Author: Uri Blass
Date: 03:26:17 01/19/02
Go up one level in this thread
On January 19, 2002 at 05:21:43, Sune Fischer wrote: >On January 19, 2002 at 03:02:41, Uri Blass wrote: >>>>>>>>Does this take into account all the possible promotions? It is possible to have >>>>>>>>9 queens on one side or 9 rooks or 9 bishops or 9 knights, or any combination >>>>>>>>thereof. Each possible promotion will make the number larger. 31 pieces on the >>>>>>>>board has more possible positions than 32 because you have to take into account >>>>>>>>the promotions. If 31 pieces are remaining there is upto 3 possible promotions. >>>>>>>>Makes the calculation a little more difficult. >>>>>>>> >>>>>>>>Chris >>>>>>>> >>>>>>> >>>>>>>Oops, make that 9 queens or 10 rooks, or 10 bishops or 10 knights. Some days my >>>>>>>fingers work faster than my brain. >>>>>>> >>>>>>>Chris >>>>>> >>>>>>You do have a point Chris. >>>>>>I tried to refine the number a little bit: >>>>>> >>>>>>All 32 pieces: >>>>>>(64*(64 - 4)*23^4*21^4*18^4*14^4*62!)/((62 - 14)!*(8!*2!*2!*2*2)^2) >>>>>>= 5.13*10^36 >>>>>> >>>>>>I put in the factor: 23^4*21^4*18^4*14^4 >>>>>>because the d and e pawns has 23 squares, the c and f pawns has 21 squares and >>>>>>the b and g has 18, a and h has 14 (unless I miscounted;) >>>>> >>>>>I do not understand it >>>> >>>>Actually there are 24 squares for a white d pawn: >>>8/pppppppp/PPPPPPPP/PPPPPPP1/1PPPPP2/2PPP3/3P4/8 w - - 0 1 >> >>I understand now your idea but with 32 pieces there are only 5 options for white >>d pawns because the white d pawn can go to another file only by capture. >> >>d2 d3 d4 d5 d6 d7 are the options. >> >>My 15 options are for white and black pawn on the d file and the same for every >>file. >> >>d2 d7 >>d2 d6 >>d2 d5 >>d2 d4 >>d2 d3 >>d3 d7 >>d3 d6 >>d3 d5 >>d3 d4 >>d4 d5 >>d4 d6 >>d4 d7 >>d5 d6 >>d5 d7 >>d6 d7 >> >>are the possible squares for d pawns when there are no captures. >> >>It is exactly 15 and the same for every file. >> >>My program did not use the 15^8 limit for the pawns squares and assumed that >>every pawn can be chosen from 48 squares. >> >>It is not close to be truth when you have 32 pieces but it becomes closer to the >>truth when there are less pieces. >> >>It is clear that if both sides have exactly 2 pawns you can choose them from the >>48 squares in the board in every possible way. >> >>It is not truth for 3 pawns and h2 h3 g2 is an example for squares that cannot >>be squares of white pawns but it is still truth for almost all the cases of 3 >>pawns. >> >>Uri > >Oh, so that's what you mean, well I'm not concerned with counting *too many* >squares since is was supposed to be an upper bound anyway. That it was easier >when the capturings began. I believe that a better upper bound can be achieved by giving every pawn 48 squares. The advantage is that the order of pawns is not important and when you assume only 24 squares for the d or the e pawns the order of pawns is important. I remember that the upper bound of my program(the last number that was posted) was better than the upper bound by your calculation. > >I did think of one interesting example; >24 pieces with 12 pawn promotions (I think that is possible): >2*4^12*(64*(64 - 4)*62!)/((62 - 22)!*(2!*3!*3!*2*2)^2) >=5.99*10^43 > >It is the highest number I can produce;) It is possible to get 12 promotions even with 28 pieces(one capture can lead to 3 promotions) I did not understand the calculation that you did here. Uri
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.