Author: Marc Bourzutschky
Date: 17:51:49 05/16/04
Go up one level in this thread
On May 16, 2004 at 20:40:35, Norm Pollock wrote: >On May 16, 2004 at 20:21:38, Marc Bourzutschky wrote: > >>On May 16, 2004 at 19:56:08, Norm Pollock wrote: >> >>>On May 16, 2004 at 17:27:10, Marc Bourzutschky wrote: >>> >>>>On May 16, 2004 at 17:12:12, Dieter Buerssner wrote: >>>> >>>>>On May 16, 2004 at 14:28:48, Marc Bourzutschky wrote: >>>>> >>>>>>Max Euwe: 4,147,200 >>>>>>Noam Elkies: 8,294,400 >>>>>>Paul Epstein: 5,317,600 >>>>>>Marc Bourzutschky: 5,149,368 >>>>> >>>>>Dieter Bürßner: 4,665,582 >>>>> >>>>>Idea: 2880 positions per side, of which 2694 have no castling possibilities. >>>>> >>>>>x = 2880^2-2694^2/2 >>>>> >>>>>I fear, I thought too simple, >>>>>Dieter >>>> >>>>If instead of 2694 in your formula you use 2508 you get the Bourzutschky result. >>>> The difference is that 2508 is the number of positions where neither the >>>>position itself, nor the mirrored position, has castling rights... >>> >>>Fwiw, I disagree with the explanation of 2508. >>> >>>I think the 2508 is just the number of positions that do NOT have castling >>>positions. I calculate 372 castling positions of the 2880 possible positions, >>>therefore 2508 in my calculations is the number of positions without castling >>>rights. >>> >>>x = 2880^2 - (2508^2/2) = 5,149,368 is still correct. >>> >>>It says take all the positions of both sides then remove the duplicate of those >>>positions where neither side had castling rights. >>> >>>-- Norm >> >>I only calculate 186 castling positions for white, assuming the white king has >>to be on e1. In addition, your argument does not seem quite right, because even >>if one side has castling rights the symmetry is broken, even if the other side >>does not have castling rights... > >Would you show me your analysis for the 186 castling positions you calculated >for white, assuming the white king to be on e1? I want to see where I differ >from you. It's a factor of 2 so it should be easy to spot. I'm putting my >analysis for 372 castling positions below. > >For ----K--R, there are 3*3 ways for 2 bishops of opp color, 1 way for the king, >2 ways for the castle at h1, 4*3/2 ways for 2 knights, 2 ways for the queen and >1 way for the 2nd castle. >Sub-result= 3*3*1*2*(4*3/2)*2*1 = 216 > There is only 1 way for the rook on h1, otherwise you will be double counting positions where only the two rooks are swapped. It looks like you have a similar issue with your other calculation, which gives a factor of 2 overall. >For R---K---, there are 4*2 ways for 2 bishops of opp color, 1 way for the king, >2 ways for castle at a1, 4*3/2 ways for 2 knights, 2 ways for the queen and 1 >way for the 2nd castle. >Sub-result= 4*2*1*2*(4*3/2)*2*1 = 192 > >For R---K--R (to remove duplicates from 2 sub-results), 2 ways for castle at a1, >1 way for castle at h1, 1 way for king at e1, 3*2 ways for 2 bishops of opp >color, 3*2/2 ways for 2 knights, and 1 way for the queen. >Sub result= 2*1*1*3*2*(3*2/2)*1 = 36 > >Result = 216 + 192 - 36 = 372 > >-Norm
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