JohannesDahlstrom comments on Fundamentally Flawed, or Fast and Frugal? - Less Wrong
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Surely there is a known way to play chess and go optimally (in the sense of always either winning or forcing a draw). You just search through the entire game tree, instead of a sub-tree, using the standard minimax algorithm to choose the best move each turn. This is obviously completely computationally infeasible, but possible in principle. See Solved game