You're on a game show. There are three doors. Behind one is a car. Behind the other two are goats.

You pick a door — say, door number one.

The host, who knows what's behind every door, opens one of the other two — say, door number three — and reveals a goat. Then he asks: do you want to switch to door number two?

Should you?

Your gut says it doesn't matter

Two doors left. One car. Surely it's fifty-fifty?

That's what almost everyone thinks. It's wrong.

You should switch. If you switch, you win the car two times out of three. If you stick, you win only one time out of three.

Why switching works

Here's the simplest way to see it.

When you first pick, you have a 1-in-3 chance of choosing the car. That means there's a 2-in-3 chance the car is behind one of the other two doors.

Now the host opens one of those other two doors — and he will always open a door with a goat behind it. He's not choosing randomly. He's giving you information.

So that 2-in-3 chance that belonged to "the other two doors" is now concentrated entirely on the one door he left closed.

Still not convinced? Imagine a hundred doors. You pick one. The host opens ninety-eight doors, all with goats, leaving yours and one other. Would you switch now?

The letters

The puzzle was named after Monty Hall, host of the American show Let's Make a Deal. In 1990, a reader posed it to Marilyn vos Savant, who wrote the "Ask Marilyn" column in Parade magazine. She gave the correct answer: switch.

The mail poured in. Thousands of letters told her she was wrong, many of them condescending, and a striking number came from people signing themselves with PhDs. Some scolded her for spreading mathematical ignorance.