The Monty Hall Problem

The Monty Hall Problem gets its name from the TV game show, "Let's Make A Deal," hosted by Monty Hall. The problem is stated below.

  1. There are three closed doors, behind one of which is a prize (the remaining doors contain "joke" prizes). Monty Hall, the game show host, asks you to pick one of the three doors.
  2. You pick a door (which remains unopened).
  3. Monty opens a door that has a joke prize.
  4. Monty then gives you the choice of either keeping your original choice, or switching to the remaining unopened door.

QUESTION : To maximize the chances of winning a real prize, should you keep your choice or switch (or does it matter)?

NOTE: This isn't really how the actual game show worked. This problem gets its name from the show, because it inspired the problem.

The problem is interesting because most people believe that after Monty shows a losing door, the two remaining unopened doors (whether chosen or not) each have a fifty-fifty chance of being a winning door. One with a real prize, the other with a joke prize. Most people are surprised that this is not the case.

At this time you can choose one of the links below. The applet is a simulation of this problem.

Run the Monty Hall Problem Applet

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