Author: Dieter Buerssner
Date: 21:33:25 01/09/03
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On January 08, 2003 at 13:41:39, S. Loinjak wrote: >I should not forget to mention Christoph Fieberg's result of N being >approximately 3.02*10^46 published in CSS 2002/feb (CSS = Computer ,Schach und >Spiele - in German). Although this result does not take into acount the color to >move, the castling and the e.p. rights (this would push the estimation to >roughly 6.0*10^48) it might be one of the rare calculations where really all >underpromotions are counted correctly. I don't know Christoph's article, but I guess that including castling rights will not make the estimate much bigger. There are 3612 legal KK positions. Of those 3612 positions, 57 have the wK on e1, 57 have th bK on e8 and 1 has wK on e1 and bK on e8. This yields in 3612 + 114*3 + 15 = 3984 legal KK positions including castling rights as an upper bound. So, at most a factor of 3984/3612 can be expected. In other words, this als means, that one can encode any KK-position including castling rights in 16-bit. Depending, how one does the combinatorics for the pawns, one can find arguments, that ep won't matter, because one could argue, that for each position with ep, one would find another illegal position. Regards, Dieter
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