KQQKQQ and the Kasparov-World Game

E. V. Nalimov, C. Wirth, G.McC. Haworth
1999 ICGA Journal  
The 1999 Kasparov-World game for the first time enabled anyone to join a team playing against a World Chess Champion via the web. It included a surprise in the opening, complex middle-game strategy and a deep ending. As the game headed for its mysterious finale, the World Team requested a KQQKQQ endgame table and was provided with two by the authors. This paper describes their work, compares the methods used, examines the issues raised and summarises the concepts involved for the benefit of
more » ... the benefit of future workers in the endgame field. It also notes the contribution of this endgame to chess itself. 1. As early as move 10, it was clear that the game was likely to go into a complex ending, and after move 39, this could still have been KRBKBN or KQPKQPP. Soon it was down to the royal pieces and their foot soldiers. Defending a notorious QP-ending, the World team called for that utopia of perfect information, an Endgame Table ( EGT), also referred to as a Database (Van den Herik and Herschberg, 1986) and a Tablebase (Edwards and the Editorial Board, 1995). The first request, for KQPKQPP, was quickly seen to be unrealistic but given its prolonged fight for a draw, the World Team had shown great restraint in not asking for EGT help much earlier. The next priority was for the KQPKQP EGT which needed at least the KQQKQQ, alias 4Q, if not all fifteen KQxKQy EGTs. Stiller (1992, 1995 and 1996) had created some 41 pawnless 6-man, White win/no-win EGTs including all KQxKQy endgames except those with xy as QB, QN, RQ, BQ and NQ. Unfortunately, none survived due to a lack of file space and they were sorely missed by the World Team. Nevertheless, Stiller's remaining summary information usefully underlined the feasibility of computing 4Q with its maximal depth to a subgame of 88 plies and its many clearly illegal positions and shallow wins. Encouraged by this and ever the optimist, Haworth sent requests for 4Q to Nalimov and Wirth, both known to be leading, active contributors in this field. Both responded quickly to the moment and to the challenge, agreeing to make any results publicly available. To everyone's surprise except their own, they produced self-consistent 4Q EGTs within days which, under all tests, confirmed each other and Stiller's results. Each chose to strength-test their code, producing almost incidentally the tables for KNNKNN, KRRKRR and KBBKBB as well. Nalimov optimised depth to mate (DTM) and Wirth optimised depth to force-conversion (DTC), adding to the degree of independence between the two sets of results. The World Team supported and implemented the authors' pro bono publico principles by publicising the existence of the 4Q EGTs and making them freely available. This was done via the game's bulletin board, the WWW Computer Chess Club (1999) and a public ftp site (Hyatt, 1999) which soon sported an upgraded version of CRAFTY exploiting 6-man EGTs. Several on the World Team downloaded both the new CRAFTY engine and the 4Q EGT. Kasparov had done the same and this raised the prospect of the game ending with perfect 4Q play. Certainly his official website showed Black dramatically securing a 4Q draw which was both immaculate and bizarre, Black sacrificing both Queens to force stalemate: see Appendix B4.2. Two 4Q-services were set up on the web (Mobley, 1999; Tamplin, 1999) and these added to the unusually significant contribution that EGTs were already making to the analysis of the game. The production of 4Q on request was notable in itself and re-opened the 6-man chapter of endgame history. It was also the first time that two authors had worked simultaneously on the same endgame. The event suggested a comparative study to Haworth. The following sections therefore describe the 6-man EGT challenge, the two approaches and the sets of results. The paper includes a survey of the concepts involved to suggest some nomenclature and principles for EGT generation in the future. THE 6-MAN ENDGAME DOMAIN A complete EGT must include the value and depth of all legal positions in its scope. It may also cover unreachable positions whose illegality its generator program has not discovered, see Table 1 which includes all positions cited in this paper. The positions are Gödel-numbered using a 1-1 function Index(Pos) that must have an inverse in Pos(Index) if a position is to be easily found from its index. The next sections introduce the key concepts of notionally considered, indexed, legal and broken positions. Considered Positions The simplest approach to creating Index(Pos) is to number the chessboard squares 0-63, define an order for the n men, say [wK, bK, wQ, ...], list the squares {s i | i ∈ [0, 63]} of the men for position Pos and define Index(Pos) = 64 n .κ + ∑ 64 i ×s i where κ = 0 or 1 for wtm or btm positions respectively.
doi:10.3233/icg-1999-22402 fatcat:jztda6y26jcbhlttiibjrdlchi