probabilityfields

Okay so you’re on the classic game show Let’s Make A Deal, and Monty Hall shows you three doors. Behind one of those doors is a NEW CAR! But behind each of the other two doors is a stinky goat. So you pick Door Number 1.

But wait, Monty says he will reveal one of goats behind one of the other two doors. He opens Door Number 3 and there it is, stinking of piss and feta. So now you’re left with two doors, and Monty gives you the option to switch doors (much like Howie Mandel does today).

So…do you switch? Does it matter? The odds are 1 in 3 no matter what, right? Might as well keep Door Number 1. Well, you’re wrong and now you’re the proud owner of a stinky goat. In fact the odds are 1 in 3 if you don’t switch, but they improve to 2 in 3 if you switch.

Think of it this way, if you picked the car first, then switching would get you a goat. But if you picked a goat, then switching would get you a car. There’s a 1 in 3 chance of picking the car first (losing), and a 2 in 3 chance of picking the goat first (winning).

The New York Times let’s you play the game and gives a wonderful graphic explanation here.