# Serkan Gur’s VB Examples Page

## Excel Mastermind with Optimal Strategy

MASTERMIND STRATEGIES

In the classical Mastermind game where the secret code is a 4 digit repeatable combination of 6 different colours, there are in fact just 5 unique types of first guesses to the game. And a player’s guess will be scored according to its correct (colour and position) and semi-correct (correct colour but wrong position) digits. If we multiply correct number of digits by 10 and add to that number semi-correct digits in the guess, we can show each score by a 2-digit number: 00, 01, 02, ……, 30, and 40. Note that 31 is not a valid score. The table below shows the number of remaining valid possibilities after the first guess for each of the possible combinations and for each possible score:

 1111 1112 1122 1123 1234 00 625 256 256 81 16 01 0 308 256 276 152 02 0 61 96 222 312 03 0 0 16 44 136 04 0 0 1 2 9 10 500 317 256 182 108 11 0 156 208 230 252 12 0 27 36 84 132 13 0 0 0 4 8 20 150 123 114 105 96 21 0 24 32 40 48 22 0 3 4 5 6 30 20 20 20 20 20 40 1 1 1 1 1 Total: 1296 1296 1296 1296 1296 Simple 1 2 8 9 52 Worst Case 625 317 256 276 312 Entropy 1.5 2.7 2.9 3 3.1 Expected Size 512 235.9 204.5 185.3 188.2 Most Parts 5 11 13 14 14

From this table, you can see which game strategy picks which first guess and why it does so by looking at the highlighted cells (these are the first guesses of each classical Mastermind strategy). This table below shows the game solution tree averages for all the classical strategies as well as the Optimal Strategy.

 Strategy Total Guesses Average Maximum Guesses 6 or more Guesses Author Year Optimal (Max: 6) 5625 4.34028 6 1 Lai 1993 Optimal (Max: 5) 5626 4.34105 5 0 Lai 1993 Weighted Entropy 5646 4.35648 6 3 Gur 2021 Most parts 5668 4.37346 6 7 Kooi 2005 Expected Size 5696 4.39506 6 3 Irving 1979 Entropy 5722 4.41512 6 12 Neuwirth 1982 Worst Case (Min-Max) 5801 4.47608 5 0 Knuth 1977 Simple 7471 5.76466 9 853 Shapiro 1983