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Subject: Nalimov-indexing: a subtlety

Author: GuyHaworth

Date: 16:37:07 05/17/04

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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



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