



from itertools import product





def 					__snake_case     (      _UpperCAmelCase       ,			_UpperCAmelCase    ):
    __a							=    sides_number
    __a							=    max_face_number * dice_number
    __a							=    [0] * (max_total + 1)

    __a							=    1
    __a							=    range(__lowerCamelCase       ,			max_face_number + 1    )
    for dice_numbers in product(__lowerCamelCase       ,			repeat=__lowerCamelCase    ):
        __a							=    sum(__lowerCamelCase    )
        totals_frequencies[total] += 1

    return totals_frequencies





def 					__snake_case     (      ):
    __a							=    total_frequency_distribution(
        sides_number=4       ,			dice_number=9    )
    __a							=    total_frequency_distribution(
        sides_number=6       ,			dice_number=6    )

    __a							=    0
    __a							=    9
    __a							=    4 * 9
    __a							=    6
    for peter_total in range(__lowerCamelCase       ,			max_peter_total + 1    ):
        peter_wins_count += peter_totals_frequencies[peter_total] * sum(
            colin_totals_frequencies[min_colin_total:peter_total]    )

    __a							=    (4**9) * (6**6)
    __a							=    peter_wins_count / total_games_number

    __a							=    round(__lowerCamelCase       ,			ndigits=7    )

    return rounded_peter_win_probability


if __name__ == "__main__":
 print(f'{solution() = }')










def 					__snake_case     (      _UpperCAmelCase    ):
    if not isinstance(_UpperCAmelCase       ,			_UpperCAmelCase    ):
        raise TypeError('''Input value must be an \'int\' type'''    )

    __a							=    0
    while number:
        position += 1
        number >>= 1

    return position


if __name__ == "__main__":
 import doctest

 doctest.testmod()





