Standard and Generalized Versions of the Monty Hall Problem

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 .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Related Curriculum Standards

US Common Core State Standards, Mathematics