Somewhere behind the glare, three hundred people are screaming advice at you at once. The host — silk suit, microphone like a torch — sweeps his arm toward three enormous doors. Behind one of them: a brand-new car. Behind the other two: goats. Real ones. You can hear one of them chewing the scenery.
You point at a door. The audience roars. But the host doesn't open it. Instead he strolls to a different door — one he knows perfectly well — and swings it open. A goat blinks out at the cameras. The audience howls.
Then he turns to you with a grin that has ended marriages: “Do you want to switch to the last door?”
Your gut says it doesn't matter — two doors left, fifty-fifty, right? Your gut is about to lose you a car. In 1990, that same gut feeling made roughly ten thousand people — including nearly a thousand PhDs — write furious letters to the woman who got it right. Play the game below and find out what they couldn't believe.
Pick a door. The host opens a goat door. Then make the call: stay or switch. The scoreboard remembers how each strategy treats you.
This is exactly how the doubters were finally convinced — not by argument, but by repetition. Marilyn vos Savant asked America's math classrooms to play the game over and over; the great Paul Erdős only surrendered when a computer simulation showed him the tally. Here's yours.
Here's the version that flips the switch in almost everyone's head. Same game — but 100 doors, one car, 99 goats. Pick a door. Then watch the host, who knows where the car is, throw open 98 goat doors, leaving just yours… and one other, suspiciously untouched.
Your first pick had a 1-in-100 chance. That never changed. So what are the odds the car is behind the one door the host carefully stepped around?
In the three-door game the logic is identical, just smaller: you pick wrong 2 times out of 3 — and every time you've picked wrong, the host's goat-reveal is a giant golden arrow pointing at the car. Switching wins exactly as often as your first guess was wrong: ⅔.
A reader named Craig F. Whitaker mailed the puzzle to Parade magazine's “Ask Marilyn” column — written by Marilyn vos Savant, then listed in the Guinness Book for the world's highest recorded IQ. She answered, correctly: switch — you'll win twice as often.
Then the mail arrived. About 10,000 letters, the great majority telling her she was wrong — close to 1,000 signed by PhDs, many on the letterheads of math and science departments. Flip the envelopes to read what they actually wrote. (These are real.)
She didn't budge. She ran the numbers again — four columns in all — and then made a masterstroke: she asked school classrooms across the country to play the game themselves with paper cups and prizes. Tens of thousands of students ran the experiment. The cups didn't care about anyone's credentials: switching won about two-thirds of the time, everywhere.
By the time the New York Times put the story on its front page (July 21, 1991), the tide had turned. One of her fiercest critics, Dr. Robert Sachs, wrote back to apologize — “I vowed as penance to answer all the people who wrote to castigate me,” he said. And Monty Hall himself? He ran 30 trials at his own dining-room table with cardboard doors, an ignition key for the car, and raisins standing in for the goats — and watched switching win, exactly as she'd promised. “Our brains are just not wired to do probability problems very well,” Harvard's Persi Diaconis told the Times. The goats, presumably, declined to comment.
Seven questions stand between you and the Big Deal of the Day. No goats will be harmed by wrong answers — only your score.