Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site cmu-cs-g.ARPA Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!genrad!mit-eddie!godot!harvard!seismo!rochester!cmu-cs-pt!cmu-cs-g!monta From: monta@cmu-cs-g.ARPA (Peter Monta) Newsgroups: net.math Subject: MasterMind, Jotto, entropy Message-ID: <246@cmu-cs-g.ARPA> Date: Fri, 8-Mar-85 02:19:37 EST Article-I.D.: cmu-cs-g.246 Posted: Fri Mar 8 02:19:37 1985 Date-Received: Sun, 10-Mar-85 05:42:25 EST Organization: Carnegie-Mellon University, CS/RI Lines: 33 > Guessing "wrong" answers in Mastermind can indeed get you to the answer > sooner than guessing only right answers. > - Joel McCormack {ihnp4 decvax ucbvax allegra}!decwrl!joel This is an important point, which took me some time to realize. I worked on a near-isomorph of MasterMind called Jotto as part of a cognitive psychology course---I finally wrote a program very similar to the description of the exhaustive table-generating program. Jotto is 26-color, 5-position MasterMind, duplicate colors permitted, guess feedback only the number of pegs (no distinction between black and white). Of course, the colors are letters, guesses are five-letter words, and feedback is a number from 0 to 5. Guesses are restricted to valid five-letter words, as are targets. My thought is that the right thing to maximize is the *information* obtained from each guess. Suppose you guess a word. The act of guessing partitions the set of all possibilities into six blocks---those with 0 letters in common with the guess, those with 1 letter in common, etc. When the opponent tells you the disposition of your guess, he gives you information in the amount of the entropy of this partition. Assuming that the targets are equally probable, the entropy is the sum over blocks of P*log P, where P is the cardinal of the block. The program would simply iterate through its dictionary, guessing the entry that maximized the entropy of the partition it induced. The technique should be applicable to any MasterMind-like game; in fact, it should do even better with black and white pegs, since this would increase the number of blocks. Peter Monta ARPA: monta@cmu-cs-g UUCP: ...!rochester!cmu-cs-pt!cmu-cs-g!monta