A casino has a new game. A gambler can bet $10 and get a 1% chance of winning $100. If the gambler loses, they can bet another $10, and their chance of winning increases from 1% to 2%. After each loss, the gambler can bet $10, and the chance of winning will increase 1%.
What is the average number of bets the gambler must place to win the $100? Is this game in favor of the gambler or the casino?
The game is definitely in favor of the casino. On average, you would spend over $120 to win $100.
Average number of bets: 12.1667
Here is the Python code to run the simulation.
import random def play_game(): bet = 10 win_probability = 0.01 num_bets = 0 while True: num_bets += 1 if random.random() < win_probability: return num_bets, 100 else: win_probability += 0.01 bet += 10 average_bets = 0 num_iterations = 10000 for i in range(num_iterations): bets, payout = play_game() average_bets += bets print("Average number of bets:", average_bets / num_iterations)