Forgive me if the answer is obvious, but I wondered about this for a while. In a game where one player can calculate all possible moves (whether the amount is more or less than atoms in universe or whatever) and another does not, would the first one always win? In a game where both players can do that, would first-mover always win, or will the games always conclude in draw? To calculate, 'see', all possible game progressions from the moments the game field is set, before the game even begins, does that mean what the game is beaten? This seems like a logical conclusion, is it?
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1I don't think this is exactly a duplicate, even if they are of course related. The other question asks whether a perfect algorithm exists, while this question asks what would be the outcome.– LeibnizGWMar 26, 2018 at 17:55
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What about chess.stackexchange.com/questions/12470/… ?– D MMar 26, 2018 at 18:03
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OK, I admit, the two questions you found cover this one for sure!– LeibnizGWMar 26, 2018 at 18:24
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1Unbeatable and always wins are two very different things.– AcccumulationMar 26, 2018 at 18:53
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"If the solution to problem X were to be found, what would that solution look like?" - I hope you see the inherent dilemma of your question. (note: SE is not the best place for speculative discussions)– AnnatarMar 27, 2018 at 11:11
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1 Answer
No, a player who can calculate for infinite time can play a perfect game of chess, but this does not automatically mean that he always wins.
From the game theory perspective, we know that chess is a finite game, so it admits a perfect strategy. Anyway we don't know what is the result of that perfect strategy. There are three possibilities: the perfect strategy could be a win for White, or it could be a draw, or it is also possible that the perfect strategy would lead to a win for Black. (This last possibility is very unlikely, and nobody believes in it, but I think it has theoretically not been ruled out. It would be amazing if the perfect strategy were a win for Black, it would mean that the initial position of chess is just a big Zugzwang!)
If the perfect strategy from both players leads to a draw, then it means that your perfect players does not necessarily win every game. Some imperfect but good opponent could manage to draw some times.
On the other hand, if the perfect strategy leads to a win for White, then your perfect player would always win with White, but as soon as he plays Black, he has a chance to draw some times against an imperfect but good opponent, and he could also lose sometimes.
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(Against the imperfect but good opponent, the perfect player might also win sometimes with Black even if the perfect strategy leads to a White win.)– EvargaloMar 29, 2018 at 8:30