The Monty Hall problem is nominally based on the American television game show “Let’s Make a Deal” and named after its original host, Monty Hall. It is so often described as a brain teaser in the form of a probability puzzle. In fact, it’s merely a riddle. The simple riddle with a simple solution has been made to be infinitely more complicated and difficult to understand by calling it a probability puzzle, when probability has zero to do with the actual problem.
Suppose you’re on a game show, given the choice of three doors. Behind one is a car; behind the others, goats. You pick a door. The host, who knows what’s behind each door, opens one of the other doors to reveal a goat. He asks: do you want to switch? You should always switch. Your original door had a 1-in-3 chance. The host’s action gives you no new information about your door — only about the other two. Switching wins 2 out of 3 times.