From: jpc@a.cs.okstate.edu (John Chandler) Newsgroups: sci.math Subject: Re: Where is archive for Monte-Hall problem? Date: 31 Aug 1995 16:19:20 GMT In article <42399l$hhq@ixnews5.ix.netcom.com>, Ken Christensen wrote: >Could someone please point me to an archive that contains the many >discussions in this newsgroup on the very infamous Monte Hall 3-door >problem. Pointers to other references on this problem are also >appreciated (e.g., was there ever a published "last word"). > >NOTE... I do *not* mean to start all over again a discussion of this >problem. I suspect that many of the regulars on this newsgroup are >rather tired of the Monte Hall problem > >Thanks!!! > > >Ken Christensen Here are the references. Steve Selvin, "A Problem in Probability", The American Statistician 29 (1975) 67 In a letter to TAS, Steve Selvin of Cal./Berkeley proposes a problem involving "Let's Make a Deal" starring Monte [sic] Hall. Steve Selvin, "On The Monty Hall Problem", The American Statistician 29 (1975) 134 In a second letter, Selvin clarifies assumptions in the problem and discusses correspondence he has received, including excerpts from a letter from Monty Hall himself. Hall's solution is correct but contains two strange comments, which probably were clear in the complete original letter. (I believe I read somewhere that Monty Hall is highly intelligent and well-read, and only went into the entertainment business when he was denied admission to medical school because of the Jewish quota in force at the time.) J. P. Morgan, N. R. Chaganty, R. C. Dahiya, and M. J. Doviak, The American Statistician 45 (1991) 284-289, 347-348 The authors discuss the problem, which they point out is equivalent to the "prisoner's dilemma" given in "Fifty Challenging Problems In Probability with Solutions" by Frederick Mosteller, Addison-Wesley 1965 (possibly reprinted later by Dover). This article followed the appearance of the problem in the column of Marilyn Vos Savant in Sunday Parade magazine. The authors discuss unstated assumptions and the various problems that result. On page 347, Vos Savant replies. My solution to avoiding ambiguity as to how Mr. Hall acts (intentionally or randomly, knowledgeably or in ignorance, etc.) is to have him say truthfully to the contestant, "Please choose a door. Then I shall open a door, not the door you chose and not the door concealing the prize. Then I will give you the opportunity to switch to the other unopened door if you wish." The solution to this game is that the "Never switch" strategy will win 1/3 of the time if the game is played repeatedly, and "Always switch" will win 2/3. Many intelligent people, including some holding Ph.D. degrees in math, do not believe this, and can sometimes be enticed into gambling on this problem, although (alas) usually only for small stakes. I'm still looking for one who will play for $100 a game or more and promise to play at least 100 games. "Baby needs another year of college tuition..." -- John Chandler jpc@a.cs.okstate.edu ============================================================================== From: jpc@a.cs.okstate.edu (John Chandler) Newsgroups: sci.math Subject: Re: Where is archive for Monte-Hall problem? Date: 7 Sep 1995 13:42:37 GMT In article <42lvbl$ok1@cantua.canterbury.ac.nz>, Bill Taylor wrote: >tchow@math.lsa.umich.edu (Timothy Chow) writes: >|> > >|> >>The problem, as originally stated in Vos Savant's column, was not well >|> >>defined. >|> >|> Incidentally, the problem *is* well-defined as stated in vos Savant's >|> column; > >I've heard both of these endlessly! > >Can someone please please PLEASE send me an actual copy of the article? I don't have the columns handy. I'll look for them. Check microfilm of U.S. newspapers for the Sunday Parade magazine sections of September 9, 1990 December 2, 1990 February 17, 1991 I thought the problem was stated reasonably clearly by vos Savant. J. P. Morgan et al. in The American Statistician 45 (1991) 284-288 state, "... vos Savant reported 'I'm receiving thousands of letters, nearly all insisting I'm wrong... Of the letters from the general public, 92% are against my answer; and of letters from universities, 65% are against my answer.' Nevertheless vos Savant does not back down, and for good reason, as, given a certain assumption, her answer is correct. Her methods of proof, however, are not." A reply from vos Savant appears on page 347 of the same reference, followed by a rejoinder. Steve Jacobs in rec.gambling has analyzed several alternatives, such as Monty Hall choosing randomly and happening not to choose the prize door, or Monty Hall making the offer only when he knows the contestant has chosen correctly in his first try, etc. -- John Chandler jpc@a.cs.okstate.edu ============================================================================== Newsgroups: sci.math From: kdq@emoryi.jpl.nasa.gov (Kevin D. Quitt) Subject: Re: Where is archive for Monte-Hall problem? Date: Thu, 7 Sep 1995 19:18:39 GMT tchow@math.lsa.umich.edu (Timothy Chow) wrote: >In article <42k986$b75@netnews.upenn.edu>, >Matthew P Wiener wrote: >>In article , tminkoff@crash (Tony Minkoff) writes: >>>In article <42cebq$6mo@netnews.upenn.edu>, >>>The problem, as originally stated in Vos Savant's column, was not well >>>defined. >>This is false. >...I have in the past repeatedly asked for evidence that the >mathematicians responding the vos Savant's column were not completely >clueless. To show that a mathematician should have known all the facts, you'd have to demonstrate that s/he had seen the show, or had learned of it other ways. Not everybody I know knows about Monty. > Nobody has ever met my challenge. I just have. >Incidentally, the problem *is* well-defined as stated in vos Savant's >column; it's just that the information provided is not enough to determine >a unique numerical answer. The critical item (does Monty know which door has the car and therefore avoid showing the car) was not specified in MvS's description of the problem. Since this alone decides the answer, it would seem a critical shortmcoming to me. -- #include _ Kevin D Quitt USA 91351-4454 96.37% of all statistics are made up ==============================================================================