Solving chess

Choose a first move in chess: push a pawn, or bring out a knight. Each choice opens many possible replies. Now imagine that neither player ever makes a mistake. Would the ordinary starting position lead to a draw, a White win or a Black win? Solving chess begins by proving which of those outcomes perfect play forces, rather than guessing from an engine’s score.[1] [2]

Ordinary chess starts with 32 pieces and many possible replies to each move. The missing result is a proof of whether perfect play from that start forces a White win, a draw or a Black win. To make that target precise, the rules and the information retained in a game state must be fixed.

Assign terminal outcomes $+1,0,-1$ from White's perspective. The game-theoretic value means the perfect-play outcome. At a White turn, it is the maximum value over legal actions; at a Black turn, it is the minimum. Correct draw claims are actions too. The state must retain side to move, castling and en-passant rights, the no-progress counter and repetition-relevant history. A king returning to its old square does not recover castling rights, so the board diagram alone cannot determine the legal game.[1] [2]

Computers play exceptionally strong chess, and databases give exact answers for many endings with few pieces. The opening still lacks an established perfect-play result. Jon Edwards’s 2026 article argues that modern tools enable practically error-free analysis. The accompanying journal editorial calls this a methodological solution, distinct from proving the game’s outcome and supplying a guaranteed strategy. A long sequence of engine draws alone cannot establish that guarantee.[3] [4] [5] [6]

The first missing result is a proof of the initial value; the stronger milestones require reproducible strategies attaining it. A weak draw strategy need not exploit every later opponent mistake, whereas a strong solution must attain each reachable state’s value. Endgame coverage is not coverage of all these states: Syzygy’s seven-piece support excludes castling rights, and its WDL probe assumes a freshly reset fifty-move counter. Edwards’s accessible abstract claims practical analysis adequacy; it does not provide the initial-value certificate needed here.[1] [4] [5] [7]

A chess move can look safe because nobody has found a refutation. A proof must also cover a reply that nobody thought to test. That difference makes chess an approachable example of computational certainty. In 2007, a checkers project crossed this boundary by proving a draw from the start, combining a forward search with solved endings. Chess asks for a comparable guarantee under its own rules.[1] [8]

A proof of a winning strategy must justify a suitable move for its own side and withstand every opponent response. A heuristic can usefully decide which branch to examine first while remaining outside the argument that establishes the result. The checkers proof made this distinction operational: estimates scheduled work, while proven bounds connected the opening to solved endings. Chess is therefore a test of proof construction, state specification and independent checking, as well as search strength.[1] [8]