Author: Rolf Tueschen
Date: 07:17:54 09/27/02
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Please let me add to this *Conclusion* my *Final Statement* from CTF on a fantastic post that should be presented to the readers of CCC too. ==================================================================== Subject: Re: New and final solution of the Monty Hall Dilemma *Final Statement* Posted by Rolf Tueschen (Profile) on September 27, 2002 at 09:54:10: In Reply to: Re: New and final solution of the Monty Hall Dilemma posted by Richard D. Boltuck on September 27, 2002 at 06:42:58: This is an excellent piece of deep thinking. Thank you so much! On September 27, 2002 at 06:42:58, Richard D. Boltuck wrote: >Rolf is correct that the conditions of the problem matter, and some of these >conditions were left implicit in its original statement. But he is incorrect in >criticizing the standard answer (SA). The SA is fully right under the implicit >conditions that we all understand were intended to apply, namely that the host >would always reveal a goat after the contestant randomly picked a door, and the >host would then always offer a switch. Obviously, if the host's conduct is >contingent on his knowledge of whether the contestant actually selected a door >with a car or with a goat, the solution would be different. In other words, >whenever the contestant initially selects a door with a goat, the host simply >opens the door and gives him a goat, for instance (in but one possibility). But >I think this is a trivial point. > >One way of thinking about the correct solution, and the mathematical illusion >that this puzzle creates is this: the mind answers the wrong question, thus >creating the illusion. The mind thinks, "whether or not the contestant >initially selected a door with a car or a goat, the host will ALWAYS be able to >reveal a goat -- so what additional information is contained in his revelation? >And if there is no additional information, how can it alter the odds of a car >being behind either of the two remaining doors, i.e. the one the contestant >selected initially and the other one available for the switch?" But this >reasoning is flawed. If the exercise were repeated many times, two thirds of >the time the host will be revealing a goat when the contestant had originally >selected a door with a goat -- hence two thirds of the time, the car is behind >the remaining door. But this does not matter. I mean it. My argument is not only based on the psychology but also the argument that the simulation model for probability doesn't fit here. It's true if you run the simulation 2/3 is the result. In the original question it was asked if the candidate could get possibly some advantage by a particular decision - in this single, I said unique, situation? Just to describe the conflict the candidate is in, let me enter the medical problem of a patient with the diagnosis cancer of prostata. Doctor says that he must do the operation. Allegedly (for this example here) with a 66% chance that all is ok and 1/3 that the patient gets infected by all the cancer caused by the operation itself. A) the patient knows that the diagnosis might be totally wrong B) the agreement to the operation is combined with a 2/3 expectency Is it allowed to reason that the patient should decide for B) or wouldn't it be better to take A)? For me it's a gamble. As a patient I didn't know if I saw an advantage in B). So in real life I would always get some more experts' opinions. If I would be forced to make a choice, after all the explanations, I would decide along my personality. - I would commit suicide in view of the deadly conflict - I would decide for A) and then go for alternative medicine - I would decide for B) and then pray that God might keep his hands over me Now I try a last time to explain the position from the candidate's view: Ok there are three doors. Let's say these door are my doors of my occasion today! I'm asked to take a door as my 'favorite'(!). Oh, I see, the host takes one door away. Now I have still two doors. And I know that I have one with a goat and another with the car. Where is the car? Let's see, two doors, I have a 50% situation. Uhmmm. Difficult situation. It's a gamble. By chance I take one of it, which one doesn't matter. Bingo, I take the one I already had as favorite. (For those who want to run simulations or who want to do complicated maths, let me state that there is _no_ probability someone could calculate for one unique event. Because for such events the case is clear, two doors, one decision, makes 1/2. And at the same time someone could say but in the long run I promiss you that you should take the door you did not choose at first. Then you have a 2/3 advantage over the always chosing of the door you had taken as your favorite at first! And both statements don't contradict each other.) I hope that this helps for now. In CCC the debate took a different way but there we also have the conclusion made. Thanks for making me the present of your beautiful input. I consider to ask you for the allowance to use your post on my webpage, is that possible? Rolf Tueschen > >I think Rolf's discussion on his web page of how these offers are actually made, >and the psychology of the scam, is quite interesting and thoughtful -- but in >the end, it is the psychological extensions to the "real world" that breach the >simplicity of the intended problem and the pedagogical point of the problem, >namely, to convey a concept in probability (and reveal the fallibility of >intuition).
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