Stay win rate
Not run
Monty Hall Simulator
Simulate stay and switch strategies under the classic host-knows Monty Hall rules.
At a glance
- Computes
- Win rates for staying and switching over repeated games, against the exact probabilities.
- You supply
- Number of doors, trials per run, animation speed, and a random seed.
- Use when
- You need the switching advantage demonstrated rather than asserted.
- Assumes
- The host always knows where the prize is and always opens a losing door.
Switch win rate
Not run
- Exact stay probability
- 33.3%
- Exact switch probability
- 66.7%
- Trials completed
- Not run
Exact probabilities stay fixed; simulation varies by seed.
Run the simulation to fill Monte Carlo metrics and convergence.
Win rate against Trial; reference at Exact switch probability
| Trial | Stay wins | Stay rate | Switch wins | Switch rate |
|---|
P(stay) = 1 / doors; P(switch) = (doors - 1) / doors
How?
How this is calculated
The simulator uses the standard host-knows rule set: the prize is placed uniformly, the contestant chooses uniformly, the host opens losing unchosen doors, and switching wins exactly when the initial choice was wrong.
Formula: P(stay) = 1 / doors; P(switch) = (doors - 1) / doors
Sources
- Wolfram MathWorld Monty Hall Problem. Wolfram MathWorld. Retrieved .
- Monty Hall problem bibliography. Wikipedia. Retrieved .
Method last reviewed