Space-efficient indexing of endgame tables for chess

Chess endgame tables should provide efficiently the value and depth of any required position during play. The indexing of an endgame’s positions is crucial to meeting this objective. This paper updates Heinz’ previous review of approaches to indexing and describes the latest approach by the first and third authors. Heinz’ and Nalimov’s endgame tables (EGTs) encompass the en passant rule and have the most compact index schemes to date. Nalimov’s EGTs, to the Distance-to-Mate (DTM) metric, require only 30.6 × 109 elements in total for all the 3-to-5-man endgames and are individually more compact than previous tables. His new index scheme has proved itself while generating the tables and in the 1999 World Computer Chess Championship where many of the top programs used the new suite of EGTs.

Reference fallible endgame play

A reference model of fallible endgame play is defined in terms of a spectrum of endgame players whose play ranges in competence from random to optimal choice of move. They may be used as suitable practice partners, to differentiate between otherwise equi-optimal moves, to promote or expedite a result, to assess an opponent, to run Monte Carlo simulations, and to identify the difficulty of a position or a whole endgame.

3-5-Man chess data

This reports the work of Karrer and Wirth in identifying percentage results and, respectively, the Depth to Mate (DTM) and Depth to Conversion (DTC) data in all 2-5-man chess endgames.

3-5-man mutual zugzwangs in chess

This note reports the work of Wirth and Karrer in twin-sourcing all mutual zugzwang positions, mzugs, in 2-5-man endgames. This paper tabulates the mzug statistical data, gives examples of maximal mzugs and refers to a chess endgame website where further data is to be found.

Self-play: statistical significance

Heinz recently completed a comprehensive experiment in self-play using the FRITZ chess engine to establish the ‘decreasing returns’ hypothesis with specific levels of statistical confidence. This note revisits the results and recalculates the confidence levels of this and other hypotheses. These appear to be better than Heinz’ initial analysis suggests.