# Standard and Generalized Versions of the Monty Hall Problem

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A prize is concealed behind one of curtains, and game show host Monty Hall asks you to guess where the prize is. After you guess, Monty opens of the curtains that do not conceal a prize (referred to in the Demonstration as "shills"), leaving closed only your original choice and one other curtain. You are given the option of staying with your original choice, or switching to the other closed curtain. Careful analysis shows that, on average, you are better off to switch. This result can be very non-intuitive for the standard case of curtains, but becomes much more plausible when .

Contributed by: John Custy (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

When the game is played with curtains, a strategy of always switching results in a win probability of and a loss probability of .

A discussion of the standard form of this game can be found in (among other places) *The Oxford Companion to Philosophy* under "The Monty Hall Problem". Generalized versions of the Monty Hall problem (including the generalization used in this Demonstration) are discussed in the Wikipedia entry.

## Permanent Citation