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.