Monty Hall Host Policies
Change the host’s policy to see why the same goat reveal can imply different odds.
Free theory articleChange the host’s policy to see why the same goat reveal can imply different odds.
Concept & interpretation
The Monty Hall problem is a famous probability puzzle based on a television game show. A contestant chooses one of three doors, hoping to win a car hidden behind it. The other two doors conceal goats. After the initial choice, the host opens one of the unchosen doors to reveal a goat. The central question is: should the contestant stay with their original choice or switch to the remaining closed door?
Experiment
You can test these conditions in the Monty Hall Host Policies module.
- Set the Host to "Informed".
- Set the Chosen door to 1 and the Opened door to 3.
- Observe that the Stay probability is 0.333333333333333 and the Switch probability is 0.666666666666667.
- Now change the Host to "Uninformed", keeping the doors the same.
- Observe that the Stay probability becomes 0.5 and the Switch probability also becomes 0.5. The observation probability (that the host opens door 3 and reveals a goat) drops to 0.333333333333333.