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I knew the theoretical answer going in (1/3 vs 2/3) so my first instinct was to just print those values and call it done.
First, clarify the problem setup and assumptions (e.g., 3 doors, one car, host always reveals a goat and offers a switch). Then, outline a Monte Carlo simulation with a fixed random seed, running n rounds for each strategy, and compute the empirical win probabilities. Finally, round the results to two decimal places and discuss the theoretical probabilities (1/3 for stay, 2/3 for switch) as validation.
Pro tip: Emphasize the importance of a fixed random seed for reproducibility and mention that with large n, the Monte Carlo estimates should converge to the theoretical probabilities, demonstrating the law of large numbers.
Confirm the rules: 3 doors, one car, host knows where the car is, always opens a goat door, and always offers the switch. Define n as the number of rounds per strategy and set a fixed random seed.
For each round, randomly place the car, have the contestant pick a door, and have the host reveal a goat door. Then record the outcome for staying with the original pick and for switching to the other unopened door.
Write code (e.g., Python) to run n rounds for each strategy, using the fixed seed. Count the number of wins for stay and switch, then divide by n to get probabilities.
Round the win probabilities to two decimal places and present them clearly. Optionally, compare with theoretical values (1/3 and 2/3) to validate the simulation.
Explain why switching is advantageous and how this relates to A/B testing (e.g., comparing strategies). Mention that increasing n improves accuracy and discuss potential variations (e.g., more doors).
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