Understanding the Monty Hall Problem

This is another example of something that is very counter intuitive but has been proved mathematically and empirically beyond a shadow of a doubt.  Professional risk takers use things like this to put you on the "wrong side" of a contract/deal.

The Monty Hall problem is a counter-intuitive statistics puzzle:

• There are 3 doors, behind which are two goats and a car.

• You pick a door (call it door A). You’re hoping for the car of course.

• Monty Hall, the game show host, examines the other doors (B & C) and always opens one of them with a goat (Both doors might have goats; he’ll randomly pick one to open)

Here’s the game: Do you stick with door A (original guess) or switch to the other unopened door? Does it matter?
Surprisingly, the odds aren’t 50-50. If you switch doors you’ll win 2/3 of the time!
Today let’s get an intuition for why a simple game could be so baffling. The game is really about re-evaluating your decisions as new information emerges.

http://betterexplained.com/articles/understanding-the-monty-hall-problem/