import random
def simulate_one_game():
# Returns number of tosses needed to get 3 in a row
tosses = []
while len(tosses) < 3 or (tosses[-3:] != ['H', 'H', 'H'] and tosses[-3:] != ['T', 'T', 'T']):
toss = random.choice(['H', 'T'])
tosses.append(toss)
return len(tosses)
def estimate_probability(n_simulations=1000000, threshold=10):
# Count games that take more than threshold tosses
count_over_threshold = 0
for _ in range(n_simulations):
tosses_needed = simulate_one_game()
if tosses_needed > threshold:
count_over_threshold += 1
return count_over_threshold / n_simulations
# Run simulation
n_sims = 1000000
threshold = 10
prob = estimate_probability(n_sims, threshold)
print(f"Based on {n_sims:,} simulations:")
print(f"Probability of needing more than {threshold} tosses: {prob:.6f}")
# Optional: Get distribution of number of tosses needed
def get_distribution(n_simulations=100000, max_tosses=50):
distribution = [0] * (max_tosses + 1)
for _ in range(n_simulations):
tosses = simulate_one_game()
if tosses <= max_tosses:
distribution[tosses] += 1
# Convert to probabilities
distribution = [x/n_simulations for x in distribution]
return distribution
# Print distribution
dist = get_distribution()
print("\nDistribution of number of tosses needed:")
for i, prob in enumerate(dist):
if prob > 0:
print(f"{i} tosses: {prob:.4f}")
