The Monty Hall Problem (Applet)

How to Use this Applet

Basic Operation

  • Follow the instructions shown in the top portion of the applet. The current "step" of the experiment of selecting doors and/or winning a real or joke prize will have a blue background.
  • When all of the doors are opened, a listing of events for the current experiment are displayed in the top portion of the applet. When the mouse button is clicked, the results will be recorded in the chart and in the graph.

Advanced operation

  • Use the popup menu at the bottom left of the applet to select between "SELECT KEEP OR SWITCH", "ALWAYS KEEP", or "ALWAYS SWITCH" modes.
  • "SELECT KEEP OR SWITCH" operational mode is described in the "Basic operation" section above. In this mode the "REPEAT n TRIALS" popup menu is inactive.
  • In "ALWAYS KEEP" or "ALWAYS SWITCH" modes, the second mouse click step is eliminated. You select a door with a mouse click and Monty then opens a door with a "JOKE" prize. The next step of keeping or switching your selection is predetermined; and all of the doors will be opened, showing you the result. The next mouse click will record the result.
  • In "ALWAYS KEEP" or "ALWAYS SWITCH" modes, the "REPEAT n TRIALS" popup menu will become active. You can use this popup menu to repeat the experiment repetitively, thus allowing a faster approach to the resulting theoretical limit. Initially you are better off NOT using this feature. Going through the experiment many times manually will result in a better feel for what is happening, and give a greater reinforcement to believing the result.


  • The maximum number of cycles is one-thousand. When the maximum is reached, you will be required to select the "RESET" button to begin the process again.

See the Description of the Monty Hall Problem

See the Result (and Proof of the Result) of the Monty Hall Problem