Originally posted by Toe The host's information changes the apriori probabilities for the second choice: Had one picked door 3 initially, switching door would clearly have improved the odds of winning (from 0 to 1/2).
I think that an implicit factor you are not considering is that the host can not reveal what is behind the door that was picked. (i.e., if door 3 were picked initially, the host would open either door 1 or door 2). I believe if you add this constraint into your random number generator you will see the benefit of switching to the door that the host could have opened, but didn't.
a close examination of some of the replies shows that there has been an assumption regarding monty's additional info: the assumption is that monty will not tell you whether the door you origionaly chose is wrong. This is not gaurenteed by the format of the question, but if you do make this assumption, then the odds ARE in favour of switching.
Although I can not prove it, I think that Monty's motivations come into play as well (specifically, if he wants me to win or lose)...which is not stated in the problem.
For example, it is not certain when I make my initial choice that he will reveal a wrong door and give me a switch opportunity. If I choose the right door and he wants me to win, he would end the game right there. Likewise if I choose the wrong door and he wants me to lose.
It's an easy fix though in the wording of the problem. Just add a sentence that states that Monty tells me in advance that he will eliminate one wrong door and offer the opportuity to switch.