Re:Perfect Information Game: On Chess
by tedsanders on Saturday June 04, 2016 @04:19AM
(#11835492)
But isn't this true of all games? In games of imperfect information, there is still a perfect, computable solution. It just happens to be a mixed strategy. And if the argument is that games of imperfect information allow exploitative strategies to succeed against non-equilibrium strategies, well the same is true of chess: the very idea of a trap is usually making a suboptimal move to hopefully exploit an imperfect opponent's likely mistake.
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Re:Perfect Information Game: On Chess
by DanWaterworth on Saturday June 04, 2016 @04:49AM
(#11835561)
When you have imperfect information, understanding the other player's strategy becomes part of the game. A perfect solution may be computable against any deterministic strategy, but its stops being a possibility when you don't know the other player's strategy.
No, tedsanders is right. If the game has imperfect information but is zero-sum (i.e. the goals of players are perfectly opposed), you can always compute the subgame-perfect Nash equilibrium in mixed strategies, and it will be the best way to play against all possible opponents, both deterministic and random.
Mind games (bargaining, precommitment, etc.) only become important in non-zero-sum games, where the goals of players align in some ways and oppose in others. For example, if chess had an additional possible outcome where both players lose, that could make it impossible to find a single best strategy.
Re:Perfect Information Game: On Chess
by DanWaterworth on Saturday June 04, 2016 @10:08AM
(#11836372)
Thanks, that's an interesting nuance.