Author: Marc Bourzutschky
Date: 13:02:54 05/16/04
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On May 16, 2004 at 15:54:02, Russell Reagan wrote: >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 >>Noam Elkies: 8,294,400 >>Paul Epstein: 5,317,600 >>Marc Bourzutschky: 5,149,368 >> >>Which one is correct, or all they all wrong? >> >>-Marc > >After reading the article, I would have to agree that 8,294,400 is the correct >count. How did you arrive at your number? If reflection on the vertical does not change the castling options for either player, the position is game theoretically equivalent to its mirrored position (because all piece movements except for castling are mirror symmetric). The 8,294,400 count double counts those positions.
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