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). According to Zermelo's theorem, a hypothetically determinable optimal strategy does exist for chess.

In a weaker sense, solving chess may refer to a proof which 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.

Partial results

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).

Predictions on when/if chess will be solved

Grandmaster Jonathan Rowson has speculated that "in principle it should be possible for a machine to ... develop 32-piece tablebases. This may take decades or even centuries, but unless runaway global warming or nuclear war gets in the way, I think it will eventually happen." However, information theorist Claude Shannon has argued that it is not feasible for any computer to actually do this, since it would either need to compare some 10¹²⁰ possible game variations, or have a "dictionary" denoting an optimal move for each of the about 10⁴³ possible board positions. It is thus theoretically possible to solve chess, but the time frame required (according to Shannon, 10⁹⁰ years on a 1 MHz processor) puts this possibility beyond the limits of any "feasible" (as of 1950) technology.

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 [of chess,] 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 that assessment. The game of checkers was (weakly) 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".

Read more:

• First-move advantage in chess (Chess-players' speculations on whether perfect play results in a draw)