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Greg Strong wrote on Thu, Jul 21, 2005 09:56 PM UTC:
Thanks for the very interesting post.

I know that hash tables (in chess programs, normally called a
Transposition Table) can lead to the program confusing positions, but I
have never heard of a high-profile case of this actually happening. 
Here's how the transposition table works...  There are different
sequences of moves that can lead to the same board position, and the
program doesn't what to re-consider a position it has already considered,
so it keeps a look-up table of positions it has already considered.  The
look-up table is normally indexed by a 64-bit value (the locations of all
the pieces on the board are 'boiled down' into a 64-bit number.)  Since
there are more than 2^64 possible board positions, some different
positions can equate to the same key value.  This leads to mis-evaluation
of the situation.  The chances against this happening, however, are
astronomical!  One-in-a-million is actually quite an understatement - it
is really more like one-in-2^64 (assuming Shreader isn't programmed in
some really silly way, and I'm assuming it isn't.)  Guess it had to
happen sooner or later! :)

Transposition tables also lead to other problems.  For one thing, the
table entry only tells you about the position, not how you got there. 
This is a problem when 3-time repetition is involved.  A position can look
really good the first time you encounter it, but the next time you
encounter it, your pre-determined response may actually lead to a 3-time
repetition, and therefore a draw!

These are known problems.  Absolutely every commercial chess program has
bugs.  Bugs that the programmers are well aware of.  But, the very
occasional problem with a transposition table is negligable compared to
the benefit, so they use them anyway...

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