Understanding Rook Endgames

A discussion and modest extension of the analysis of the Rook Endgame, the subject of 'Understanding Rook Endgames' by Műller and Konoval

Chess endgame knowledge advances

This review of recent developments starts with the publication of Harold van der Heijden's Study Database Edition IV, John Nunn's second trilogy on the endgame, and a range of endgame tables (EGTs) to the DTC, DTZ and DTZ50 metrics. It then summarises data-mining work by Eiko Bleicher and Guy Haworth in 2010. This used CQL and pgn2fen to find some 3,000 EGT-faulted studies in the database above, and the Type A (value-critical) and Type B-DTM (DTM-depth-critical) zugzwangs in the mainlines of those studies. The same technique was used to mine Chessbase's BIG DATABASE 2010 to identify Type A/B zugzwangs, and to identify the pattern of value-concession and DTM-depth concession in sub-7-man play

Secrets of Pawnless Endings

It is now 32 years since Ströhlein’s pioneering computation of KRKN and ten years since the publication of Nunn’s Secrets of Rook Endings. This book defined a new genre under his authorship and editorship (Nunn, 1992, 1994, 1995; Müller and Lamprecht, 1999, 2001) and has merited a second edition. Now comes the second edition of Secrets of Pawnless Endings

Can Deep Blue™ make us happy? Reflections on human and artificial expertise

Sadly, progress in AI has confirmed earlier conclusions, reached using formal domains, about the strict limits of human information processing and has also shown that these limits are only partly remedied by intuition. More positively, AI offers mankind a unique avenue to circumvent its cognitive limits: (1) by acting as a prosthesis extending processing capacity and size of the knowledge base; (2) by offering tools for studying our own cognition; and (3) as a consequence of the previous item, by developing tools that increase the quality and quantity of our own thinking. These ideas are illustrated with chess expertise

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

CEN: Understanding Rook vs Minor Piece Endgames

This is a response to 'Understanding Rook vs Minor Piece Endgames' by Mueller and Konoval, the third volume in their 'Understanding ...' series. It provides a selection of positions for comment and instruction. The supplementary material provides the full set of maxDTC(onversion) positions which are in the URME domain, together with DTC-optimal play from those positions

Representation of Knowledge for Chess Endgames Towards a Self-Improving System

This thesis describes an investigation of the problems involved in representing knowledge within the task area of elementary Chess endgames. Two major criteria are taken for the choice of a model of & the chessplayer's knowledge : firstly, that algorithms constructed using the model should be natural from the viewpoint of a chessplayer and commensurate with his, view of the complexity of the task, and secondly that the algorithms should be capable of refinement in the light of experience in a manner which preserves the previous property. Elementary chess endgames are studied as a field in which programs based on tree-searching and traditional evaluation functions have achieved poor results and where tree-searching seems to play little or no part for people. It is therefore possible to examine problems of knowledge representation and program refinement largely independently of the tree-searching paradigm. A long term aim of the research is to develop a representation suitable as the basis for a fully automatic system of algorithm refinement, whilst maintaining the criteria given above. A model is proposed and algorithms are given for two endgames, King and Rook against King (KRK) and King and Pawn against King (KPK) using this model. It is argued that both algorithms are reasonably natural and compact representations and experiments in refining these algorithms are described in detail. In both cases, the process of refinement is shown to be a reasonably straightforward one (for people) and one which maintains the properties of naturalness and compactness. The possibility of automating this process is considered

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

Generalization in chess thinking

In this work we deal with generalization in chess thinking. Generalization is a complex process based on information people acquired during previous experiences. In the field of chess, chess books, chess education and personal game practice supply the information for generalization to occur. The way in which generalization is performed in chess is still a topic that deserves more research. In this article we dwell on early theories about chess thinking. We underline the role played by what we call configural concepts, in which geometrical patterns and logical expected developments coexist. We suggest that the idea of configural concepts, along with generalization and abduction constitute the basis of chess thinking

Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to $n \times n$ board (for natural $n$ greater than $3$). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs