Author: Sune Fischer
Date: 01:22:47 11/30/02
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On November 29, 2002 at 17:01:39, Uri Blass wrote: >>P.S: I hope I will be able to prove exactly that there are less than 10^42 or >>even less than 10^40 positions. This requires a combination of techniques from >>operations research with classic tree search algorithms and combinatorics >>theory. >> >>P.S.2: Please correct me if I express sthg in the wrong way - english is not my >>primary language. > >I do not know the number and it is only a guess but my guess is that you are >going to be unable to prove that there are less than 10^40 position for the >simple reason that there are more than 10^40 positions. I think you are right. We discussed this a long time ago (perhaps it's in the archieves). My first upper bound estimates were about 10^36 IIRC, but I didn't consider that it is possible to generate 14 promoted pieces, something which you were quick to remind me of :) This blew the counting to over 10^40 because promoting to knights, bishops and rooks beside queens, give a very large variaty of piece combination on the board. I think if there weren't a promotion rule, then it would be less than 10^40, but I don't remember the (rather long) equation anymore. -S.
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