from lib_misc import get_item_counts


def acc(scores, faces, rem):
    if rem == 0:
        return scores
    nscores = []
    for f in faces:
        for s in scores:
            nscores.append(f + s)
    return acc(nscores, faces, rem - 1)


def euler_205():
    scores_four = acc([0], [1, 2, 3, 4], 9)
    scores_six = acc([0], [1, 2, 3, 4, 5, 6], 6)
    all_combinations = len(scores_four) * len(scores_six)

    four_won_count = 0
    for four_value, four_count in  get_item_counts(scores_four).items():
        current_six_count = 0
        for six_value, six_count in get_item_counts(scores_six).items():
            if four_value > six_value:
                current_six_count += six_count
        four_won_count += (four_count * current_six_count)

    p = four_won_count / all_combinations
    return f"{round(p, 7)}"


if __name__ == "__main__":
    solution = euler_205()
    print("e205.py: " + str(solution))
    # assert(solution == 0)