Monday, April 14, 2008
The Monty Hall Problem
This is unbelievable. It is the most counter-intuitive thing ever (well, aside from curved space-time). It's the Monty Hall game, where you are given three doors to choose from. Behind one door is a car, behind the other two are goats. You choose a door, but before it is opened you are shown a goat behind one of the other doors. You are then given an opportunity to stay with your guess or switch your choice to the other door.
It doesn't seem like it would matter - now that there are two doors left you have a 50/50 chance of getting the car, right? Nope. You are vastly more likely to win if you switch your choice.
I could explain why, but it's better to check it our yourself. You can play the game here: http://www.nytimes.com/2008/04/08/science/08monty.html
I played it 200 times (yes, busy day at work). 100 times I stayed with the original door (I won 31% of the time). 100 times I switched doors (I won 63%). The site has an explanation of how it works.