You all have missed the obvious- the first Monty Hall article was a copyright trap.
Exactly. All this confusion is created when people try to expand it to all the cases, because different people have different ideas about what “all the cases” includes. Does it include the case where Monty doesn’t open any other doors? Does it include the case in which Monty opens another door, but it happens to be the grand prize, so he says “sorry, you lose”? What people don’t seem to realize is that there is not such thing as an isolated probality (they’re kinda like quarks that way); the probability of one event must always be phrased in terms of another event(s) (i.e. what is the probability of X given that Y happens?).
The Ryan, you are correct. That is why the prototypical “Monty Hall Problem” is usually clearly stated in such terms to limit those possibilities. For instance, declaring that in all cases the host knows which prizes are behind which doors, and in all cases the host reveals a dud prize and offers a switch. (And of course the unstated assumption that the contestant wants the car and not a goat.) With those caveats, the probability problem is the sneaky non-intuitive answer of 2/3 rather than 50-50. When not stated with those parameters, the situation is much broader and much less definitive.