Author: Rolf Tueschen
Date: 02:20:29 09/26/02
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On September 26, 2002 at 00:32:54, Matthew Hull wrote: >On September 25, 2002 at 12:38:06, Rolf Tueschen wrote: > >>Please take a look at my revolutionary solution of this confusing problem: >> >>http://hometown.aol.de/rolftueschen/monty.html >> >> >>At first I went into the net and collected all sort of data for my page. I >>wanted to show how important methods and methodology are for science and also >>statistics. In special the exact defining of the terms. >> >>Then suddenly I had the inspiration and in a few minutes whitewashed a million >>people who as pupils, students or even professors let them be proved wrong by >>Marilyn vos Savant who has an IQ of 228. For decades now the Monty Hall Problem >>is taken as example for conditioned probability, which is wrong! >> >>Hope you enjoy my revelations. Please tell me if you want to comment. >> >>Rolf Tueschen > > >Rolf, I have read the posts and your replies. I will try to summarize your >position and you can tell me if I got it right. > >If you get to play 100 times (as per the simulation programs), then yes, you >want to always switch. But if you only get to play once, then there is no >advantage per se in switching, because you only get to play once. In that case >it's 50:50. Toss up, Even. Just flip for it. > >How did I do? Ok, you found a summary how it could look like what I meant, but it's not exact enough, in parts it's almost false. 1. Your first idea with the simulation is trivially true. So let's stay with the Monty show, if I had 100 chances in a row (with the same setting, see below) I certainly would adopt the option 'switch'. 2. If I were captain of a group of 100 people (all going for the show one after the other no matter when exactly but with the same setting always) I would also tell them to follow the strategy of 'switch'. If I were a journalist I would write that 'switch' should be the option for the "standard" setting of Monty's show. (But I hope you agree that Monty were forced to change his setting, and that was exactly what happened in real, just read in my monty.html. So let me come to the _real_ problem a single (unexperienced) candidate had to face. 3. The real problem for an innocent candidate with a unique chance to win the car (if we follow closely the question of Mr. Whitaker, which was the base for Marilyn vos Savant, so with the knowledge that the host knows exactly where the car is) is to decide in a 50:50 situation. That alone would make him happy, because he had only a 33% chance before. Because the candidate is not in the position to look through the _complete_ setting (therefore I called it a psychological and not a logical situation) the only thing that he does know for sure is that the car must be behind one of the two remaining doors. I think that the whole confusion with this problem has a source in a misinterpretation of probability. You can't define a probability for unique, isolated cases. And nowhere in the original question it was said that Monty would _always_ open a door. That was added as tacit understanding by Marilyn vos Savant. If you have a _unique_ situation you can't invent a simulation routine for 10, 100 or 1000 trials. But only then you would get a value for P. This is all very trivial. So - to make a summary, it was well justified that all the mathematicians disagreed with the 2/3 solution. Simply because it requires certain assumptions which were missing in the original question. Therefore Marilyn was wrong. In his unique situation the candidate had no information to see advantagesin either direction. Rolf Tueschen
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