Monty Hall Simulator
The Monty Hall problem is the probability puzzle that fools almost everyone: pick one of three doors, the host — who knows where the car is — opens a different door to reveal a goat, and now you choose whether to stay or switch. This simulator lets you play by hand and also fires thousands of automatic games at once, plotting the running win rate for the switch and stay strategies until they lock onto their true values of 2/3 and 1/3. A generalised mode with up to 50 doors (the host opening all but one of the rest) makes the advantage of switching impossible to miss.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Switching wins whenever your first pick was a goat, which happens with probability 2/3 — so switching wins two games in three over the long run.
- The host’s knowledge is what breaks the symmetry: opening a losing door on purpose leaks information, so the two remaining doors are not equally likely.
- With n doors, switching after the host opens all but one other door wins with probability (n−1)/n — the edge grows as doors are added.
- Runs 100% in your browser — simulations are computed locally on your device.
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