Monty Hall Problem Calculator

Compare staying versus switching in the Monty Hall problem.

Win by switching (%) 66.667

Win by staying (%) 33.333

Formula: stay = 1/N; switch = (N−1)/(N·(N−2))

Step-by-step with your numbers:

1. Values used:

2. Number of doors = 3

4. Win by switching = 66.667%

5. Win by staying = 33.333%

Did we solve your problem today?

After the host opens one losing door, switching beats staying — counterintuitively.

The math behind it

Staying wins 1/N; switching wins (N−1)/(N(N−2)) when the host opens one door. For 3 doors that's 2/3 vs 1/3.

3 doors → stay 33.3%, switch 66.7%.

Why is switching better?

Your first pick is usually wrong, so the host's reveal concentrates the prize on the other door.