Author: Norm Pollock
Date: 17:40:35 05/16/04
Go up one level in this thread
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 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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