Let’s Make a Deal!

I recently read about a brainteaser involving probabilities related to the old game show Let’s Make a Deal. After much brain pain, I finally believe I know why the answer is what it is. The script below is meant to “prove” the answer right. (I won’t try to explain what’s going on here mathematically. I’ll leave that to the experts.)

The script simulates 100 games of Let’s Make a Deal. First, it randomly picks one of three “doors” as the winner. Then it randomly selects the player’s choice of doors. Next, it removes one of the two losing doors and records whether the “player” would have won in each of the following three cases:

  1. she always stayed with her original choice of door
  2. she randomly chose to stay or switch doors, or
  3. she always switched doors

The lists below will display a tally of wins and losses.

New! I added a version of this page that does the calculation 10,000 times for greater accuracy. Neato!

Newer! Kahn Academy has an excellent explanation of the Monty Hall Problem. Worth the 7:23!

Always Stay 50/50 Switch/Stay Always Switch

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