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Monty Hall Switching Probability Calculator — result sheet
Calculate stay and switch win probabilities for a generalized Monty Hall game with one prize door.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Stay win probability=1/doors; switch win probability=(doors−1)/doors when the host reveals all but one losing alternative.
The host rule is explicit because switching probabilities depend on the host knowing the prize and always revealing a losing door.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of doors — minimum 3; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Number of doors | 3 |
Stay probability =33.333%; switch probability =66.667%.
Assumptions and limits
- One door contains the prize and the initial choice is uniform.
- The host knows the prize and reveals every eligible losing door except one switching alternative.
- Random host behavior, multiple prizes, and strategic host choices are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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