Author: Telmo C. Escobar
Date: 13:51:29 05/16/04
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On May 16, 2004 at 16:34:25, Marc Bourzutschky wrote: > >Your calculation ignores the fact that all chess moves except castling are >mirror symmetric, so you will double count some game theoretically equivalent >positions. For example, suppose both sides start with a first row of: > >KQRRBBNN > >This is game theoretically equivalent to both sides starting with > >NNBBRRQK > I ignored this because there is no reason for not ignoring it, or at least no reason was given. You call "theoretically equivalent" two positions such that there is a natural 1-1 correspondence between games starting from those positions. While I admit that, strategically, both games would be identical, I don't see any good reason to regarding both are identical from a mathematical point of view. So I still think 8294400 is the correct answer. Amyway, the question about how many "different from the point of view of chess strategy" setups there are, is interesting as well. Obviously the only correction one has to make (in my original calculation) is just to take the half of the setups where castling could be eventually made. I'll make the calculation in a few minutes (a physiological urgence needs to be attended first) Telmo >The tricky part (missed by Euwe) is that starting position such as > >RNNKBBRQ > >are not equivalent with the reflected position > >QRBBKNNR > >because in the latter position there is the possibility of short castling.
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