File:Monty Hall Problem Simulation.png

English: Results of simulating multiple instances of the (canonical 3-door) Monty Hall Problem.

Each point shows, for the number of instances indicated (x-axis), the proportion (y-axis) of times "switching" wins the prize. For each x-value, 200 simulations are run, and the mean of the proportion of times "switching" wins is plotted in green.

Each instance is simulated in a literal application of the game's rules (and assuming random and independent selection of the prize, the user's selected door, and — where relevant — the door to reveal): by first selecting a random integer from 1 to 3 as the location of the prize, then independently selecting a random integer from 1 to 3 as the player's choice, and then selecting a random integer from 1 to 3 that is neither the prize nor the choice as the reveal, and finally noting whether the prize is neither the choice or the reveal — i.e. whether "switching" wins the prize.

Each point is plotted at ~1% opacity, so that darker points represent multiple occurrences of the same outcome.