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Subject: Re: A question about underpromotion danger

Author: Robert Hyatt

Date: 06:19:02 08/06/99

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On August 05, 1999 at 23:28:47, Ricardo Gibert wrote:

>You just hit upon why Nunn's statistic is biased! The defending king is more
>often on some relevant square than on some random square. With RP pawn there are
>more bad squares for the K, but they are not equally likely, which is why such
>statistics are bogus. Each position generally has a different number of ancestor
>positions, which in turn are not equally likely either, etc.
>
>Just curious. Do EGTBs include illegal positions such as W: Kf6, Rg7, Ph7; B:
>Kh8 (white to move)? One reason I ask is it can be problematical to determine
>whether a given position is legal. On the other hand, they can be avoided with
>the retrograde analysis. What does a EGTB do when it is given such a position?
>If it includes them, this can also skew some staistics derived from EGTBs.


EGTBs are probed using a "Godel" number which (simply stated) is just the
concatenation of 5 6-bit numbers that represent the locations of the 5
pieces.  Eugene's tablebases eliminate some obviously bad positions (adjacent
kings and such) and then restricts one king to a small part of the board to
shrink this quite a bit.   But yes, there are always "broken" positions that
are legal positions, but which can't be reached from a real game, and there are
some illegal positions as well...

the positions are generally 'marked' during the build process, because you
can recognize that the position has no valid successor position.  I haven't
seen Eugene's statistics recently, but the old Edward's format generator
produced a summary that gave the number of 'broken' positions, etc...



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