machrider comments on Swords and Armor: A Game Theory Thought Experiment - Less Wrong

14 Post author: nick012000 12 October 2010 08:51AM

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Comment author: machrider 13 October 2010 02:27:35AM *  4 points [-]

Agreed, re: the limitations of my method. As you suggested, I ran another pass using only the top 7 candidates (wins >= 19 in my previous comment). Here are the results:

3: blue/red
5: blue/green
7: blue/blue
7: green/green
7: green/red
9: green/blue
11: green/yellow

Choosing the top 10 (wins >= 17 from before):

7: blue/red
7: red/green
9: green/green
9: green/red
11: blue/blue
11: blue/green
11: blue/yellow
11: green/blue
11: yellow/yellow
13: green/yellow

Yellow/yellow pops up as a surprise member of the 5-way tie for second place. The green sword is less effective once you introduce these new members. There are probably a lot of surprises if you keep varying the members you allow. And all of this still assumes a normal distribution, which is unlikely.

Comment author: machrider 13 October 2010 02:58:16AM *  6 points [-]

Pursuing this stupidity to its logical conclusion, I just did an elimination match with 16 rounds. Start with all combinations and cull the weakest member every round. Here's the result: http://pastie.org/1217255

Note the culling is sometimes arbitrary if there's a tie for last place. By pass 14, we have a 3-way tie between blue/blue, blue/green, and green/yellow. Those may very well be the best three combinations, or close to it.

Final version of program here: http://pastie.org/1217284

(Removed randomness and just factored in the probability of evasion into damage directly. This lets me use smaller numbers and runs much faster. Verified that the results didn't change as a result of this.)

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