Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83 (MC840302); site boring.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!philabs!cmcl2!seismo!mcvax!boring!lambert 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