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Some Notes on Chess Endgames

This document presents a comprehensive examination of chess endgames, focusing on current statistics and theoretical approaches. It covers critical topics such as endgame table statistics, mutual zugzwangs, and the emerging principle of "Discarding Like Pieces." The paper also discusses the Depth by the Rule (DTR) metric and its implications for DTC and DTM endgames. Furthermore, it highlights the need for improved algorithms and the challenges of generating efficient endgame tables while reviewing major findings and potential advancements in endgame theory.

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Some Notes on Chess Endgames

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  1. Some Notes on Chess Endgames Guy Haworth Reading, Berkshire, UK <guy.haworth@icl.com>

  2. Chess Endgames, 2001 • Current Situation • Endgame Table Statistics • %-results, maximals, and mutual zugzwangs • “Discarding Like Pieces” • an ‘established’ principle • statistical evidence not convincing so far • Depth by the Rule • correction to previously defined algorithm • better news about the computability of DTR EGTs

  3. The Current Situation • All 3-to-5-Man DTC and DTM EGTs • http://chess.jaet.org/endings/ EGT service c/o John Tamplin and Thomas Lincke of ETH(Zûrich) • ftp://ftp.cis.uab.edu/pub/hyatt/TB/ ... EGTs c/o Rob Hyatt • http://www.chessbase.com/ ... CDs from ChessBase • Some 6-Man DTC EGTs • http://cm.bell-labs.com/cm/cs/who/ken/chesseg.html • Some 6-Man DTM EGTs • http://chess.jaet.org/endings/ … EGT service c/o John Tamplin • ftp://ftp.cis.uab.edu/pub/hyatt/TB/ ... EGTs c/o Rob Hyatt

  4. EGT Statistics • Useful for … • highlighting rare phenomena • maximals, mzugs, under-promotion, draws by minority force • comparing one EGT with another • ad hoc removal of unreachable positions is not in fact helpful • Nalimov, Wirth, and Karrer work • reported at this workshop on their behalf • % of wins, draws and losses, wtm and btm • maxDTC and maxDTM results, wtm and btm • overlap of maxDTC and maxDTM positions not computed • some ‘fringe’ oddities thrown up by the DTC metric • mutual zugzwangs: ww, bw, fpz twin-sourced results on distinct positions in full agreement

  5. “Discarding Like Pieces” • guideline: 6+-man positions can usually be evaluated by ignoring like pieces? Does this mean: • look at the statistics, or • remove the like pieces from the board and evaluate the position? • full stats information exists on the 2-4 and 3-5 comparison • but theory is covering these endgames already • some data available on 4-6 comparisons • statistics do not seem to support the guideline • Wirth provides DTC data for 3-5-man endgames • enabling shallow wins to be discounted • what about the uncomputed ‘shallow draws’?

  6. Depth by The Rule • Depth by the Rule (DTR) = dr = the least k such that best play avoids a k-move draw claim • “Constrained Optimisation….”, ICGA J v23.1 • proposed revival of DTZ EGTs • proposed use of DTC, DTM and DTZ EGTs in combination • defined the DTR metric above • defined the incorrect DTR algorithm AL1 using dz • !! The ‘standard’ retrograde analysis algorithm • works for computing DTR EGTs • requires the use of the ‘phase count’ instead of dz

  7. Endgame Challenges • create more efficient codes for generating DTM EGTs • c.f. Wu/Beal, Info. Sciences, Vol. 135 (June 2001), pp. 207-228 • create EGTs • to the DTZ and DTR metrics and/or with correct depths in plies • identifying ‘finite-depth’ draws forced by one side or the other • derived from basic EGTs, e.g., bitmap win/no_win EGTs • mine EGTs for unique moves, studies, problems • various definitions of ‘unique move’ • is Walter’s KBNK “Mate in 31” wKh2Ba3Nb1/bKd4+w beatable? • annotate studies (a subset of the “annotation challenge”) • classify studies by theme • define more sophisticated strategies based on EGTs • cite instances of deep endings won over the board • progress Awari, Chess (Chinese, Western, Losing, Mini), other … add value to, rather than displace, human experience

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