Monty Hall Simulator

Stay vs switch, simulated and exact

You pick one of N doors hiding a single car. The host, who knows where the car is, opens K other doors that all hide goats, then offers to let you switch. Staying keeps your original 1/N odds; switching concentrates the rest of the probability onto the doors the host left closed.

P(stay) = 1/N = 1/3, P(switch) = (N−1)/(N(N−1−K)) = 2/3
Win by staying
33.33%
1/3
Win by switching
66.67%
2/3
Switching wins 2× as often as staying.
Simulated · Stay
33.61%
3,361 wins · ±0.47 pts (1σ)
Simulated · Switch
66.39%
6,639 wins · ±0.47 pts (1σ)
of 10,000 games
Monty Hall SimulatorWith 3 doors and the host opening 1 goat door(s), staying wins 33.33% of the time and switching wins 66.67% of the time.×1your pick×1opened×1switch?33.33%Stay66.67%SwitchSimulated