Three doors. One informed host.
Your first choice wins one time in three. An informed host always opens an unchosen goat door and always offers a switch. Switching wins precisely when your first choice was wrong.
Inside this model
The prize is uniform across three doors. If the host has a choice of goat doors, the host chooses randomly. Batch results evaluate staying and switching on the same games; their wins sum to the number of games.
Out in the world
A practical use
When interpreting an interview shortlist or a revealed clue, ask how the information was selected. A deliberate reveal and an accidental observation can support different inferences.
A useful lens. Not a universal law.
- The two-thirds switching result depends on this host policy. A host who sometimes reveals the prize or selectively offers a switch changes the problem.
Further reading
Explore the original research or the teaching reference behind this experiment.
David Aldous — The role of modelling in Monty Hall ↗