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Some Notes on Chess Endgames

Some Notes on Chess Endgames. Guy Haworth Reading, Berkshire, UK <guy.haworth@icl.com>. Chess Endgames, 2001. Current Situation Endgame Table Statistics %-results, maximals, and mutual zugzwangs “Discarding Like Pieces” an ‘established’ principle

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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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