Giuseppe Forte

The Monty Hall problem, simulated

A prize sits behind one of three doors. You pick a door. The host then opens one of the two doors you did not pick, and it turns out to be empty. Should you switch to the remaining closed door?

Switching wins two times in three, and the reason is the host’s knowledge. A host who knows where the prize is never opens its door, so the door left closed carries information. A host who opens a door at random might have revealed the prize; when the prize happens to stay hidden, the host’s choice tells you nothing, and switching wins only half the time.

Play the game many times below and watch the shares of wins settle.

With a random host, the shares count only the episodes in which the prize was not revealed: those are the only ones where the contestant faces the same choice.