Author: Uri Blass
Date: 04:54:37 09/26/02
Go up one level in this thread
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). > >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
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