Author: Guido
Date: 15:53:59 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 ... > >Regards, >Dieter I follow the same logic, but the value you obtain 462*62=28644 doesn't take into account that positions of the Queen/Rook are not 62 when the two Kings are on the diagonal a1h8. There are 21 of such positions for the Kings, and in these cases the Queen/Rook has only 34 square. Therefore: 28644 - 21*(62-34) = 28056 Using the same reduction it is possible that you obtain the same number as me also for wtm. Ciao Guido
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