Author: Andrew Dados
Date: 15:23:45 07/12/99
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On July 12, 1999 at 12:41:18, blass uri wrote:
[snipped]
>some numbers:
>The upper bound:
>3.70106301212072366*10^46
>29 pieces on the board:2.18...*10^46
>28 pieces on the board 9.45...*10^45
>30 pieces on the board 4.58...*10^45
>
>Uri
(Note that those 3 figures above add up to 3.9*10^46, which is somehow more
then your total...)
I will try to put my idea into small program as soon as I get some time, but
for now let me describe it:
Let's take into account possible pawn configurations.
For each file if no capture was done (32 pieces on board) we have 15 distinct
positions for one white and one black pawn... which gives us 15^8 pawn
configurations (2,526,890,625). This is many orders less then your bound there.
Now lets consider one capture. I'll mark P=pawn; O=other piece.
We have 4 possibilities:
1. OxO (piece captures piece) - no pawnstructure changes; still 15^8 pawn
configurations; no promotions possible;
2. PxP: up to 2 promotions can be done here:
2a) no promotions; pawn structure number can be estimated at 15^7*6*4;
2b) 1 prom; psn<=15^7*(6+4);
2c) 2 proms; psn<=15^6*6*6;
3. OxP: a) 15^7*6 with no proms and
b) 15^7 with one promotion
4. PxP a) 15^7*6*4 with no proms;
b) 15^7*(6+4) and one prom
c) 15^6*6*6 and 2 proms...
For second capture each of cases above breaks down further etc.... looks like
mundane work, but smart program can surely be written.
I think one should give it a try....
One more thought: positions with, say, 0-0 castling availible are less then
(1/48)*(1/48) of all positions (K is positioned on e1 in 1/48 of all
positions), so neglible. EP can be available way more often, but still below 1/8
of all positions.
-Andrew-
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