Author: Rafael Andrist
Date: 10:54:36 03/10/02
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On March 10, 2002 at 13:38:10, Dieter Buerssner wrote: >On March 10, 2002 at 04:23:21, Rafael Andrist wrote: > >>On March 10, 2002 at 02:29:18, Les Fernandez wrote: >> >>>Sometime ago Dieter had provided me the following info regarding number of legal >>>KRk positions: wtm = 175,168 btm = 223,944 >>> >>>Does anyone know the same figures for KQk for wtm and btm ? >> >>KQK: >>phyically distinct positions: >>wtm: 144508 >>btm: 223944 > >I get the same number here. The later is easy to calculate: 3620 legal KK >positions times 62 squares for the Q. > >>logically distict positions: >>wtm: 22589 >>btm: 34968 > >But for this, I get different numbers. Perhaps, I do not understand your meaning >of logically distinct. The easier case is btm, because all positions with legal >KK are legal. There are 462 "logically distinct" legal KK positions (with the >idea of Nalimov, to restrict one K to a triangle, for example a1-d1-d4, and when >the K is on the diagonal, restrict the other K to a big triangle a1-h1-h8). >There will be 62 squares for the Q left, which makes 62*462=28644 different >positions. For white to move, not all positions are legal, and I get 18492 >different legal positions. > >My numbers are also different to those Guido has posted ... Your numbers of logically distinct positions are correct, I wrongly counted positions like the following two as different: [D]8/8/8/5k2/8/8/1Q6/K7 w - - dm 10; [D]8/8/4k3/8/8/8/1Q6/K7 w - - dm 10; I forgot that there are also symmetries for the black king when the other pieces are on a long diagonal. regards Rafael B. Andrist
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