Author: Marc Bourzutschky
Date: 17:33:25 05/17/04
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On May 17, 2004 at 19:37:07, GuyHaworth wrote: > >The Kings are never adjacent because 'positioning' the pieces starts with Kk, >and these are explicitly enumerated. > >Actually, this might be achieved as a specific case of the general 'no >unblockable checks' rule. > >The subtlety comes in calculating how many squares are left to position a piece >(or set of like pieces) on, e.g. for the 'R' in KQRK after the Kk and Q have >been placed for wtm positions. This is done per Kk-positioning and not after >the Q is placed. > >The R cannot occupy a checking position adjacent to the K, but the program does >not assume that the Q is not occupying one of these squares [which it could if >the chessic intelligence was built in]. Therefore, the program calculates that >there is one more square available to the R than there actually is. > >I can't remember whether this means there is one unused position in the index, >or whether the R is placed, on one occasion, on top of the Q and then this >position is made 'broken'. Some experimenting with index-numbers and positions >would reveal what goes on here. > >But I think you will find there is some slight wasteage of this kind in such >endgames as KQRK where there are different types of piece on one side and/or the >other. KBNK would have the same problem, as one has to assume that the B is on >a N-checking square which it would in fact sometimes legally be. > >g No, all the pairs (and triplets in endings that have 3 non-kings of the same color) are explicitly enumerated, avoiding the issue you are describing. That is also one of the reason why it would be tedious to have 4 non-kings of the same color in this scheme. Pieces on the same square do occur in the Nalimov scheme, but only if there are pawns present. The reason is that if there are N pieces on the board, you know that if you add another non-pawn there are only 64-N squares available, but if you add a pawn, there will not necessarily be only 48-N squares available, because some of those N pieces may be on the the 1st or 8th rank and not interfere with the pawn. I had to figure all of this out in detail when generalizing the Nalimov program to arbitrary rectangular board dimensions, but simply looking at the number of broken positions in a few .tbs files will make this pretty clear as well. -Marc
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