[taejo]

> One strategy which is obviously optimal is to use minimax (recursively, not like Knuth's Mastermind strategy which was mentioned by @christiangenco), however this strategy is not computationally feasible.

With some restrictions it's possible to do a full minimax. In that case, you still don't know if it's optimal, but you've at least got an upper bound. And it turns out, it's possible to guarantee victory while finishing in an expected 3.554 guesses. Alternatively, you can finish in an expected 3.212 guesses if you don't mind a small chance of taking more than six guesses.