The Monty Hall problem: why switching doors doubles your chances
The Monty Hall problem: the game show puzzle almost 1,000 PhDs got wrong
On a game show, you pick one of three doors. The host opens another one, shows a goat and offers you a switch. Two doors are left, so it must be 50-50. After a magazine column in 1990, thousands of readers, close to 1,000 of them with a PhD, wrote in to say so. They were wrong.
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1
You are on a TV game show, and Rono is the host. Behind one of these three doors is a new car. Behind each of the other two is a goat.
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2
Rono hid the car himself, so he knows where it is. You don't. You pick door 1, and it stays shut for now.
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3
Rono never opens your door, and he never shows the car. He opens door 3, and a goat looks out at you. Then he asks if you want to switch to door 2.
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4
Two closed doors are left, and one of them hides the car. It feels like 50-50, so why change? Most people stay. In one study, only 13 people in 100 switched.
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5
In 1990, a reader sent this same puzzle to Marilyn vos Savant, who answered questions in Parade magazine. Her answer: switch. You win the car 2 times in 3.
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6
About 10,000 letters came back, most of them to say she was wrong. Close to 1,000 were signed by people with a PhD, and many came from math departments.
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7
She was right. In 1991, Monty Hall, the real host the puzzle is named after, played it at his dining table. In 10 games where the player stayed, the player won 4 cars. In 10 games where the player switched, the player won 8.
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8
Still, two closed doors and one car look like a fair coin toss. So where does door 2, the door you can switch to, get its extra chance?
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Go further
Where the puzzle comes from.