[FOM] Checkers is a draw

joeshipman@aol.com joeshipman at aol.com
Thu Jul 26 11:30:09 EDT 2007

I have a master's rating, and I own several Grandmaster-level chess 
engines. I rarely beat them when playing "straight", but I find it 
quite easy to beat any of them when I am allowed to use the "move 
takeback" option repeatedly.

The point of this observation of mine is that the gap between "perfect 
play" and the strongest Grandmasters can't be more than a few hundred 
rating points (they would occasionally draw a "straight" game against a 
perfect player), so it seems to me that with backtracking they would be 
able to satisfy themselves that Chess was a draw in the same way that I 
can satisfy myself about exactly how strong a chess engine I am playing 
is. Unfortunately, this is not the kind of certainty that can be 
communicated easily to someone who does not have a highly sophisticated 
intuitive understanding of chess.

The "moral certainty" is of the same type that a lesser chessplayer can 
have about an easier proposition, for example the proposition "if you 
remove White's Queen Knight from the initial position, then Black has a 
forced win." There is no hope of a mathematical proof of this 
mathematical  fact, but I claim that a good enough chessplayer's 
conviction about this qualifies as actual "knowledge" (justified true 

-- JS

-----Original Message-----
From: Bob Wolf <robertswolf at yahoo.com>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Wed, 25 Jul 2007 12:35 pm
Subject: Re: [FOM] Checkers is a draw

     I don't understand, or perhaps more frankly I
don't believe, your statement that "I can very easily
and quickly find a way to beat them if I am allowed to
backtrack and they are committed to playing the same
move when they get the same position." Would you
please explain/justify this claim? Thanks.

               Bob Wolf

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