Monty Hall

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?

5 thoughts on “Monty Hall

  1. > Once Monty reveals the Donkey, and you are given what is in reality a new problem

    You’re not given a new problem. You have been given extra information on the problem you had. In other words, if you forget or ignore what has happened up to Monty opening the door, you are losing information. That information is what increases the odds from 50% to 66% if you choose not to ignore it.

    Another way to look at it: When you choose one door, the odds of the prize being in one of the other two doors is 2/3. In fact, Monty is giving you the chance to choose the other two doors at the same time, so to speak.

    Hope this helps.

  2. You are simply missing, that the person who opens a door for you does this based on his knowledge of the right solution.

  3. It’s simple. The point ist that the act of revealing doesn’t provide an additional information
    about your first choice. Hence, the probabilty, that you already have made the right choice, stays the same.

Comments are closed.