Solving chess

Solving chess means finding an optimal strategy for playing chess, i.e. one by which one of the players (White or Black) can always force a victory, or both can force a draw (see Solved game). It also means more generally solving chess-like games (i.e. combinatorial games of perfect information), such as infinite chess. According to Zermelo's theorem, a hypothetically determinable optimal strategy does exist for chess and chess-like games.

In a weaker sense, solving chess may refer to proving which one of the three possible outcomes (White wins; Black wins; draw) is the result of two perfect players, without necessarily revealing the optimal strategy itself (see indirect proof).

No complete solution for chess in either of the two senses is known, nor is it expected that chess will be solved in the near future. There is disagreement on whether the current exponential growth of computing power will continue long enough to someday allow for solving it by "brute force", i.e. by checking all possibilities.

Endgame tablebases have solved chess to a limited degree, determining perfect play in a number of endgames, including all non-trivial endgames with no more than seven pieces or pawns (including the two kings).

One consequence of developing the 7-piece endgame tablebase, is that many interesting theoretical chess endings have been found. One example is a "mate-in-546" position, which with perfect play is a forced checkmate in 546 moves.

Such a position is beyond the ability of any human to solve, and indeed no chess engine plays it correctly (unless the engine itself is designed to have access to the tablebase).

Finding positions such as this can make one speculate what other interesting chess situations will be found, as more chess positions are solved. Unfortunately, adding only one single new piece to a chess position expands the complexity of the game-tree by such a vast amount, that the development of an 8-piece endgame tablebase is currently considered an intractable problem.

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