Solving chess-The Daily Ledger

Solving chess consists of finding an optimal strategy for the game of chess; that is, one by which one of the players (White or Black) can always force a victory, or either can force a draw (see solved game). It is also related to more generally solving chess-like games (i.e. combinatorial games of perfect information) such as Capablanca chess and infinite chess. 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 (if ever). 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. Progress to date is extremely limited; there are tablebases of perfect endgame play with a small number of pieces (up to seven), and some chess variants have been solved at least weakly. Calculated estimates of game-tree complexity and state-space complexity of chess exist which provide a bird's eye view of the computational effort that might be required to solve the game.

Solving chess

Partial results

Endgame tablebases

Endgame tablebases are computerized databases that contain precalculated exhaustive analyses of positions with small numbers of pieces remaining on the board. 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).

Solving chess

One consequence of developing the seven-piece endgame tablebase is that many interesting theoretical chess endings have been found. The longest seven-piece example is a mate-in-549 position discovered in the Lomonosov tablebase by Guy Haworth, 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, which initially (in 2014) required 140 TB of storage space and the use of a supercomputer but was later reduced down to 18.4 TB through the Syzygy tablebase. As of January 2023, the longest known forced mating sequence for the eight-piece tablebase (also ignoring the 50-move rule) was 584 moves. This was discovered in mid-2022 by developer, computer chess enthusiast, and physicist Marc Bourzutschky. The eight-piece tablebase is currently incomplete, though, so it is not guaranteed that this is the absolute limit for the eight-piece tablebase.

Solving chess

Chess variants

A variant first described by Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is provable with a strategy stealing argument that the first player has at least a draw thus: if the first player has a winning move, let him play it, else pass. The second player now faces the same situation owing to the mirror image symmetry of the board: if the first player had no winning move in the first instance, the second player has none now. Therefore, the second player can at best draw, and the first player can at least draw, so a perfect game results in the first player winning or drawing.

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.