Author: Dieter Buerssner
Date: 13:15:31 05/16/04
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On May 16, 2004 at 14:28:48, Marc Bourzutschky wrote: >In a book review at www.chesscafe.com there is a discussion of an older version >of Fischer Random Chess, called pre-chess. > >The main difference between FRC and pre-chess is that in pre-chess black and >white can have different piece arrangements on the first row. The only >constraints are that each side has to have opposite colored bishops, and that >castling is only allowed like in classical chess (i.e., white can only castle if >the king is on e1, and there is a rook on a1 or h1, etc). However, it is not >required that the starting position must allow castling. > >How many game theoretically different positions are there in pre-chess? I know >of 4 different suggestions, 2 by famous and 2 by less famous chess enthusiasts: > >Max Euwe: 4,147,200 I think, this is certainly too low. >Noam Elkies: 8,294,400 And this is certainly too high. This number is (8*4*6*5*3*2)^2 Intention: First B has 8 squares, second B has four squares (the ones remaining with different color), first N has 6 squares, etc; square it for both sides. But the formula counts many position twice. For all positions where no castling is possible, there will be a mirror position (mirror at the line between d and e) that is the same, game theoretically. Euwe obviously just devided by two. But this ignores, that positions with castling possibilities will not mirror. >Paul Epstein: 5,317,600 >Marc Bourzutschky: 5,149,368 Perhaps, I will try to find it out more carfully soon. First in the head calculation seems to indicate, that the Epstein number is too high. Regards, Dieter
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