I think the k doors case is the best way to develop an intuition for the problem.
Suppose there were 100 doors, you choose one. Then Monty goes ahead and opens 98 non-winning doors from the remaining 99, leaving one door unopened. I think the decision to switch makes more intuitive sense here, and then you can see that the intuition still applies when you scale back to 3 doors.
Great explanation!
I think the
kdoors case is the best way to develop an intuition for the problem.Suppose there were 100 doors, you choose one. Then Monty goes ahead and opens 98 non-winning doors from the remaining 99, leaving one door unopened. I think the decision to switch makes more intuitive sense here, and then you can see that the intuition still applies when you scale back to 3 doors.
You are right! Since he never chooses that winning door so we increase our belief that is the one every time he opens the new door.