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Imagine a scenario where you have two perfect players (i.e. they can consider all the possibilities in a very short amount of time and they choose always the right movement).

If they decided to play against each other, would all of their games end up on a draw?

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    That depends on whether chess is drawn or not with optimal play. Nobody knows that.
    – Scounged
    Commented Jan 3, 2017 at 2:17

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The answer is currently unknown. If you don't consider the opening (generally the first 8-15 moves or so), strong AI like Stockfish will generally show a clear optimal move in any position, and the majority of openings tend to yield a draw in these computer matches. However, as there are an incredibly large variety of openings, and this number scales exponentially with the number of moves, it is infeasible, at least in the present, for us to find a definitive answer to this question.

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