


'''simple docstring'''

from itertools import product

def 							__magic_name__(						lowerCamelCase						,				lowerCamelCase):
						__lowerCAmelCase							       =				sides_number
						__lowerCAmelCase							       =				max_face_number * dice_number
						__lowerCAmelCase							       =				[0] * (max_total + 1)

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

						return totals_frequencies

def 							__magic_name__(						):
						__lowerCAmelCase							       =				total_frequency_distribution(
						    sides_number=4						,				dice_number=9)
						__lowerCAmelCase							       =				total_frequency_distribution(
						    sides_number=6						,				dice_number=6)

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

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

						__lowerCAmelCase							       =				round(SCREAMING_SNAKE_CASE_						,				ndigits=7)

						return rounded_peter_win_probability


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





'''simple docstring'''

from manim import *


class       a__				( __A      ):







				"""simple docstring"""



				def 					_snake_case  (self		):
										__lowerCAmelCase							       =				Rectangle(height=0.5       ,			width=0.5		)
										__lowerCAmelCase							       =				Rectangle(height=0.4_6       ,			width=0.4_6		).set_stroke(width=0		)

										__lowerCAmelCase							       =				[mem.copy() for i in range(6		)]
										__lowerCAmelCase							       =				[mem.copy() for i in range(6		)]
										__lowerCAmelCase							       =				VGroup(*__lowercase		).arrange(__lowercase       ,			buff=0		)
										__lowerCAmelCase							       =				VGroup(*__lowercase		).arrange(__lowercase       ,			buff=0		)
										__lowerCAmelCase							       =				VGroup(__lowercase       ,			__lowercase		).arrange(__lowercase       ,			buff=0		)
										__lowerCAmelCase							       =				Text('''CPU'''       ,			font_size=24		)
										__lowerCAmelCase							       =				Group(__lowercase       ,			__lowercase		).arrange(__lowercase       ,			buff=0.5       ,			aligned_edge=__lowercase		)
										cpu.move_to([-2.5, -0.5, 0]		)
										self.add(__lowercase		)

										__lowerCAmelCase							       =				[mem.copy() for i in range(1		)]
										__lowerCAmelCase							       =				VGroup(*__lowercase		).arrange(__lowercase       ,			buff=0		)
										__lowerCAmelCase							       =				Text('''GPU'''       ,			font_size=24		)
										__lowerCAmelCase							       =				Group(__lowercase       ,			__lowercase		).arrange(__lowercase       ,			buff=0.5       ,			aligned_edge=__lowercase		)
										gpu.align_to(__lowercase       ,			__lowercase		)
										gpu.set_x(gpu.get_x() - 1		)

										self.add(__lowercase		)

										__lowerCAmelCase							       =				[mem.copy() for i in range(6		)]
										__lowerCAmelCase							       =				VGroup(*__lowercase		).arrange(__lowercase       ,			buff=0		)

										__lowerCAmelCase							       =				Text('''Model'''       ,			font_size=24		)
										__lowerCAmelCase							       =				Group(__lowercase       ,			__lowercase		).arrange(__lowercase       ,			buff=0.5       ,			aligned_edge=__lowercase		)
										model.move_to([3, -1.0, 0]		)

										self.play(
										    Create(__lowercase       ,			run_time=1		)       ,			Create(__lowercase       ,			run_time=1		)       ,			Create(__lowercase       ,			run_time=1		)       ,			)

										__lowerCAmelCase							       =				MarkupText(
										    F"""First, an empty model skeleton is loaded\ninto <span fgcolor='{YELLOW}'>memory</span> without using much RAM."""       ,			font_size=24       ,			)

										__lowerCAmelCase							       =				Square(side_length=2.2		)
										key.move_to([-5, 2, 0]		)

										__lowerCAmelCase							       =				MarkupText(
										    F"""<b>Key:</b>\n\n<span fgcolor='{YELLOW}'>●</span> Empty Model"""       ,			font_size=18       ,			)

										key_text.move_to([-5, 2.4, 0]		)

										step_a.move_to([2, 2, 0]		)
										self.play(Write(__lowercase       ,			run_time=2.5		)       ,			Write(__lowercase		)       ,			Write(__lowercase		)		)

										self.add(__lowercase		)

										__lowerCAmelCase							       =				[]
										__lowerCAmelCase							       =				[]
										__lowerCAmelCase							       =				[]
										for i, rect in enumerate(__lowercase		):
																__lowerCAmelCase							       =				Rectangle(height=0.4_6       ,			width=0.4_6		).set_stroke(width=0.0		).set_fill(__lowercase       ,			opacity=0.7		)
																cpu_target.move_to(__lowercase		)
																cpu_target.generate_target()
																__lowerCAmelCase							       =				0.4_6 / 4
																__lowerCAmelCase							       =				0.4_6 / 3

																if i == 0:
																						cpu_target.target.next_to(cpu_left_col_base[0].get_corner(DOWN + LEFT		)       ,			buff=0.0_2       ,			direction=__lowercase		)
																						cpu_target.target.set_x(cpu_target.target.get_x() + 0.1		)
																elif i == 3:
																						cpu_target.target.next_to(cpu_targs[0].target       ,			direction=__lowercase       ,			buff=0.0		)
																else:
																						cpu_target.target.next_to(cpu_targs[i - 1].target       ,			direction=__lowercase       ,			buff=0.0		)
																cpu_targs.append(__lowercase		)

																first_animations.append(rect.animate(run_time=0.5		).set_stroke(__lowercase		)		)
																second_animations.append(MoveToTarget(__lowercase       ,			run_time=1.5		)		)

										self.play(*__lowercase		)
										self.play(*__lowercase		)

										self.wait()

