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The Monty Hall Paradox

The last Mythbusters* episode I watched tested the Monty Hall Paradox. The last time it was popular in mainstream was on the game show Let's Make a Deal.

Essentially, contestants are presented with three doors. Behind one door is a BRAND NEW CAR!!! and behind the other two are goats (the non-prize). The objective is to pick a door. Then the host will open one of the other two doors that does not contain the car. The contestant is then given the option to switch to the other unopened door or stick with their original door.

It's been widely accepted that switching will always increase your chances of winning the car. But in true Mythbusters fashion, Adam and Jamie re-created the game show and recruited a bunch of people to participate in an effort to test this theory. Each participant picks an initial door, then one of the other doors would be opened and the participant would decide if he/she wanted to switch or stick. This worked well but it was time consuming and there were a limited number of people. So they tried another method.

The two built a system that allowed them to test the scenarios quicker. It had two sections, with 3 doors each. Jamie was the participant on one section and Adam, the other. To test if switching is better, Jaime would always stick and Adam would always switch. They did this 100 times with the car being behind a different door each time.

At the end of the 100 rounds, Adam, the switcher, won the car many more times than Jamie did. About twice as much.

Being the eternal skeptic, I decided to test it out myself. For the sake of transparency, I JSFiddled it so you can see the logic. The code creates 3 doors and 2 players. In each round, it randomly selects one of the doors as the winning door. Then both player 1 and player 2 randomly select a door. Player 1 always stays and player 2 always switches. Everytime a player ends with a door with the prize, she gets a point. If you run the code with...say...10,000 round, you can see player 2 always has about twice as many points.

Still don't understand why this is? Neither did I..until I watched this video.

*I love the show and the people on their team are my heroes. Some of the myths they take on are just an incredible undertaking...like the "Dropped vs. Fired Bullet" myth.

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