Author: Marc Bourzutschky
Date: 09:04:45 02/12/06
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On February 11, 2006 at 04:53:29, h.g.muller wrote: >Interesting. I did a lot of 4- and 5-men TBs including fairy pieces (mainly >leapers) in a systematic effort to assign an accurate end-game value to pieces >(in absense of pawns). It never occurred to me to use non-standard board-size, >though. I guess the 10x8 board is of practical interest, due to >Capablanca/Gothic Chess. > >Is your (or Marc's)work published somewhere? Vaclav Kotesovec has done a lot of work on fairy pieces, including leapers on generalized boards: http://web.telecom.cz/Vaclav.kotesovec/ John Beasley and I looked at Q vs. R endings on generalized boards, because the lack of an obvious systematic winning procedure on 8x8 suggested o John it may not be a general win on larger boards. Indeed, it is only a general win on boards up to 15x15, but on 16x16 it is in general a draw. John had also thought it would be a draw on 8x12 (which is used in a variant called "Modern Courier Chess") but the queen still wins there. This was published in the "British Endgame Study News" in June and September 2004. Regarding leapers, John Beasley, Noam Elkies, and I have studied "doublet leapers", which are pieces that combine two leapers into one piece. There is only a small number of doublet leapers that can force mate, and only on board up to 16x16. This was published in "Variant Chess" February 2005. We have also looked at "triplet leapers", combining three leapers into one. Here one can construct cases that win on an arbitrarily large board. However, it is only a finite set, and there are some triplets for which we are not sure whether they are a general win or not. I have run tablebases on up to 90x90 for some of these. -Marc
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