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Subject: Re: Computational question for mathematicians, philosophers & computer-geeks

Author: Dieter Buerssner

Date: 03:14:58 03/03/05

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On March 03, 2005 at 06:00:24, Reinhard Scharnagl wrote:

Hmm, I can't follow.

>Pawn constellations at 8 files:      15^8

16 squares are taken now. Leaving 48 free squares.

>placing white w Bishop in average:   16
>placing white b Bishop in average:   16

I'd say. Placing w Bishops:           24*24 worst case
When the pawns take more white than black squares, you get numbers like 23*25,
which are always smaller.

>placing black w Bishop in average:   15
>placing black b Bishop in average:   15

23*23

>placing 2 white Knights:             28*27/2

20 squares taken now, leaving 44 empty. so 44*43/2
etc.

>e.p. is possible or not              2
>affected e.p. file                   8

So, ep needs 4 bits. My inclusion of ep needs less, namely

17^8 / 15^8 = 2.7, so less than two bits.

>castling rights (s+w)                4*4

4 bits for castling. Again my estimation (encoding castling together with legal
KK position) needs less.

2*17^8*23^2*24^2*4096*42!/(32!*2*2*2*2) = ~ 2^112

Regards,
Dieter




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