def entropy_to_expected_score(ent):
    """
    Based on a regression associating entropies with typical scores
    from that point forward in simulated games, this function returns
    what the expected number of guesses required will be in a game where
    there's a given amount of entropy in the remaining possibilities.
    """
    # Assuming you can definitely get it in the next guess,
    # this is the expected score
    min_score = 2 ** (-ent) + 2 * (1 - 2 ** (-ent))

    # To account for the likely uncertainty after the next guess,
    # and knowing that entropy of 11.5 bits seems to have average
    # score of 3.5, we add a line to account
    # we add a line which connects (0, 0) to (3.5, 11.5)
    return min_score + 1.5 * ent / 11.5