Author: Uri Blass
Date: 06:58:59 01/19/02
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On January 19, 2002 at 06:55:11, Sune Fischer wrote: >On January 19, 2002 at 06:26:17, Uri Blass wrote: > >>>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. > >That isn't possible with 32 pieces, and with 31 I assumed a promotion and 64 >squares. >My plan was to get a descending sequence, but the promotion factor does blow >things up beyond my wildest dreams. > >>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. > >What is your lowest upper bound? >I get 10^46 when running your code. I got 3.701063012120722292782714774208595e46 but no doubt that it can be improved because there are a lot of impossible pawn structure and even some impossible material strucutures Here is an example for impossible material structure(unchanged means the same as the initial position) White:2 queens,3 rooks and 6 pawns,unchanged black:0 queens,unchanged It means that white captured the black queen and it means that white can promote only one pawns so having 2 queens and 2 rooks is impossible. My program counted it as possible because white can get 2 promotions by one capture but did not consider the fact that it cannot be achieved without capturing a pawn. It is possible to change my program by assuming that capturing a piece that is not a pawn can lead only to one promotion for both sides and I cannot think of example when the number of promoted white pawns is bigger than the number of captures+the number of captured black pawns. we need to prove this theorem mathematically because impression is not enough and I did not try to write a formal proof. The number of promoted white pawns is a variable that can be increased by more than 2 with one capture The number of good pawns by my previous definition also can be increased by more than 1 by capturing a black piece that is not a pawn so they are not enough for a mathematical proof. I do not remember if there was a formal proof by retko v tomic in the posts about this subject that were posted about a year ago(I do not remember the exact date). I remember that retko v.tomic got a better number but still bigger than 10^46. Uri
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