Perhaps a real mathematician can help me here. I just don’t understand the supposed solution to the Monty Hall problem.
I understand the reasons that it is supposed “unintuitive” but I still believe them. Allow me to forumlate the objection in a way that seems novel.
Once Monty reveals the Donkey, and you are given what is in reality a new problem – pick a door with a 50% probablity of any one being the right one. The thing is that switching from your originally selected door doesn’t change the probability of the door being the right one. Merely the act of revealing the donkey behind one of the unselected doors does.
So what’s critical is selecting a door under these new odds – which is exactly what Monty is letting you door. The key for me is that even choosing to keep the door you already have is a selection.
What am I missing?