> I kind of like to think of games (of perfect information) in terms of what > chance does a top human (or future human) player have a beating or drawing a > player who is omniscient in the game. If that chance is very close to > zero, it's a good game and it doesn't make it a "better game" to make the > chances even lower. In fact what is "better" is pretty subjective, isn't > it? > > All games of perfect information are rigged anyway. They have a > predetermined outcome that will be reached with perfect play, so they are > basically sophisticated puzzles. >
you kind've answered your own question here. a better measure might be: "what is the smallest computer program (for some fixed language) that can compute a correct (i.e. perfect, when the position isn't a losing one) move given as input a board position, superko information, and size to move"? the usual time and space complexity measures need varying board sizes to make any sense of this question, and have undesirable features (like, they might not apply until the board size is much larger than anyone will ever play). but this (which is essentially a kolmogorov measure) should capture the game nicely. this should measure the inherent complexity of the game, although it ignores the amount of time required to compute that correct move. i don't know much about board sizes other than the standard ones, but i'd be interested in hearing arguments for why a larger board size would be easier (which would be counterintuitive to me). s.
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