Depth to mate and the 50-move rule

The most popular endgame tables (EGTs) documenting ‘DTM’ Depth to Mate in chess endgames are those of Eugene Nalimov but these do not recognise the FIDE 50-move rule ‘50mr’. This paper marks the creation by the first author of EGTs for sub-6-man (s6m) chess and beyond which give DTM as affected by the ply count pc. The results are put into the context of previous work recognising the 50mr and are compared with the original unmoderated DTM results. The work is also notable for being the first EGT generation work to use the functional programming language HASKELL

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

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

Chess endgames: 6-man data and strategy

While Nalimov’s endgame tables for Western Chess are the most used today, their Depth-to-Mate metric is not the most efficient or effective in use. The authors have developed and used new programs to create tables to alternative metrics and recommend better strategies for endgame play

Stalemate and 'DTS' depth to stalemate endgame tables

Stalemating the opponent in chess has given rise to various opinions as to the nature of that result and the reward it should properly receive. Here, following Lasker and Reti, we propose that ‘stalemate’ is a secondary goal, superior to a draw by agreement or rule – but inferior to mate. We report the work of ‘Aloril’ who has created endgame tables holding both ‘DTM’ depth to mate and ‘DTS’ depth to stalemate data, and who should be regarded as the prime author of this paper. Further, we look at the classification of ‘Chess Stalemate Studies’ in the context of a ‘Lasker Chess’ which recognises the stalemate goal

FinalGen revisited: new discoveries

Romero’s FINALGEN of 2012 creates designer endgame tables for specific chess positions that feature no more than one non-pawn piece per side. Larger hard discs and faster solid-state discs have extended the reach of this software and encouraged its greater use. Some new discoveries illustrate here what is now feasible and how FINALGEN may be combined with other tools to reach definitive and likely truths

Performance and prediction: Bayesian modelling of fallible choice in chess

Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration applications address questions frequently asked by the chess community regarding the stability of the rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The last include alleged under-performance, fabrication of tournament results, and clandestine use of computer advice during competition. Beyond the model world of games, the aim is to improve fallible human performance in complex, high-value tasks

Zugzwangs in chess studies

Van der Heijden’s ENDGAME STUDY DATABASE IV, HHDBIV, is the definitive collection of 76,132 chess studies. The zugzwang position or zug, one in which the side to move would prefer not to, is a frequent theme in the literature of chess studies. In this third data-mining of HHDBIV, we report on the occurrence of sub-7-man zugs there as discovered by the use of CQL and Nalimov endgame tables (EGTs). We also mine those Zugzwang Studies in which a zug more significantly appears in both its White-to-move (wtm) and Black-to-move (btm) forms. We provide some illustrative and extreme examples of zugzwangs in studies

Deeper model endgame analysis

A reference model of Fallible Endgame Play has been implemented and exercised with the chess-engine WILHELM. Past experiments have demonstrated the value of the model and the robustness of decisions based on it: experiments agree well with a Markov Model theory. Here, the reference model is exercised on the well-known endgame KBBKN