Solving chess means finding an optimal strategy for playing chess, i.e. one by which one of the players can always force a victory, or both can force a draw. It also means more generally solving chess-like games, 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 is the result of two perfect players, without necessarily revealing the optimal strategy itself. 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.
Partial results
s 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. 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, ignoring the 50-move rule. Such a position is beyond the ability of any human to solve, and no chess engine plays it correctly, either, without access to the tablebase.
Predictions on when/if chess will be solved
argued in 1951 that it is not feasible for any computer to actually solve chess, since it would either need to compare some 10 possible game variations, or have a "dictionary" denoting an optimal move for each of the about 10 possible board positions. It is thus theoretically possible to solve chess, but the time frame required puts this possibility beyond the limits of any feasible technology. The number of mathematical operations required to solve chess, however, may be significantly different than the number of operations required to produce the entire game-tree of chess. In particular, if White has a forced win, only a subset of the game-tree would require evaluation to confirm that a forced-win exists. Furthermore, Shannon's calculation for the complexity of chess assumes an average game length of 40 moves, but there is no mathematical basis to say that a forced win by either side would have any relation to this game length. Indeed, some expertly played games have been as short as 16 moves. For these reasons, mathematicians and game theorists have been reluctant to categorically state that solving chess is an intractable problem. Hans-Joachim Bremermann, a professor of mathematics and biophysics at the University of California at Berkeley, further argued in a 1965 paper that the "speed, memory, and processing capacity of any possible future computer equipment are limited by specific physical barriers: the light barrier, the quantum barrier, and the thermodynamical barrier. These limitations imply, for example, that no computer, however constructed, will ever be able to examine the entire tree of possible move sequences of the game of chess." Nonetheless, Bremermann did not foreclose the possibility that a computer would someday be able to solve chess. He wrote, "In order to have a computer play a perfect or nearly perfect game, it will be necessary either to analyze the game completely... or to analyze the game in an approximate way and combine this with a limited amount of tree searching.... A theoretical understanding of such heuristic programming, however, is still very much wanting." Recent scientific advances have not significantly changed these assessments. The game of checkers was solved in 2007, but it has roughly the square root of the number of positions in chess. Jonathan Schaeffer, the scientist who led the effort, said a breakthrough such as quantum computing would be needed before solving chess could even be attempted, but he does not rule out the possibility, saying that the one thing he learned from his 16-year effort of solving checkers "is to never underestimate the advances in technology".
Chess variants
Some chess variants which are simpler than chess have been solved. A winning strategy for black in Maharajah and the Sepoys can be easily memorised. The 5×5 Gardner's Minichess variant has been weakly solved as a draw. Although Losing chess is played on an 8x8 board, its forced capture rule greatly limits its complexity and a computational analysis managed to weakly solve this variant as a win for white. The prospect of solving individual, specific, chess-like games becomes more difficult as the board-size is increased, such as in large chess variants, and infinite chess.
