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.

KQQKQQ and the Kasparov-World Game

The 1999 Kasparov-World game for the first time enabled anyone to join a team playing against a World Chess Champion via the web. It included a surprise in the opening, complex middle-game strategy and a deep ending. As the game headed for its mysterious finale, the World Team re-quested a KQQKQQ endgame table and was provided with two by the authors. This paper describes their work, compares the methods used, examines the issues raised and summarises the concepts involved for the benefit of future workers in the endgame field. It also notes the contribution of this endgame to chess itself.

The Kasparov-World Match

The Kasparov-World match was initiated by Microsoft with sponsorship from the bank First USA. The concept was that Garry Kasparov as White would play the rest of the world on the Web: one ply would be played per day and the World Team was to vote for its move. The Kasparov-World game was a success from many points of view. It certainly gave thousands the feeling of facing the world���s best player across the board and did much for the future of the game. Described by Kasparov as ���phenomenal ... the most complex in chess history���, it is probably a worthy ���Greatest Game��� candidate. Computer technology has given chess a new mode of play and taken it to new heights: the experiment deserves to be repeated. We look forward to another game and experience of this quality although it will be difficult to surpass the event we have just enjoyed. We salute and thank all those who contributed - sponsors, moderator, coaches, unofficial analysts, organisers, technologists, voters and our new friends.

Strategies for Constrained Optimisation

The latest 6-man chess endgame results confirm that there are many deep forced mates beyond the 50-move rule. Players with potential wins near this limit naturally want to avoid a claim for a draw: optimal play to current metrics does not guarantee feasible wins or maximise the chances of winning against fallible opposition. A new metric and further strategies are defined which support players��� aspirations and improve their prospects of securing wins in the context of a k-move rule.

Deepest Chess Win Revisited

An examination of the deepest win in KRNKNN in the context of Ken Thompson's results.

Chess Endgames and Neural Networks

The existence of endgame databases challenges us to extract higher-grade information and knowledge from their basic data content. Chess players, for example, would like simple and usable endgame theories if such holy grail exists: endgame experts would like to provide such insights and be inspired by computers to do so. Here, we investigate the use of artificial neural networks (NNs) to mine these databases and we report on a first use of NNs on KPK. The results encourage us to suggest further work on chess applications of neural networks and other data-mining techniques.

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: Maximals and mzugs

This article reports the combined results of several initiatives in creating and surveying complete suites of endgame tables (EGTs) to the Depth to Mate (DTM) and Depth to Conversion (DTC) metrics. Data on percentage results, maximals and mutual zugzwangs, mzugs, has been filed and made available on the web, as have the DTM EGTs.

Depth by The Rule

This note corrects a previous treatment of algorithms for the metric DTR, Depth by the Rule.

Discarding Like Pieces

The guideline of ���discarding like men��� to estimate the merit of a chess position is well known. This note compares it with some statistics.

Chess endgame news

The Endgame Tables Online initiative and p2p community have made available all published Nalimov DTM EGTs. It now looks forward to the 16 unpublished EGTs computed by August 9th and presumed to be still in existence, particularly as Marc Bourzutschky���s FEG results independently confirm all Nalimov���s published 3-3p DTM EGT statistics including those for KPPKPP.

Chess endgame news

A report of the new Bourzutschky/Konoval chess endgame depth record of DTC = 330 moves, and of the progress of the Kryukov peer-group to disseminate Nalimov's DTM EGTs. The question of data integrity and assurance is raised.

Chess endgame news

News that Bourzutschky confirms there is no sub-7-man pawnless zugzwang, and that Bourzutschky and Konoval are generating DTC EGTs with a new program. News also of Kristensen's work on EGTs using OBDDs, Ordered Binary Decision Diagrams.

Chess endgame update

This is a review of progress in the Chess Endgame field. It includes news of the promulgation of Endgame Tables, their use, non-use and potential runtime creation. It includes news of data-mining achievements related to 7-man chess and to the field of Chess Studies. It includes news of an algorithm to create Endgame Tables for variants of the normal game of chess.