Crack the Code The Optimal Mathematical Strategy for Winning Mastermind Revealed

Ever played Mastermind and felt like you were just guessing? Well, hold on to your colour pegs! A new mathematical analysis, detailed in Erik Göransson Gaspar's aptly named "Optimal Mastermind," reveals the most efficient way to crack the code every time. Forget random stabs in the dark – this is about logic, information, and a dash of mathematical wizardry.

The core of Mastermind lies in deciphering a secret sequence of four coloured pegs. The Code Master creates this sequence, choosing from six different colours, and the player attempts to guess it. After each guess, the Code Master provides clues: a black peg indicates a correct colour in the correct position, a white peg indicates a correct colour in the wrong position, and no pegs mean none of the colours are in the secret code.

The secret sauce? Information theory! Each guess eliminates potential codes, providing information measured in bits. The optimal strategy involves maximising the information gained with each move, which can be calculated using entropy – a weighted average of all possible information based on the Code Master's responses. In simple terms, choose the move that best reduces the number of possibilities. By using this method, a game of Mastermind can be solved in an average of about 4.47 moves. This result aligns with other classical algorithms, such as Donald Knuth's from 1976, which also averaged around 4.4 moves. This shows that you should be able to win every game within 5 moves by using this mathematical strategy to optimise your gameplay and choice of colours!

Fuente Original: https://www.microsiervos.com/archivo/matematicas/estrategia-matematica-optima-jugar-mastermind.html

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