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What is the Monty Hall problem?
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Quick answer
The Monty Hall problem is a famous probability puzzle: behind three doors are two goats and one car; after you pick, the host opens a goat door and offers a switch. Counterintuitively, switching wins the car two-thirds of the time, not half.
Key things to understand
- Your first pick has a 1/3 chance of the car; the other two doors together hold 2/3.
- The host knowingly opens a goat, concentrating that 2/3 onto the one remaining unopened door.
- Switching therefore wins 2/3 of the time; staying wins only 1/3.
- It fools almost everyone because the host's knowledge changes the odds — it isn't a fresh 50/50.
People also ask
Why isn't it just 50/50 after a door opens?
Because the host never opens the car or your door — that knowledge transfers the eliminated door's probability to the other door, not to yours.
Does switching guarantee a win?
No. Switching wins about 2 of 3 times; you can still lose a single game, but over many games switching is clearly better.
Who is it named after?
Monty Hall, host of the game show 'Let's Make a Deal,' whose door-reveal format inspired the puzzle.