"""
Project Euler problem 205:


Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4.
Colin has six six-sided (cubic) dice, each with faces numbered 1, 2, 3, 4, 5, 6.

Peter and Colin roll their dice and compare totals: the highest total wins. The result
is a draw if the totals are equal.

What is the probability that Pyramidal Pete beats Cubic Colin? Give your answer rounded
to seven decimal places in the form 0.abcdefg
"""

from itertools import product


def probability_of_sums(
    dice_min: int = 1, dice_max: int = 6, dice_number: int = 6
) -> (list, list):
    """
    Returns the list of possible sums and their probabilities of dice_number dices with
    numbers from dice_min to dice_max
    """
    sums = []
    counter = []
    for dices in product(range(dice_min, dice_max + 1), repeat=dice_number):
        s = sum(dices)
        if s not in sums:
            sums.append(s)
            counter.append(1)
        else:
            idx = sums.index(s)
            counter[idx] += 1
    total = sum(counter)
    probability = [_t / total for _t in counter]
    return sums, probability


def solution():
    """
    Returns the probability of Peter winning in dice game with nine four-sided
    dice (1, 2, 3, 4 points) against Colin who has six six-sided dice (1, 2, 3, 4, 5,
    6). Winner of a match is who has more total points.
    Algorithm calculates the possible point sums for each player and their
    probabilities. Peter's probability to win is summed up from all the permutations
    where he has more points than Colin.

    >>> solution()
    0.5731441
    """
    peter_wins = 0
    colin_wins = 0
    draw = 0
    for s_peter, p_peter in zip(
        *probability_of_sums(dice_min=1, dice_max=4, dice_number=9)
    ):
        for s_colin, p_colin in zip(
            *probability_of_sums(dice_min=1, dice_max=6, dice_number=6)
        ):
            p_branch = p_peter * p_colin
            if s_peter > s_colin:
                peter_wins += p_branch
            elif s_colin > s_peter:
                colin_wins += p_branch
            else:
                draw += p_branch

    return round(peter_wins, 7)


if __name__ == "__main__":
    print(solution())