Stay or switch?
Pick a door, then stay or switch. After that the page plays 10,000 games each way, so you can see which one wins more often.
One door hides a car. The other two hide goats. Pick a door.
Your rounds: none yet.
Always stay: - won
One third is 3,333
Always switch: - won
Two thirds is 6,667
Each run draws 10,000 fresh games from your browser's random numbers. A fair run usually lands within about 100 games (one point) of those figures. A gap of more than 3 points (300 games) would mean a fault.
The rules this page follows
One of three doors hides a car, the other two hide goats. You pick a door. The host knows where the car is. He always opens a goat door you did not pick, and always offers you the switch. If both other doors hide goats, he picks one of them at random.
The nine cases
| Car behind | You pick | Stay wins | Switch wins |
|---|
Staying wins in 3 of the 9 cases, one third. Switching wins in the other 6, two thirds. When you first pick a goat, the host has to open the other goat, so the door left over hides the car.
If the host does something else
If the host did not follow these rules, the answer changes. This page does not model that. This page follows the rules above. A real game could follow other rules.
Where the random numbers come from
Every draw uses your browser's own secure random numbers. One byte value in 256 is thrown away and drawn again, so each door has exactly the same chance. This page only tests the draws in this browser.