I think a way to answer Bruce Sampsell's question might be to run a simulation with the choice being made after the host has opened the door, and show that that agrees with his prediction. Thus you show why his intuition is correct, and also why his intuition is wrong (depending on whether one's first choice is made before or after the host opens the door). I find it necessary to satisfy my intuition - if I can't show why it is wrong, how do I my "right" answer is right?
posted by Andrew Tan
August 28, 2008 @ 9:32 AM
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 @ 12:43 PM
Liked the above article. I frequently convey technical information; I find it easy to get someone to agree that my analysis is correct, but harder to get them to agree enough to act on it.
For the Monte Hall problem I have a simple method that helps convince people that my answer (the correct answer of switching doors after Monty Hall shows the door with goat) is correct -- I offer to play for money! I often even odds, and will play for as long as they like. If you know anyone who want to play, let me know; for sufficiently high stakes, I will even travel to them!
posted by dan zwillinger
September 20, 2008 @ 11:14 AM
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