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Entry 2 of 3 in Curiosities Play with itExhaustive

A game, exactly solved Curiosities

King + Rook vs King — all 399,112 legal positions, labeled once

Math: Zermelo's theorem (1913) — a finite two-player game with perfect information and no chance has a value at every position, computable by retrograde analysis working backward from terminal states. Dev: the exact same algorithm family, WIN/LOSE labeling by backward induction, as the Althöfer Prize 3 game analysis on Challenges — applied here to a chess endgame instead, as a standalone playable exhibit rather than a competition submission.

Not a chess engine, not a heuristic: every legal (king, rook, king, side-to-move) state in this endgame — 399,112 of them — was labeled exactly, once, by working backward from every checkmate, stalemate, and capture-the-rook terminal position. Independently verified two ways: a from-scratch Python re-implementation gives identical counts, and the result matches the textbook fact that every won King+Rook vs King position is mated in at most 16 full moves with best play. Move any piece on the board and the verdict — forced win in N, draw, or illegal — comes from that exact table, not a live search.

399,112 legal positions · 376,868 forced wins · 22,244 draws · max 16 moves to mate

Play any position, toggle whose move it is, or jump to a random legal one — then watch "Play optimal line" step through both sides' best moves, straight out of the table, until checkmate or a draw.

Open the chess tablebase →

The interest behind this was sparked by the work of Dr Dan Rust (ORCID), especially “Queen reflections: a modification of Wythoff Nim” — an acknowledgment of inspiration, not a collaboration; the full note is on the chess page.

← Previous in this roomThe endgame as a 3D surface Next in this room →Axelrod’s tournament, replicated

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