re: Marilyn vos Savant and the history of the Montel Hall question

Thanks Monk for proving my point.

In your explanation, you are absolutely correct--but only because you consider it all one game.

However, the problem is always described by asking what the odds are of choosing the car once one door is eliminated (and is always a goat). That IS a new game, and the probabilities are 50/50. If mathematicians don't like the fact that people perceive it correctly to be a new game, that is fine, they can continue to run it all together as one multi-stage probability exercise. But that is mere slight of hand, not math.

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Again, the problem with this riddle is that the mathematical explanations always start with the premise that you must carry forward the old 33/66 probabilities from the first problem into the second. That is the cheat--you don't. The Monty Hall problem really is a 33/66 probability problem changed into a 50/50 problem, but discussed mathematically (incorrectly)after the basic premise has been changed as if it is still a 33/66 problem.

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Your logic here is incorrect, and the reason so many people have trouble with it.

It is still a 33/66 problem after one goat door is eliminated.

Look at it this way.

Host: You can either pick one door or two doors.

You obviously pick two doors.

Host: But wait; if you pick two doors, I will show you a goat behind one of your doors before opening your other door. Would you like to change to just one door?

Since you already know that at least one of the two has a goat, you wouldn't care and would go with the two doors anyway.

That's the exact math behind the problem as is. You are choosing between 1 door or two doors, one of which is revealed to contain a goat.