Sources page biographical material

4.B.11. MASTERMIND, ETC.
There were a number of earlier guessing games of the Mastermind type before the popular version devised by Marco Meirovitz in 1973 -- see: Reddi. One of these was the English Bulls and Cows, but I haven't seen anything written on this and it doesn't appear in Bell, Falkener or Gomme. Since 1975 there have been several books on the game and a number of papers on optimal strategies. I include a few of the latter.

NOTATION. If there are h holes and c choices at each hole, then I abbreviate this as c^h.

A. K. Austin. How do You play 'Master Mind'. MTg 71 (Jun 1975) 46-47. How to state the rules correctly.

S. S. Reddi. A game of permutations. JRM 8:1 (1975) 8-11. Mastermind type guessing of a permutation of 1,2,3,4 can win in 5 guesses.

Donald E. Knuth. The computer as Master Mind. JRM 9:1 (1976-77) 1-6. 6⁴ can be won in 5 guesses.

Robert W. Irving. Towards an optimum Mastermind strategy, JRM 11:2 (1978-79) 81-87. Knuth's algorithm takes an average of 5804/1296 = 4.478 guesses. The author presents a better strategy that takes an average of 5662/1296 = 4.369 guesses, but requires six guesses in one case. A simple adaptation eliminates this, but increases the average number of guesses to 5664/1296 = 4.370. An intelligent setter will choose a pattern with a single repetition, for which the average number of guesses is 3151/720 = 4.376.

A. K. Austin. Strategies for Mastermind. G&P 71 (Winter 1978) 14-16. Presents Knuth's results and some other work.

Merrill M. Flood. Mastermind strategy. JRM 18:3 (1985-86) 194-202. Cites five earlier papers on strategy, including Knuth and Irving. He considers it as a two-person game and considers the setter's strategy. He has several further papers in JRM developing his ideas.

Antonio M. Lopez, Jr. A PROLOG Mastermind program. JRM 23:2 (1991) 81-93. Cites Knuth, Irving, Flood and two other papers on strategy.

Kenji Koyama and Tony W. Lai. An optimal Mastermind strategy. JRM 25:4 (1994) 251 256. Using exhaustive search, they find the strategy that minimizes the expected number of guesses, getting expected number 5625/1296 = 4.340. However, the worst case in this problem requires 6 guesses. By a slight adjustment, they find the optimal strategy with worst case requiring 5 guesses and its expected number of guesses is 5626/1296 = 4.341. 10 references to previous work, not including all of the above.

Jörg Bewersdorff. Glück, Logik und Bluff Mathematik im Spiel -- Methoden, Ergebnisse und Grenzen. Vieweg, 1998. Section 2.15 Mastermind: Auf Nummer sicher, pp. 227-234 & Section 3.13 Mastermind: Farbcodes und Minimax, pp. 316-319. Surveys the work on finding optimal strategies. Then studies Mastermind as a two-person game. Finds the minimax strategy for the 3² game and describes Flood's approach.