Knuth (1976-77) showed that the codebreaker can always succeed in five or fewer moves (i.e., knows the code after four guesses). His technique uses a greedy strategy that minimizes the number of remaining possibilities at each step, and requires 4.478 guesses on average, assuming equally likely code choice.
How is the game of Mastermind played on a board?
The game is played on a Mastermind board, which has 10 rows on it. In each row, there are 4 slots for the codebreaker to place their guesses. Next to each set of 4 slots, there are 4 smaller slots for the mastermind to place their feedback for each guess. To start, one player is the mastermind and the other player is the codebreaker.
Why do I play Mastermind with numbers instead of colours?
I play Mastermind with numbers instead of colours, because I first learned it in the second grade as Bagel Pico Fermi which uses numbers. For the rest of my answer, I will refer to red pegs as “bagels”, and white pegs as “picos” (and holes without pegs as “fermis”). The system I tend to use is suboptimal but very easy to follow. It goes as follows:
Do you have to put pegs in every hole in mastermind?
This is the code that the codebreaker will try to guess. If you’re playing a video game version, the computer will usually do this instead of a player. The code maker must put a peg in every hole. He has the option to use more than one peg of the same color.
Which is the best algorithm for mastermind strategy?
Robert W. Irving, “Towards an optimum Mastermind strategy,” Journal of Recreational Mathematics 11 (1978), 81-87 [while staying within the “at most 5” achieves 5664 ⇒ ≈4.37] E. Neuwirth, “Some strategies for Mastermind,” Zeitschrift fur Operations Research 26 (1982), B257-B278 [achieves 5658 ⇒ ≈4.3657]
How does the code maker work in mastermind?
The code maker must put a peg in every hole. He has the option to use more than one peg of the same color. For example, he could put down Green Yellow Yellow Blue. Have the code breaker place her first guess. The other player, or the only player in video game versions, tries to guess what the hidden code is.
What’s the minimax value for solving mastermind?
The minimax value in the sense of game theory is 5600/1296 = 4.321. MathWorld’s page on Mastermind also gives a nice synopsis and mention a few more strategies: Knuth (1976-77) showed that the codebreaker can always succeed in five or fewer moves (i.e., knows the code after four guesses).
Who is mastermind in the X-Men comics?
Comics Mastermind (comics), several characters Mastermind (Jason Wyngarde), a Marvel Comics supervillain, an adversary of the X-Men Lady Mastermind, one of his daughters. Mastermind (Martinique Jason), his other daughter Mastermind (computer), the alien artificial intelligence that first appeared in Captain Britain
