"you might gain _less_ than one bit on average [...], but you can't gain more."
On. Average.
That's a true statement. Can't gain more than one bit on average.
One bit, however, is not “the maximum possible amount” you can gain from an oracular answer to a yes/no question. The OP covers exactly this point re: the “Guess Who?” game.
That's why people are talking about the maximum expected value.
One bit, however, is not “the maximum possible amount” you can gain from an oracular answer to a yes/no question. The OP covers exactly this point re: the “Guess Who?” game.