Here is a simple way to explain without simulation, or increasing door count, and which breaks the illusion of symmetry.
Clearly, Monty starts with a 2/3 chance of having the prize, and you start with 1/3. Then he always offers you the best of his doors, which is the same thing as offering you both doors and allowing you to look behind both of them before choosing one. It is just that he has peeked behind for you.
So, the doors are not all the same because the door he offers is a "best of two" door.
With regard to the point of the editorial, I think this problem illustrates that controversies will continue either until someone sees a way of explaining things so clearly they are widely understood, or until the general level of sophistication and collateral/related knowledge rises to the point where the large majority of interested people can understand the matter. Both phenomena happen over time. In areas where neither happens, there remain controversies and a struggle for clarity should continue.
posted by Tanj Bennett
September 4, 2008
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