The role of probability in solving the Monty Hall problem

[Excited Penguin]

Then the choice has been 50/50 all along, and it doesn't change in the least. You're just either in on it or not, that's all that changes. The chances of you being right, however, are the same throughout.

If you think the odds are ever 50/50, then you simply don't understand the math. The odds are one in three if you don't switch and two in three if you do switch after Monty's reveals that one of the doors you didn't choose is a goat..  The only way  you'd get to 50/50 is if Monty showed you a goat first, and then you choose either of the remaining two doors.  But that would be a different and not very interesting puzzle.

The odds are not one in three since there were only ever going to be two doors to choose from in the end, not three, since he was going to eliminate one all along. You can't both have your cake and eat it. When he shows you the goat is irrelevant, all that matters is that he does. And the fact that he only lets you choose between two possible doors doesn't affect the chances in the least. They are still two doors you have no knowledge of, the third one you do get information about after your first decision, regardless of whether you know this will happen or not.


As I said, just a trick. How deluded can people be about it is particularly interesting though. Even explaining it to you on your own terms doesn't seem to work. Fascinating.