The Monty Hall problem

A pub is (A) the best place to have a discussion (B) the worst place to have a discussion. A couple of days ago I had a lengthy discussion with a friend in a pub about the Monty Hall Problem. In short the Monty Hall problem is the following:

Imagine yourself in a gameshow, you can pick out of 3 doors, after 2 doors will be a goat after 1 door you will have a brand new car. Lets say you pick door 1, now the showhost is opening an other door and asks you if you want to stay with your original pick or you still want to switch. In my opinion switching will increase your changes of winning. The pictures below will ilustrate why.


In the beginning situation you will have a 1/3 change of picking the correct door. When you pick this door the change that the car is behind one of the other doors is 2/3 (2*1/3). Now the showhost is opening one of those doors so you know that you that the car is not behind this door and the 2/3 change is now on one single door. Making it a better pick than your original door, which still has a 1/3 change.

This little puzzle is the source for some discussion, I had the discussion and a lot of other people did also have very very heated debates about this. Try to make up your own mind and google some on the topic. A nice brain trainer.....