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This got me closer to understanding. But, after 999,998 doors are opened, although the one other door is conspicuously closed, my door is also closed. That seem
by oswald433 6y ago
This got me closer to understanding. But, after 999,998 doors are opened, although the one other door is conspicuously closed, my door is also closed. That seems conspicuous, too. In that moment, there are 2 doors to pick from and so 50/50 makes sense.
As some other comments have mentioned, I think this isn't a fully satisfying explanation because it's hard to reason about the difference between a general strategy vs. an in-the-moment choice; why does it matter that I've watched Monty narrow the choices down to 2 doors, vs. seeing 2 doors from the start?
- danielscrubs 6y agoIt’s easier to think that you aren’t opening 1 door. You are opening 999,999 doors, someone else just did it for you.
- oswald433 6y agoGreat way of phrasing it
- ZephyrBlu 6y agoI think the 1 million doors explanation does a very poor job of explaining why switching is the correct choice and only gives a more intuitive answer, not more intuitive understanding. This is how I understand the Monty Hall problem (Using 3 doors): 1) You are asked to choose a door from A, B or C. You choose A. Probabilities: p(A = Car) = 1/3 p(not A = Car) = p(B or C = Car) = 2/3 2) Monty opens a door and shows you a goat. Let's say he opens door B and gives you the choice to switch from door A. Probabilities with B eliminated: p(A = Car) = 1/3 p(not A = Car) = p(C = Car) = 2/3 3) The probability of the car being behind door A remains unchanged at 1/3, therefore the probability of the car being behind not A is also still 2/3. Since door B has been eliminated, this means the probability that the car is behind door C _must_ be 2/3! Therefore, we choose to switch from door A to door C.
- chippy 6y agoThank you!
- chrisweekly 6y agoBravo! This explanation wins in every way.
- smogcutter 6y agoMonty never opens your door until the end of the game. So Monty opening 999,998 other doors doesn’t give you any information about your door, just the other one that remains closed. If you made a one in a million guess the first time, your door has a car. If you didn’t, the other remaining door must have the car. Which do you choose?