I seem to recall that Knuth has written about this subject (Mastermind, but that seems essentially to be the same game, except that mastermind allows for repeats). IIRC, he has proven that (at least for a certain number of colours that positions), the best play after the first move is the one (or one of the ones) that minimizes the maximum number of possibles left, over all possible "pico/fermi/bagel" responses. I cannot remember what he said about first moves.

In reply to Re: Challenge: Optimal Bagels Strategy by JavaFan
in thread Challenge: Optimal Bagels Strategy by Limbic~Region

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