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 ...