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riddler-castles/castle-solutions: 65

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

This data as .json

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?
65 11 11 11 11 11 19 26 0 0 0 I enjoyed this weekäó»s Riddler. I attacked it, not mathematically, but by brute force and trial näó» error. I learned that the best strategy would involve trying to win a few key battles (i.e. not all of them), loading to ensure victories in those battles, and that it would entail barely winning in the end; i.e. a small margin of victory. My first thought was to look at ways to lock up the highest-value castles. Winning the battles for the top 3 castles is 27 points, only 1 short of victory, so my approach involved throwing a lot of soldiers at the top 3, a chunk at a lower-value one, and deploying 1 soldier at the remaining ones (to win battles against zero soldiers). An example of this approach is 0-2-1-1-1-1-1-30-31-32. This wins against many strategies but fails against a simple one of 10-10-10-10-10-10-10-10-10-10. Loading up on one lower-value castle to 11 (to defeat that strategy) leads to too few soldiers at the higher-value castles. Then I thought of the opposite approach; i.e. concede the battles for the 3 higher-value castles and try to win the remaining 7 (which would yield 28 points, and a win). The best approach I found was 11-11-11-11-11-19-26-0-0-0-. The 26 is necessary to defeat a strategy of deploying Œ_ of oneäó»s soldiers (i.e. 25) to each to the top 4 castles, the 11 is to beat the 10x10 strategy, and assigning the remaining 8 soldiers to the 5th highest castle. This strategy works against almost every strategies, especially the ones that many people likely would choose. It fails against strategies involving loading up on the mid-value castles; e.g. 0-0-1-4-11-20-25-20-15-4. However, as those strategies lose to many other ones I thought people would not choose them.
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