riddler-castles/castle-solutions: 916
Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette
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? |
---|---|---|---|---|---|---|---|---|---|---|---|
916 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 32 | 32 | 32 | Tell us denote a particular deployment by a 10-tuple, castle 1 first. So the above deployment is (1, 1, 1, 1, 0, 0, 0, 32, 32, 32). I have been considering 3 broad classes of strategy. (Obviously there are deployments which don't fit into this schema, but which may still be meritorious.) I call these classes Paper, Scissors and Stone. Paper strategies cover all the castles with forces approximately proportional to the value of the castle, for example (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). I also consider an equal distribution of forces, 10 to each castle, to be a Paper deployment. Scissors surgically target a winning subset of castles, for example (10, 0, 0, 0, 0, 0, 0, 30, 30,. 30). Clearly Scissors will defeat paper. Stone strategies target subset of castles insufficient to win on their own, but additionally hope to win or tie enough other castles to gain the extra points to win the war. (1, 1, 1, 1, 0, 0, 0, 32, 32, 32) is a stone strategy. It will win if it wins castles 8, 9, and 10 and either wins castle 1 or ties any other castle. Stone loses to paper (it wins its targeted castles but loses the rest). It mostly wins against scissors because both strategies are likely to contest at least one high-value castle, and stone's forces will be more concentrated. It's my expectation that the majority of depoyments submitted will be Scissors or paper-scissors hybrids. My original idea was the stone (1, 0, 0, 0, 0, 0, 0, 33, 33, 33) This is elegant in that it wins precisely when it wins castles 8, 9, and 10, and any other castle is uncontested by the opponent. The first condition is nearly certain against a scissor strategy since these must target at least four castles, and it will be very difficult to commit as many as 33 soldiers to any one of them. The second condition is much less certain. I cannot predict how many competitors will decide to contest every castle. I decided to tweak my original idea as I suspect that rather more scissor players will put at least one soldier into every castle than will put exactly 32 into one of 8, 9, and 10. I consider it unlikely that a scissor strategy would put more than 1 soldier into castles 2, 3, and 4, without also commuting similar or greater forces to castles 5, 6, and 7. If he does that, it's not really a pure scissor, more a paper-scissors hybrid. |