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From: AST@postman.hsn.no (Alf Steinbach)
Subject: Re: Complexity of TicTacToe
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Message-ID: <AST.184.786206043@postman.hsn.no>
Date: Wed, 30 Nov 1994 14:34:03 GMT
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References: <3bhi7kINNf8t@sbusol.rz.uni-sb.de> <3bhl7f$42f@xmission.xmission.com>
Organization: Nordland College

In article <3bhl7f$42f@xmission.xmission.com> rjones@xmission.com (Ray Jones) writes:
>From: rjones@xmission.com (Ray Jones)
>Subject: Re: Complexity of TicTacToe
>Date: 30 Nov 1994 03:47:11 -0700
>cyrano@jurassix.cs.uni-sb.de (Andreas Birk) writes:
>
>>I would like to know how many different situations are possible in the
>>game TicTacToe.
>
>About 49 (maybe 45, I'm pulling this from memory) when you remove
>reflections/rotations. 
>
>Small enough that someone built a computer out of tinker-toys that
>played a perfect game.  (I think I saw this in Scientific American
>some years back.)
>
>Ray Jones

When you remove reflections/rotations, and also assume that the program
uses a search for directly winning moves (gets 3) and directly forced
moves (must block 2 from opponent), then the number of boards you *must*
recognize, if you check board situations directly, is very very small.
I ended up with a larger number of situations when the number of moves
open to the computer should be as large as possible, to ensure variety.
The number of rules for this was 42  -  possibly needing 4-5 rules extra
if all winning situations should be exploited.  The number of rules for
simply *not losing* would be much smaller, I suspect about 15-20.
