Tuesday, 29 May 2012

Monty Hall Problem

I like to think of myself as a fairly smart guy. I like to think that I have a very logical mind. I like to think that I can work most things out, given enough time.

But there is one thing that I cannot get my head around: the Monty Hall problem.

The idea is simple: a game show host (Monty) as you to pick one of three door to get a big prize. You pick one of the doors (say A). He then opens another door (say B) which does not reveal the car and asks if you would like to change your choice to the other door (C) or stick with the one you have chosen.

When presented with this situation, most people will not change. Why should they?

But the best option here is to change. Doing so changes you chances of winning from 1 in 3 (picking one door from three) to 1 in 2 (picking one door from two).

My mind understands this. On some level.

But there is another part of my mind which cannot see how changing from one of the three doors to another one of the three doors could actually impact the likelihood of winning!

I have been aware of this conundrum for some years so I have concluded that my mind will never be able to full wrap itself around this one.