Author: Rolf Tueschen
Date: 12:30:42 09/26/02
Go up one level in this thread
On September 26, 2002 at 07:54:37, Uri Blass wrote: >On September 26, 2002 at 07:36:04, Rolf Tueschen wrote: > >>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. > >I do not see it. >It increases the knowledge only for one remaining door (the door that the host >did not open and you did not choose). That is wrong. See at the bottom. >> >>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 ... > >The pure logic of a lot of people is wrong. > >Uri You are wrong because we had only one question. Was Marilyn right for the exact text of the question. I said no, because the question did not make clear that the host must _always_ open a door. Looks not so good if we are unable to concentrate on the question. BTW that was the reason why I brought the topic. I will discuss that where someone asked exactly the question what this had to do with CC. Rolf Tueschen
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