Strategies for Constrained Optimisation

Haworth, Guy

doi:10.3233/icg-2000-23103

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…As conjectured by Haworth (2000), KQPKQ and KBBKNN provide positions where ali combinations of SC, SM-and SZ" fail to safeguard a win available under the 50-move rule: the examples here were found by Bourzutschky (2003). Similar positions for other endgames were found by Tamplin (2003).…”

Section: Endgame Strategiesmentioning

confidence: 54%

“…DTM data is of interest in itself, even if conversion, i.e., change of force, is usually adopted as an interim objective in human play. However, more effective endgame strategies using different metrics can be adopted, particularly by computers (Haworth, 2000. A further practica!…”

Section: Introductionmentioning

confidence: 99%

“…It can draw by repeating positions, e.g., position NN-P4 6 • SZ 0 H50-should therefore be augmented by as deep and perceptive a forward search as possible, denoted here by '*'as in SZ 0 Hso-*. .3 DTR = Depth by The Rule (Haworth, 2000, i.e. the minimum k s.t.…”

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confidence: 99%

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Chess Endgames: Data and Strategy

Tamplin¹,

Haworth²

2004

Advances in Computer Games

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While Nalimov's endgame tables for Westem Chess are the most used today, their Depth-to-Mate metric is not the only one and not the most effective in use. The authors have developed and used new prograrns to create tables to alternative metrics and recommend better strategies for endgame play.Keywords: chess, conversion, data, depth, endgame, goal, move count, statistics, strategy IntroductionChess endgames tables (EGTs) to the 'DTM' Depth toMate metric are the most commonly used, thanks to cades and production work by Nalimov (Nalimov, Haworth, and Heinz, 2000a,b;Hyatt, 2000). DTM data is of interest in itself, even if conversion, i.e., change of force, is usually adopted as an interim objective in human play. However, more effective endgame strategies using different metrics can be adopted, particularly by computers (Haworth, 2000. A further practica! disadvantage of the DTM EGTs is that, with more men, DTM increases and file-compression becomes less effective.Here, we focus on metrics DTC, DTZ 1 and DTZ50 2 ; the first two were previously used by Thompson (1986Thompson ( , 2000 and Wirth (1999). New programs by Tamplin (2001) and Bourzutschky (2003) have enabled a complete suite of 3-to-5-man DTC/Z/Z50 EGTs to be produced.Section 2 outlines these two new algorithms. Sections 3 to 5 review the new DTC, DTZ and DTZ50 data tabled in the Appendix. Finally, improved endgame strategies are recommended for the 50-move context: New Approaches to EGT GenerationBelow we briefly describe two new approaches to EGT generation. The frrst one is described adequately in the literature; the second so far not. 2.1Tamplin's Wu-Beal Code Tamplin (2001) combined the Wu-Beal (2001a,b) algorithm with Nalimov indexing in a new code whose objectives were primarily Nalimovcompatibility, simplicity, maintainability and portability. Most pawnless 3-to-5-man DTC EGTs were generated, the new code including an inverseindex function mirroring Nalimov's index function. 2.2Bourzutschky's Modified-Nalimov CodeBourzutschky (2003) modified Nalimov's DTM-code to enable it also to generate EGTs to metrics DTCk and DTZk. This involved generalising some DTM-specific aspects of the algorithm, as well as the obvious changes to the iterative formula for deriving depth. For DTC, the code retains the efficiencies ofthe DTM-code while requiring maxDTC rather than maxDTM cycles. Because EGT generation to the DTZ metric has not yet been implemented generically as a sequence of sub-EGT generations, each based on a fixed pawn structure, this is not the case for DTZk computations. These can also require somewhat more than DTC cycles but the difference is insignificant. 3.The DTC Data DTC EGTs are interesting, not only for completeness, but because conversion is an intuitively obvious objective and the DTC EGTs document precisely the phase of play when the material nominated is on the board.The remaining 3-to-5-man DTC EGTs were generated. Table 1 in the Appendix lists for each endgame the number of positions of maxDTC, wtmlbtm and 1-0/0-1. The ICGA ...

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Section: Endgame Strategiesmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

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Chess Endgames: Data and Strategy

Tamplin¹,

Haworth²

2004

Advances in Computer Games

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“…As with all extant EGTs, castling is assumed not to be an option, currently reasonable as castling rights have never survived to move 49 [43], but this does mean that EGTs will not help solve some Chess Studies. 15 There are arguments for computing EGTs to a variety of metrics [45] and therefore they need to identify their particular metric to any chess-engine using them. It can be demonstrated that when a chess-engine mistakes a DTZ EGT for a DTM EGT, it will prefer the position-depth in the current phase of play before a capture to that in the next phase, resulting in the bizarre refusal of a piece en prise.…”

Section: Phase 3: Usementioning

confidence: 99%

Data Assurance in Opaque Computations

Hurd

Haworth

2010

Lecture Notes in Computer Science

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Abstract. The chess endgame is increasingly being seen through the lens of, and therefore effectively defined by, a data 'model' of itself. It is vital that such models are clearly faithful to the reality they purport to represent. This paper examines that issue and systems engineering responses to it, using the chess endgame as the exemplar scenario. A structured survey has been carried out of the intrinsic challenges and complexity of creating endgame data by reviewing the past pattern of errors during work in progress, surfacing in publications and occurring after the data was generated. Specific measures are proposed to counter observed classes of error-risk, including a preliminary survey of techniques for using state-of-the-art verification tools to generate EGTs that are correct by construction. The approach may be applied generically beyond the game domain.

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“…In a drawn position, how best can the attacker pressure the defender or the defender resist the attacker (Levy 1987(Levy , 1991Nunn, 2002;Schaeffer 1991Schaeffer , 1997? How can the opponent be given the best opportunity to concede depth in a situation where a draw claim is possible (Haworth, 2000(Haworth, , 2001? How can a player identify and adapt to apparent opponent fallibility?…”

Section: Introductionmentioning

confidence: 99%

Reference Fallible Endgame Play

Haworth

2003

ICG

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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.

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Strategies for Constrained Optimisation

Cited by 8 publications

References 18 publications

Chess Endgames: Data and Strategy

Chess Endgames: Data and Strategy

Data Assurance in Opaque Computations

Reference Fallible Endgame Play

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