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Subject: Re: Counting & Encoding Any Chess Position in 157 bits

Author: Ratko V Tomic

Date: 16:55:55 11/10/99

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> I think that it is more than 20% above because there are many
> positions when both kings are in check(I guess close to 20%)
> and it is not the only case.

Even a single king in check of the side not to move is illegal (whether you
encode side-to-move or not, it still is always only one side's turn, and since
for each position there is a reversed color twin, for every check you find, it
is either illegal, or its reverse color twin is illegal), so the number of
positions may be greater (not a product of two probabilities which would
decrease the odds). Since what we may picture as a "typical" position (from
human games) is not what these positions are, it's hard to say without
experiments. The typical thing is that an "average" material content will
produce 10^38 positions, so even a single "typical" material content case cannot
be examined in full, and there are 58 million distinct material states. Checks
may indeed be much more numerous here than in "normal" game positions.


> There are many positions when it is possible to prove by the pawn
> structure and the number of pieces that the position is illegal.

Not sure that these cases would amount to much.



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