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.
The numeric output will vary, but look something like:
> print(summary(games$strategy) / nrow(games))
The following code does this in a rather short R example: