I came across the Monty Hall Problem while reading last night, and initially, I thought the author must have been mistaken. Of course, he made no mistake. He did, however, succeed in proving the common failures of human reasoning.

For those unfamiliar with the Monty Hall Problem, a short explanation:

• 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!

The article does a decent job of explaining this baffling situation. You can even play the game yourself. Believe it or not, you win more often when you switch.

I prefer the following explanation: If you picked the car and you switch, you’ll lose every time. On the other hand, if you picked the goat and you switch, you’ll win every time (the car must be in the remaining door since the two goats have already been revealed). Now, remember, there was a 33% chance of picking the car, and a 66% chance of picking a goat. So let’s rephrase that — there’s a 33% that switching will result in losing every time, but there’s a 66% chance that switching will result in winning every time.

Counterintuitive, but true.