From Wikipedia:
The Monty Hall problem is a brain teaser, in the form of a probability
puzzle (Gruber, Krauss and others), loosely based on the American television
game show Let's Make a Deal and named after its original host, Monty Hall.
The problem was originally posed in a letter by Steve Selvin to the American
Statistician in 1975 (Selvin 1975a), (Selvin 1975b). It became famous as a
question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn"
column in Parade magazine in 1990 (vos Savant 1990a):
Suppose you're on a game show, and you're given the choice of three doors:
Behind one door is a car; behind the others, goats. You pick a door, say
No. 1, and the host, who knows what's behind the doors, opens another door,
say No. 3, which has a goat. He then says to you, "Do you want to pick door
No. 2?" Is it to your advantage to switch your choice?

This script simulates the Monty Hall problem and proves that the
contestant is more likely to win if they switch doors!