The Monty Hall Problem!

The Monty Hall problem is a brain teaser with an answer that most peole find surprising.

Imagine that you are a contestant on a game show, the "Monty Hall Game". The host of the show, Monty Hall himself, points to three doors standing in front of you. He explains that behind one of the doors there is a brand new, luxury car, and behind the others there are goats. You get to keep the contents of whichever door you choose to open.

You pick a door, but before you can open it Monty stops you and says "To help you out, and make things more interesting, I'm going to open one of the other doors, one that has a goat behind it." He opens one of the doors you didn't pick, and sure enough, there's a goat inside. "Now, would you like to stick with your original guess, or switch?"

What do you do?

Most people think that it doesn't matter if they switch or stay, that they have a 50/50 chance of winning either way. But you actually have a better chance of winning the car by switching your guess. In fact, if you stick with your original guess you only have a 33.3% chance of winning, but if you switch your odds go up to 66.7%. But why? This website aims to help you understand this unexpected answer using real data, simulations, and graphical representations of the problem.