By Ulrich Thiel, with data from the Nalimov databases. This web interface was vibe coded by Claude.ai.
A chess endgame is the phase of the game in which only a few pieces remain on the board. The transition from the middlegame to the endgame is not sharply defined, however. Some endgames—such as king and rook versus king—are governed by simple winning principles, apart from a small number of clearly drawn positions. Others, however, turn out to be remarkably subtle, and determining the outcome under optimal play can be extremely difficult.
The emergence of computers made it possible, for suitably small endgame configurations, to resolve these questions definitively by exhaustively analyzing all legal continuations of a given position. This approach, pioneered by researchers such as Richard Bellman, Thomas Ströhlein, and Ken Thompson, led to the development of endgame tablebases: databases that assign to every legal position its theoretical outcome (win, draw, or loss) together with optimal play. One of the most influential such tablebases was created in 1998 by Eugene Nalimov, whose work provided complete and highly compressed data for all endgames with up to five pieces.
Computational endgame analysis overturned several long-held assumptions. A famous example is the endgame king and queen versus king and rook, long believed to be a routine win for the stronger side. Tablebase analysis revealed that, with perfect defense, the win can be extraordinarily difficult to achieve. In a well-known 1978 experiment, Grandmaster Walter Browne failed to defeat the chess computer BELLE in this endgame and resigned after 45 moves, realizing that he would inevitably violate the fifty-move rule—despite the existence of a forced win with flawless play.
The table below presents theoretical statistics for a range of elementary endgames, using standard notation such as KQK. The data shown here is derived from the Nalimov tablebases for positions with at most five pieces (we may update this to 6 pieces later), presented in a condensed and accessible form.