Monty Hall Problem Calculator
Calculate the probability of winning the classic Monty Hall problem by staying with your original choice versus switching doors.
About the Monty Hall Problem Calculator
In the Monty Hall problem, you pick one of several doors hiding a prize behind just one of them. A host who knows where the prize is then opens every other losing door except one, and asks whether you want to switch to that remaining door.
Formula: P(win by staying) = 1 ÷ n · P(win by switching) = (n − 1) ÷ n, where n is the number of doors
Your first pick has only a 1-in-n chance of being correct, and that never changes just because other doors are opened. Since the host's knowledge concentrates all the remaining probability onto the one door left standing, switching always wins more often than staying — for the classic 3-door version, that's 2/3 versus 1/3.