Author: Paul
Date: 16:37:04 03/19/00
The last couple of hours I've spent trying to find the number of
possible positions with 3 pieces on the board. I've come up with
the number 3891550, using a little program I just wrote.
This number is lower than Hans Havermann's, but higher than
KarinsDad's. Maybe someone can straighten this out :)
Some details:
- side to move was included
- pawns were restricted to the quadrant a2-h7
- positions where the side to move was able to capture the
opponents king were not counted
- first I calculated 3891168 positions excluding castling.
- then I added the number of positions where castling looked
possible, this raised the number to 3891590.
- I found that 2 types of those castling positions were
not really possible however (hope that's clear :) :
- the first type is like this, where the side to move is in check,
and the side not to move can castle (but not really) :
[D]8/8/8/k7/8/8/8/R3K3 b Q -
Here obviously the rook has moved last.
This leaves 3891556 possible positions.
- the second type is like this, where the side to move cannot
castle because of the vicinity of the opponents king :
[D]8/8/8/8/8/8/1k6/R3K3 w Q -
This leaves 3891550 positions.
Now, I haven't double checked any of this, and it's getting early
now :) These are the first numbers I've calculated, so there are
probably a number of errors in here. Any thoughts?
cheers,
Paul
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.