
"""simple docstring"""




from abc import ABC, abstractmethod
from argparse import ArgumentParser







class     lowercase(_lowercase       ):



     @staticmethod
     @abstractmethod
     def 			lowercase__  (							__SCREAMING_SNAKE_CASE   )		->     Tuple:







         """simple docstring"""



         raise NotImplementedError()




     @abstractmethod
     def 			lowercase__  (							self   )		->     Optional[Any]:







         """simple docstring"""



         raise NotImplementedError()




"""simple docstring"""




from itertools import product



def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		int     )     ->						list[int]:
    a__		=			sides_number
    a__		=			max_face_number * dice_number
    a__		=			[0] * (max_total + 1)

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

    return totals_frequencies



def     __magic_name__		(					)     ->						float:
    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(UpperCamelCase							,		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(UpperCamelCase							,		ndigits=7     )

    return rounded_peter_win_probability


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


