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From: dim@whuxlm.UUCP (McCooey David I)
Newsgroups: net.games.chess
Subject: Re: Deterministic Chess (Re: Perfect Play?)
Message-ID: <915@whuxlm.UUCP>
Date: Wed, 26-Mar-86 14:39:55 EST
Article-I.D.: whuxlm.915
Posted: Wed Mar 26 14:39:55 1986
Date-Received: Thu, 27-Mar-86 07:39:25 EST
References: <912@whuxlm.UUCP> <5149@alice.uUCp>
Organization: AT&T Bell Laboratories, Whippany
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> >	1. Since there is no way we will ever be able to fully analyze
> >	   chess, is it possible nonetheless to determine the PROBABILITY
> >	   of BLACK having a forced win from the opening position?
> >	   (The same goes for a forced DRAW or for a forced WHITE win.)
> 
> I don't know what this question means.  Either black has a forced
> win or black doesn't.  The probability is either 1 or 0.

I agree, but we will (probably) never know which it is.  I am interested
in the following issue:

	Say we restrict ourselves to the class of chess positions where:
		1. All 32 pieces are on the board
		2. The position is symmetric
		3. Each side is 'set up' on its own first two ranks
		4. It is WHITE's move
	or some similar class of positions.  The point is that we want
	the opening position to be a member of this class.

	Now, if we had some oracle which would tell us who had a forced
	win (or draw) in each position in this class, we could calculate
	a PROBABILITY of BLACK having a forced win for a RANDOMLY chosen
	position from this class.  (i.e. before we choose the position,
	what the probability is of it being a BLACK win.)  This would
	give us grounds to make a guess at the probability of BLACK
	having a forced win in the opening position.

	This is an attempt to clarify the problem and not an attempt at a
	solution because clearly the probability mentioned above depends
	on the class we choose, and, moreover, we do not have an oracle.

	Another way to look at it is this:  Say we had an oracle that knew
	the right answer (yes or no).  What would be "fair odds" for it
	to give someone who did not know the answer?