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.
Endgame tablebases are computerized databases that contain precalculated exhaustive analyses of positions with small numbers of pieces remaining on the board.
A variant first described by Claude Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”.
[7] Although losing chess is played on an 8×8 board, its forced capture rule greatly limits its complexity, and a computational analysis managed to weakly solve this variant as a win for White.
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 (i.e. with no refutations from Black).
For these reasons, mathematicians and game theorists have been reluctant to categorically state that solving chess is an intractable problem.
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."
The game of checkers was (weakly) solved in 2007,[13] but it has roughly the square root of the number of positions in chess.