I 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

I 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.