Monty Hall

This is a continuation of the previous posts under this title.

The essential element in the Monty Hall problem is that he knows where the car is, and will never reveal it - so if you've chosen badly (two-thirds chance) he is bound by the rules to implicitly tell you where the car is (behind the other door). It is this that makes swopping worthwhile. But now suppose he doesn't know where the car is - suppose he simply opens one of the two doors you haven't chosen at random. What then? Well, a third of the time you will have chosen the correct door, and you will win the car, a third of the time MH will open the door with the car behind it (and we will assume that when this happens the game is void) and a third of the time the car will be behind the "other" door. So swopping doors simply exchanges one one-third chance for another one-third chance, and so there is nothing to be gained. I have to say that I find this more difficult to get my head round - my instinct tells me that if I have chosen Door A, MH has opened Door B and shown it to be empty, then using the logic in the previous post, I must double my chances by swopping to Door C, irrespective of whether MH knows where the car is or not. But that in fact is wrong, and we'll look at this next time in what (hopefully) will be the last in this series of posts.