Author: Rolf Tueschen
Date: 04:36:04 09/26/02
Go up one level in this thread
On September 26, 2002 at 07:22:03, Uri Blass wrote: >On September 26, 2002 at 06:26:36, Rolf Tueschen wrote: > >>On September 26, 2002 at 06:01:22, Uri Blass wrote: >> >>>On September 26, 2002 at 05:20:29, Rolf Tueschen wrote: >>> >>>>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. >>> >>>The situation of the candidate was not clear from the question and when things >>>are not clear you can assume what you want so Merilyn was right. >>> >>>I know that a lot of people who did not agree with the 2/3 did not explain their >>>opinion by the assumption that the candidate does not know that the host has to >>>open a door so they were wrong. >>> >>>If you know that the host is going to open another door at the beginning of the >>>game then it is clear that you should switch. >>>It is not clear from the question if you know or you do not know so people can >>>assume what they want. >>> >>>I think that a better question should be the following: >>> >>>Suppose you are on a game show, and you're given a choice of three doors. >>> >>>You know that the game has the following rules: >>>1)Behind one door is a car; >>>2)behind the others, goats. >>>3)After you are going to pick a door the host has to open another door that >>>has a goat. >>>4)The host is going to ask you if you want to switch doors. >>> >>>Is it to your advantage to switch your choices? >>> >>>Uri >> >>Two objections. >> >>1. In maths it's not trivial to present invalide proofs. What you implied with >>yor statement that because the question wasn't clear Mailyn had the right to >>calculate whatever she wanted. >> >>2. What is the meaning of your notion "advantage"? You mean I could have >>certainty to get the car or not? Because I have the two doors in mind... >>You know what I mean? Or would you say that I coud have advantage to take the >>other door and _still_ the car could be behind the not-advantageously-chosen >>door? But would you still stickt o your notion "advantage"? > >In other words I mean: >Do you increase your probability to get the car by switching the choices? > >If my assumptions are correct then you do it. > >It is clear that if you know that the host is going to open a door then the fact >that he opens a door does not change the probability of 1/3 if you do not >switch. > >The point is that opening a door does not give you a new knolwedge about what is >behind the door that you chose in the first place. Objection: If host opens one door, the knowledge increases the odds for each remainig door, sur. For one single, unique event. So, also my chosen door gets the plus. The plus with 3 doors is 1/6. What leads you to 1/2 each remaining door. What do you mean with probability for such unique events? 1/2 is pure logic, not probability ... Rolf Tueschen > >Uri
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