

from itertools import product





def      A__					(			__A  :						int     ,				__A  :						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      A__					(			)					->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() = }""")







'''simple docstring'''





from ..utils import DummyObject, requires_backends



class  snake_case__						(    metaclass=SCREAMING_SNAKE_CASE_				):
 A__				= ['''note_seq''']
 def __init__(   self						:							Tuple      ,     *__a						:							int      ,     **__a						:							List[str]  )      ->   Any:







       '''simple docstring'''
       requires_backends(self      ,     ['note_seq']  )
 @classmethod
 def A_   (   cls						:							Optional[Any]      ,     *__a						:							Optional[Any]      ,     **__a						:							List[str]  )      ->   Union[str, Any]:







       '''simple docstring'''
       requires_backends(cls      ,     ['note_seq']  )





 @classmethod
 def A_   (   cls						:							List[Any]      ,     *__a						:							Union[str, Any]      ,     **__a						:							List[str]  )      ->   Any:







       '''simple docstring'''
       requires_backends(cls      ,     ['note_seq']  )



