The Monty Hall problem, played 100 times.
Don't take anyone's word for it. See it for yourself.
Most people do not believe the answer until they watch it happen. So play 100 games. We keep the tally for you. At the end you see how often switching would have won, and it lands near 2 times in 3. Your run is then added to everyone else's.
It takes about ten minutes. No account. No sign-up.
How a game works
One. You pick a door. The car is behind one of the three.
Two. A door you did not pick opens. It always shows a goat. It is never the car.
Three. You stay or switch. Every door opens. Then the next game starts.
What the Monty Hall problem is
The puzzle is named after Monty Hall. He hosted an American game show called Let's Make a Deal, which began in 1963. Steve Selvin wrote the puzzle down in 1975. It became famous in 1990, when Marilyn vos Savant answered it in a magazine column and said you should switch. About ten thousand readers wrote in to tell her she was wrong. Around a thousand of them had doctorates. She was right.
Most people get it wrong for the same reason. Two doors are left, so it feels like a 50-50 guess. It is not. The door that opens is not picked at random. The host knows where the car is, and he never opens that door. So the open door tells you something, and all of it points at the door you did not pick.
Why switching wins
Say you always pick door 1. The car can only be in three places, and each is as likely as the others. So you can just list them all.
The car is behind door 1, the door you picked. The host opens door 2 or door 3. Either way it is a goat.
Staying wins. Switching loses.
The car is behind door 2. The host cannot open your door, and he will not open the car. So he opens door 3.
Switching wins. Staying loses.
The car is behind door 3. For the same reason, he opens door 2.
Switching wins. Staying loses.
Count them. Staying wins in 1 case out of 3. Switching wins in 2 cases out of 3. That is the whole puzzle.
If it still feels wrong, picture 100 doors instead. You pick one. The host then opens 98 doors, every one a goat, and leaves a single door shut. Would you keep your first guess, or take the door he went out of his way to leave alone?
Why a hundred games
One game proves nothing, and ten games can go any way. Over a hundred games the two answers pull apart. If switching really wins 2 times in 3, your first pick should come out wrong about 67 times. If the two shut doors were really an even bet, it would be about 50. A run of a hundred is long enough to tell those two numbers apart. A run of ten is not.
What we record
- The door you picked first, the door that opened, and whether you stayed or switched.
- Where the car was.
- Whether you played all 100 games or stopped early.
Nothing that can identify you. No account, no email, no name. See what we store.
What you get at the end
- How many of your 100 first picks were wrong. The expected number is 67.
- How often you ended up with the car, and what each strategy would have won you.
- Everyone else's numbers, and whether they add up to two thirds.