only four castles: 1, 8, 9, and 10. I concentrated all my forces on those four keeps. I split up my army to assail those keeps with a distribution of 3, 29, 31, and 37 warriors, respectively. I chose those numbers because like a good commander I know my troops. And I know my warriors fight best when arranged in groups of Prime Numbers.
376 2 5 0 0 0 21 31 41 0 0 give up the high points castles to win the middle castle points with a small attempt to win the bottom two
599 2 0 0 8 10 12 14 16 18 20 Let's see what happens
600 2 0 0 0 0 0 0 32 33 33 I need to win the top 3 castles plus one so I tried to optimise for this result.
601 2 0 0 0 0 0 0 31 33 34  
948 1 0 0 39 0 60 0 0 0 0 I assume a lot of people are going to go all out on Castle 10. I just am trying to avoid confrontation and maximize my chances of beating people who went all on ten.
949 1 0 0 1 18 20 20 20 20 0 Forfeit the richest castle to increase odds at the next five. Figure I'll get some of the 2 & 3 values by ties, but hope for an easy point for the 1 pointer. By my estimation of likelihood of winning/tying each castle, I estimate I'll average 29.25 points out of 55. With a bunch of smart people competing, I figure that's not half bad.
950 1 0 0 0 1 15 15 15 20 33 There were far more points to be gained in the high value castles than in the low value castles, so I weighted my distribution heavily toward the upper end, calculating that if I gain control of the high value casualties, I could afford the loss of the low value castles.
951 1 0 0 0 0 0 0 33 33 33  
954 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!
955 0 20 0 20 20 0 0 20 20 0 Guesswork
956 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.
960 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.
961 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.
962 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.
963 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.
964 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.
965 0 12 0 0 18 20 22 28 0 0  
966 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.
968 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.
969 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).
970 0 11 0 0 16 17 27 29 0 0  
971 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.
972 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.
973 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.
974 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.
975 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.
978 0 10 0 12 0 20 0 28 0 30 Each even castle is worth more than the odd castle before it
979 0 10 0 0 25 25 28 12 0 0 Just hoping I get lucky, if I'm being honest, Ollie.
980 0 10 0 0 20 20 25 25 0 0 28 to win!
981 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.
982 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.
983 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.
985 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.
986 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.
987 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.
988 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.
989 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.
990 0 8 0 0 18 20 22 32 0 0  
991 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!
992 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.
995 0 7 0 14 0 21 25 0 33 0 Ranked by troop efficiency points by expected value, all-in
996 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.
997 0 7 0 0 18 22 25 28 0 0 If I win email me and I'll explain.
998 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.
999 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.
1000 0 7 0 0 16 16 26 31 2 2  
1002 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.
1003 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.
1004 0 6 0 0 15 21 27 31 0 0 If I win the five castles I put troops at I win by one.
1012 0 5 0 15 20 20 20 20 0 0  
1013 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
1014 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.
1015 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.
1016 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.
1017 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.
1018 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.
1021 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.
1022 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).

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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
);
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