deal_or_no_deal.py

import random


def simulate_deal_or_no_deal_simple(prizes, swap=False):
	# setup
	prizes = prizes.copy()
	random.shuffle(prizes)
	case_indices = list(range(len(prizes)))

	# choose our case
	my_case = random.choice(case_indices)
	case_indices.remove(my_case)

	# open all the other cases
	while len(case_indices) > 1:
		random_case = random.choice(case_indices)
		case_indices.remove(random_case)

	# swap?
	if swap:
		other_case = case_indices[0]
		my_case = other_case

	# result
	return prizes[my_case]


def simulate_deal_or_no_deal_with_short_circuit(prizes, swap=False):
	min_prize, max_prize = min(prizes), max(prizes)

	# setup
	prizes = prizes.copy()
	random.shuffle(prizes)
	case_indices = list(range(len(prizes)))

	# choose our case
	my_case = random.choice(case_indices)

	# short circuit
	if prizes[my_case] != min_prize and prizes[my_case] != max_prize:
		return False

	case_indices.remove(my_case)

	# open all the other cases
	while len(case_indices) > 1:
		random_case = random.choice(case_indices)
		case_indices.remove(random_case)

	other_case = case_indices[0]

	# short circuit
	if prizes[other_case] != min_prize and prizes[other_case] != max_prize:
		return False

	# swap?
	if swap:
		my_case = other_case

	# result
	return prizes[my_case]


if __name__ == '__main__':
	iterations = 1_000_000
	prizes = [0.01, 1, 5, 10, 25, 50, 75, 100, 200, 300, 400, 500, 750,
	          1000, 5000, 10000, 25000, 50000, 75000, 100000, 200000, 300000, 400000, 500000, 750000, 1000000]

	# prizes = [0.01] * 25 + [1_000_000]

	total_prize = 0
	runs = 0
	for i in range(iterations):
		outcome = simulate_deal_or_no_deal_with_short_circuit(prizes=prizes, swap=False)
		if outcome:
			runs += 1
			total_prize += outcome

	print(f"Average prize if you don't swap ({runs} runs): ${total_prize / runs}")

	total_prize = 0
	runs = 0
	for i in range(iterations):
		outcome = simulate_deal_or_no_deal_with_short_circuit(prizes=prizes, swap=True)
		if outcome:
			runs += 1
			total_prize += outcome

	print(f"Average prize if you do swap ({runs} runs): ${total_prize / runs}")

monty_hall.py

import random


def simulate_monty(door_count=3, swap=False) -> bool:
	# setup
	doors = ["🐐"] * (door_count - 1) + ["🚗"]
	random.shuffle(doors)

	# our turn
	my_door = random.randrange(0, door_count)

	# Monty's turn
	if doors[my_door] == "🐐":
		montys_door = doors.index("🚗")
	else:
		montys_door = random.choice(
			[door for door in range(len(doors)) if door != my_door]
		)

	# our turn
	if swap:
		my_door = montys_door

	# result
	return doors[my_door] == "🚗"


if __name__ == '__main__':
	runs = 1_000_000
	doors = 26

	wins = 0
	for _ in range(runs):
		wins += simulate_monty(door_count=doors, swap=False)

	print(f"We won {wins} times out of {runs} without swapping.")

	wins = 0
	for _ in range(runs):
		wins += simulate_monty(door_count=doors, swap=True)

	print(f"We won {wins} times out of {runs} while swapping")