Switch or stay?
Three doors. Two goats. One car. Put your intuition to the test.
THE MONTY HALL PROBLEMRound 1
Pick your first door.
A car is hidden behind one door. Which one will you choose?
The host knows where the car is and always reveals a goat.
How does it work? The rules & the mathematics
The host’s promise
The car is placed randomly. After your first pick, the host opens an unchosen door with a goat, then always offers you a switch. If either goat door is available, the host chooses randomly.
Why switching wins more often
Your first pick has a 1 in 3 chance of being the car. Staying wins only when that first pick was right. Switching wins whenever your first pick was wrong: 2 out of 3 times, on average.
Expected win rates: switch ≈ 66.7%; stay ≈ 33.3%. Small samples can look very different. Try both strategies over many rounds.