Author: Uri Blass
Date: 07:25:52 01/19/02
Go up one level in this thread
On January 19, 2002 at 09:58:59, Uri Blass wrote: >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 I believe that it can be proved by changing the deifinition of good pawns. a good pawn should be defined as one of the following: 1)passed pawns 2)pawn that is not a passed pawn but has another pawn in the same file that it's ditance from the queening square is bigger. It means that if there are white pawns at a2 a3 and both pawns are not passed pawns then a3 is a good pawn when a2 is not a good pawn. Now it is only needed to prove that the number of white good pawns is increased by at most 2 when the only case that it may be increased by more than 1 is when white is capturing a pawn. I believe that it is not hard to write the formal proof but I leave it for other people because I have other things to do. Uri
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