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From: lambert@boring.UUCP
Newsgroups: net.math
Subject: Re: MasterMind, Jotto, entropy
Message-ID: <6350@boring.UUCP>
Date: Sat, 9-Mar-85 08:02:10 EST
Article-I.D.: boring.6350
Posted: Sat Mar  9 08:02:10 1985
Date-Received: Mon, 11-Mar-85 04:37:36 EST
References: <246@cmu-cs-g.ARPA>
Reply-To: lambert@boring.UUCP (Lambert Meertens)
Organization: CWI, Amsterdam
Lines: 29
Summary: 
Apparently-To: rnews@mcvax.LOCAL

Jim Davis writes:
> The next move should be chosen so as to minimize the size of the largest
> set of posibilities remaining after the reply to that move.
Peter Monta writes:
> My thought is that the right thing to maximize is the *information*
> obtained from each guess.

The right heuristic depends on whether you try to maximize the worst-case
or the average number of guesses required.  In playing against an opponent,
where the player first to hit the solution wins, the second seems more
appropriate--unless you know that s/he/it follows the first strategy.
But if you know that your opponent is very near the solution, desparate
guesses may be better than steadily gathering information.

There is an amusing variant of Jotto etc. in which a player does not have
to freeze the initial position, as long as the answers given are consistent
with *some* initial position.  This can, in principle, also be done in the
original game, in which case it is cheating.  For a human player, it is
hard to play this "Floating" Jotto to his/her advantage, since it is hard
not to make mistakes.  For a program, it is quite feasible: keep a list of
initial positions that are still open, and when posed a question, divide
the items in the list into classes, depending on the answer required for
each item, and give the answer corresponding to the largest class (which
then becomes the new list).
-- 

     Lambert Meertens
     ...!{seismo,philabs,decvax}!lambert@mcvax.UUCP
     CWI (Centre for Mathematics and Computer Science), Amsterdam