Compare staying and uniform switching under an informed-host Monty Hall protocol, with optional aggregate simulation.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
Stay probability=1/n. Uniform switching among remaining alternatives wins with probability (n−1)/[n(n−m−1)].
Assumptions and limits
One uniformly located prize. An informed host always opens m losing doors other than the initial choice and always offers switching. The switch choice is uniform among all remaining alternatives. A host who may reveal the prize is another protocol.
Worked example
With three doors and one losing door opened, stay probability is 1/3 and switch probability is 2/3. Optional simulations vary from run to run around the model probabilities.
Worked reading and practical questions
- Monty Hall: The Host’s Rules Are Part of the Probability
- More Doors and Partial Reveals: Which Switching Rule?
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
One uniformly located prize. An informed host always opens m losing doors other than the initial choice and always offers switching. The switch choice is uniform among all remaining alternatives. A host who may reveal the prize is another protocol.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.