Author: KarinsDad
Date: 13:35:32 05/28/99
Go up one level in this thread
On May 28, 1999 at 16:11:37, Dann Corbit wrote: >Your calculations are excellent and show a lot of thought. But again, these >show positions which are legal but possibly not achievable. (See my previous >pawn examples for legal positions that cannot be achieved in a game). How so Dann (sorry, I did not read your other pawn examples, when/where did you post them)? The idea I just posted included eliminating a lot of unachievable positions (either due to a king being in check or a piece not being able to get beyond a pawn chain). I gave rough percentages, but I doubt that the percentages are very high. For the pawn chains, remember that the pieces could move to the other side of the board BEFORE the chain gets close to being locked down. There are very few pawn/bishop cases in what I presented where the white e or g pawns were not pushed, hence the white white square bishop could not get out (or anything similar for the other 3 bishops). The other limitation on the bishops is when the opposing same color pawns are not pushed with respect to getting to the back rank of the opposing side. The same goes for the queens and rooks. The rooks are the most difficult since they require that at least a pawn gets pushed 2 spaces to get to the middle of the board and an opposing pawn gets pushed 2 to get to the opponent's back rank. So, a rook cannot move up much when it's pawns are pushed no more than 1 square (and it cannot get into the enemy back rank(s) if the enemy does not push a pawn at least 2 squares). Also, I did not take into account illegal positions where the side to move king is in check by more than 2 pieces, but this is probably a small percentage as well. I think this is one of those impossible problems to solve and even best guess estimates may be off by quite a bit (but not by too many magnitudes of order). KarinsDad :) > For every >legal but impossible position like that, we can permute the other pieces and >find more combinations. In any case, I think this is an area for a lot more >exploration.
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.