![]() ![]() The unit for evaluation is centi-pawns which is intuitively unclear but generally anything more than a magnitude of 1.5 is significant (human masters will almost certainly convert this to a win) and anything more than a magnitude of 4 is completely winning or losing. At times it can calculate a forced mate for either side in which case the evaluation will be either #n or -#n (strictly dominating and dominated strategies) and a forced draw with perfect play in which case it outputs exactly 0.0 (pareto-optimal strategy, neither side has a payoff). Although, theoretically, any arbitrary chess position only has one of three evaluations (0.0 (draw given perfect play from both sides), #n (forced mate in maximum of n moves by white), -#n (forced mate in maximum of n moves by black)) Stockfish uses a probabilistic approach to generate a decimal which is significantly negative if it thinks black is winning, significantly positive if it thinks white is winning and close to zero if it thinks the position is drawish. This means engines must take a probabilistic approach to maximizing their chances of winning. However, since chess is not fully deterministic there is an element of randomness. ![]() The most popular and strongest engine to date is Stockfish so we will be considering how it uses game theory.Ĭhess is a deterministic game which means that one can infer what the evaluation of the position is just based on logical concepts, without having to traverse the roughly 10^120 nodes to all final game states possible (Shannon’s number) which is, of course, unfeasible. Game theory is utilized in the development of computer engines which play chess and also other turn-based games. Game Theory: How Stockfish Mastered Chess ![]()
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