Some Notes on Chess Endgames

1
Some Notes on Chess Endgames

• Guy Haworth
• Reading, Berkshire, UK
• ltguy.haworth_at_icl.comgt

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 Walters KBNK Mate in 31 wKh2Ba3Nb1/bKd4w
  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