The Monty Hall Problem is famous in the world of statistics and probability. For those struggling with the intuition, simulating the problem is a great way to get at the answer. Randomly choose a door for the prize, randomly choose a door for the user to pick first, play out Monty’s role as host, and then show the results of both strategies.

Simulating the strategies of Monty Hall

The numeric output will vary, but look something like:

> print(summary(games$strategy) / nrow(games))
stay switch
0.342 0.658

The following code does this in a rather short R example: