What this calculator does
Monty Hall problem works out win probability from staying versus switching after the host reveals losing doors. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaWith n doors, one prize and the host opening all but one of the remaining losing doors: P(stay) = 1/n, P(switch) = (n−1)/n
The inputs explained
| Field | What to enter |
|---|---|
| Number of doors | A number. Starts at 3. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with number of doors
Every other input is held at the calculator’s starting values while number of doors varies. Select any row to load that scenario into the calculator.