Author: Andrew Dados
Date: 06:37:12 07/12/99
Go up one level in this thread
On July 12, 1999 at 02:49:49, blass uri wrote:
>passed pawns,pawns on the same file and promoted pawns are declared to be good
>pawns
>The other pawns are declared to be bad pawns and have no chance to promote
>before improving their behaviour.
>
>It is easy to check that the number of white good pawns is at most the sum of
>the number of captured white pieces and twice the number of black pieces that
>were captured
>because every capture of white piece increases the number of white good pawn by
>at most 1 and every capture of black piece increases the number of white good
>pawns by at most 2.
>
>I use this observation to develop my new c program to calculate an upper bound
>for the number of chess positions.
>
>please tell me if I have a mistake in the program and if you know a way to
>calculate the exact integer.
>
>I got 9.27397309111305334*10^43
>
>You should multiply it by 2 because I did not consider side to move.
>I also did not consider other things like castling
>
>
>#include <stdio.h>
>#include <conio.h>
>main()
>{
>clrscr();
>char x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,i,j;
>long double k,n=0;
>long double m[65];
>m[0]=1;
>for (i=1; i<65; i++)
> m[i]=m[i-1]*i;
>for (x1=0; x1<9; x1++)
> for (x2=0;x2<11-x1;x2++)
> for (x3=0;(x3<11-x1&&x1+x2+x3<13);x3++)
> for (x4=0;(x4<11-x1&&x1+x2+x4<13&&x1+x3+x4<13&&x1+x2+x3+x4<15);x4++)
> for (x5=0;(x5<10-x1&&x1+x2+x5<12&&x1+x3+x5<12&&x1+x4+x5<12&&\
> x1+x2+x3+x5<14&&x1+x2+x4+x5<14&&x1+x3+x4+x5<14&&x1+x2+x3+x4+x5<16)\
> ;x5++)
>{
>k=m[x2]*m[x3]*m[x4]*m[x5];
>i=0;
>if (x2>2) i=i+x2-2;
>if (x3>2) i=i+x3-2;
>if (x4>2) i=i+x4-2;
>if (x5>1) i=i+x5-1;
>printf("%Lf\n",n);
>for (y1=0; y1<9; y1++)
> for (y2=0;y2<11-y1;y2++)
> for (y3=0;(y3<11-y1&&y1+y2+y3<13);y3++)
> for (y4=0;(y4<11-y1&&y1+y2+y4<13&&y1+y3+y4<13&&y1+y2+y3+y4<15);y4++)
> for (y5=0;(y5<10-y1&&y1+y2+y5<12&&y1+y3+y5<12&&y1+y4+y5<12&&\
> y1+y2+y3+y5<14&&y1+y2+y4+y5<14&&y1+y3+y4+y5<14&&y1+y2+y3+y4+y5<16)\
> ;y5++)
> {
> j=0;
> if (y2>2) j=j+y2-2;
> if (y3>2) j=j+y3-2;
> if (y4>2) j=j+y4-2;
> if (y5>1) j=j+y5-1;
> if ((i<=2*(15-y1-y2-y3-y4-y5)+(15-x1-x2-x3-x4-x5))&&
> (j<=2*(15-x1-x2-x3-x4-x5)+(15-y1-y2-y3-y4-y5)))\
> n=n+(m[48]/(m[x1]*m[y1]*m[48-x1-y1]))*(m[64-x1-y1]/\
> (k*m[y2]*m[y3]*m[y4]*m[y5]*m[62-x2-x3-x4-x5-y2-y3-y4-y5]));
> }
>}
>
>printf("%Lf\n",n);
>}
>
>
>
>Uri
Hello Uri! Can you possibly modify output and post position numbers breakdown
for total piece numbers in your upperbound? (I'm interested in position number
bound for 32-25 pieces especially... they seem to dominate in your sum and they
can be brought down a bit with some tricks, I think...).
-Andrew-
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