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 the optimal to the anti-optimal choice of move. They may be used as suitably skilled practice partners, to assess a player, to differentiate between otherwise equi-optimal moves, to promote or expedite a game result, to run Monte-Carlo simulations, and to identify the difficulty of a position or a whole endgame

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

Skill Rating by Bayesian Inference

Systems Engineering often involves computer modelling the behaviour of proposed systems and their components. Where a component is human, fallibility must be modelled by a stochastic agent. The identification of a model of decision-making over quantifiable options is investigated using the game-domain of Chess. Bayesian methods are used to infer the distribution of players’ skill levels from the moves they play rather than from their competitive results. The approach is used on large sets of games by players across a broad FIDE Elo range, and is in principle applicable to any scenario where high-value decisions are being made under pressure

Gentlemen, stop your engines!

For fifty years, computer chess has pursued an original goal of Artificial Intelligence, to produce a chess-engine to compete at the highest level. The goal has arguably been achieved, but that success has made it harder to answer questions about the relative playing strengths of man and machine. The proposal here is to approach such questions in a counter-intuitive way, handicapping or stopping-down chess engines so that they play less well. The intrinsic lack of man-machine games may be side-stepped by analysing existing games to place computer engines as accurately as possible on the FIDE ELO scale of human play. Move-sequences may also be assessed for likelihood if computer-assisted cheating is suspected

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

Understanding distributions of chess performances

This paper presents evidence for several features of the population of chess players, and the distribution of their performances measured in terms of Elo ratings and by computer analysis of moves. Evidence that ratings have remained stable since the inception of the Elo system in the 1970’s is given in several forms: by showing that the population of strong players fits a simple logistic-curve model without inflation, by plotting players’ average error against the FIDE category of tournaments over time, and by skill parameters from a model that employs computer analysis keeping a nearly constant relation to Elo rating across that time. The distribution of the model’s Intrinsic Performance Ratings can hence be used to compare populations that have limited interaction, such as between players in a national chess federation and FIDE, and ascertain relative drift in their respective rating systems

The Effect of Endgame Tablebases on Modern Chess Engines

Modern chess engines have the ability to augment their evaluation by using massive tables containing billions of positions and their memorized solutions. This report examines the importance of these tables to better understand the circumstances under which they should be used. The analysis conducted in this paper empirically examines differences in size and speed of memorized positions and their impacts on engine strength. Using this technique, situations where memorized tables improve play (and situations where they do not) are discovered

Intrinsic chess rating

This paper develops and tests formulas for representing playing strength at chess by the quality of moves played, rather than by the results of games. Intrinsic quality is estimated via evaluations given by computer chess programs run to high depth, ideally so that their playing strength is sufficiently far ahead of the best human players as to be a `relatively omniscient' guide. Several formulas, each having intrinsic skill parameters s for `sensitivity' and c for `consistency', are argued theoretically and tested by regression on large sets of tournament games played by humans of varying strength as measured by the internationally standard Elo rating system. This establishes a correspondence between Elo rating and the parameters. A smooth correspondence is shown between statistical results and the century points on the Elo scale, and ratings are shown to have stayed quite constant over time. That is, there has been little or no `rating inflation'. The theory and empirical results are transferable to other rational-choice settings in which the alternatives have well-defined utilities, but in which complexity and bounded information constrain the perception of the utility values

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