Talk:Monty Hall problem/Archive 5

message: It may be instructive to contrast the situation in the Monty Hall Problem with the situation that occurs in the game show Deal or No Deal when the player in Deal or No Deal is down to two cases and facing the decision to switch the case he or she originally selected with the only other remaining case.  Suppose that in Deal or No Deal there are 26 cases containing different prize amounts and the highest prize possible is $1,000,000 as in the original version of the show.  If there are only two prize amounts left on the board and one of them is $1,000,000 while the other is $0.01, the probability of winning $1,000,000 does not increase if the player switches the case he or she originally selected with the only other case remaining.  However, if the host Howie Mandel eliminated the other 24 cases because he knew they didn't contain $1,000,000 then the probability that the player would win $1,000,000 by switching cases would be 25/26.  Now what if Howie helped out in eliminating some of the 24 cases and the player got lucky in eliminating the others?  :-) —Preceding unsigned comment added by 69.141.232.16 (talk • contribs) 
:Well from my knowledge of Deal or No Deal from the Australian version, it's more complicated/different. In Deal or No Deal, if you end up with two cases, one with $0.01 and one with $1,000,000, your choices are to take the bank offer which would be about $500k or assume your cases is the $1 million. If your case has the $0.01, you end up with $0.01. You can't choose the other case as such, you only choose between whatever is in your case and the bank offer. If the host knowingly opens 24/26 cases without the $1 million, it will be a very, very bad idea for you to think your case has 1$ million since there's a 1/26 chance it does whereas as 25/26 chance it only has $0.01. So the chances are very likely you'd end up with $0.01. Far better to accept the bank deal. Of course, if the host does do that, then it doesn't really make sense for the bank to offer you about $500k either Nil Einne 18:17, 9 December 2006 (UTC)
replies: text: Yeah, I'd take the $500,000 bank offer.  In that situation, a 'fair' bank offer would be $1,000,000 * (1/26) + $0.01 (25/26) ~= $38,461.55.  That reminds me of something I've wondered about Deal or No Deal:  Suppose, in the normal version of the show where the host doesn't help out, that there are three cases left, $0.01, $500,000 and $1,000,000 and the player turns down a reasonable offer, say $450,000.  If the player then opens the case containing $500,000, the banker could force the player to get lucky by offering a really low amount, like $0.02.  I wonder if there's anything stated in the rules of the show about the offers or if the player is supposed to just trust that the banker wouldn't do such a thing.  :-)  69.141.232.16 21:30, 9 December 2006 (UTC)
thread_title: Deal or No Deal vs. Let's Make a Deal

message: Vos Savant's answer makes it seem that the host's cluelessness makes a difference. In fact it does not. The contestant now knows that the open door hid a goat. As the contestant originally had only a 1/3 chance of choosing the door with the car, there is a 2/3 chance of getting the car by switching, just as in The solution above. --Lorenzo Traldi 20:05, 19 December 2006 (UTC)
replies: text: In actual fact it does make a difference, please see #can someone please explain the whole "what if monty doesn't know" (above). -- Rick Block (talk) 20:19, 19 December 2006 (UTC)

text: The difference in the clueless host stems from the fact that in the original problem, it's a "clean" probability situation - you can consider all the options and draw out a standard probability tree. In the clueless situation, however, you need to arbitrarily lop branches off. Instead of "Any of these options could have happened", it's "any of these options could have happened, except for these two which, just by luck, didn't. You're restricting yourself to analysing a certain subset of all possible states, a subtree of the total probability tree, in which a particular random event went a specific way. Maelin (Talk | Contribs) 01:01, 20 December 2006 (UTC)

text: I'm sorry, Lorenzo, but talking about 'what happens in those situations where Monty opens the door and it shows the car' is only going to confuse people (including yourself) to no benefit, because the problem states that this does not happen.  Introducing a case that does not happen and saying "when this happens, the player is offered a chance to switch to the car that has been revealed" has nothing to do with the problem under discussion because it is part of the problem statement that the door opened reveals a goat. -- Antaeus Feldspar 15:33, 20 December 2006 (UTC)

text: Clarifying that instead of having three results, all of which are possible from our randomizer and all of which are possible according to the evidence, we have six results, all of which are possible from our randomizer but only four of which are possible according to the evidence, is indeed a good thing.  But to speculate on what happens "when" those two results which our problem statement makes clear don't happen, happen, is not really clarifying anything. -- Antaeus Feldspar 14:18, 21 December 2006 (UTC)

text: In this case, do over or not is not specified.  All we can, and should, do is compute the conditional probabilities in the case where the host accidentally does not reveal the car.  As has been explained above several times, given the host picked randomly and given the host did not reveal the car, the resulting situation is a 50/50 case.  -- Rick Block (talk) 21:33, 14 January 2007 (UTC)
replies: text: Many people work their way through problems like this one by doing thought experiments.  You are absolutely right, Rick, that "imagine that Monty chooses a door at random, and happens to pick a door with a goat instead of a car" gives exactly the same probabilities as "imagine that Monty chooses a door at random, and if he picks the car, we do the whole problem over and over until he picks a goat."  However, if you ask someone who isn't already following to imagine that random chance just "happens to" come out a particular way, they will almost certainly think that you are asking them to twist the rules of probability in order to lead to an incorrect conclusion.  If you tell them that they can simulate the random choice themselves, using any randomizer they like and simply treating any result which does not correspond to the conditions specified in the problem as a signal for a "do-over", they are more likely to be able to carry out an appropriate thought-experiment and reach the correct answer. -- Antaeus Feldspar 01:02, 15 January 2007 (UTC)
thread_title:  Comment about clueless host 

message: ...If the host shows one of the goats the game provability is no more 1/3 or 2/3 or whatever: it becomes 1/2, right?
In fact the game was never 1/3 because one of the doors with a goat will always be eliminated, so the goat door 1 and the goat door 2 are, in a kind of way, the same door (aka the same result).It doesn't matter if you choose a door with a goat or not, when in the end you have to choose there are just two doors and one goat. In my point of view the game starts when there are only two doors and 50% of changes for each door.
PS: Feel free to correct me
PS2: I'm sure you will ;)
:What you're saying isn't stupid; however, it is incorrect.  You are saying that when there are only two doors, there are only two possibilities:  either the car is behind the player's door, or it is behind the other unopened door.  If the probabilities of these two possibilities are equal, then they must each be 1/2.
:However, it is not true that the probability of these two possibilities are equal, because there are twice as many ways to get to "the car is behind the other unopened door" as there are to get to "the car is behind the player's door".  If the player picks the first goat (1/3 probability), Monty shows the second goat, and the car is behind the other unopened door.  If the player picks the second goat (1/3 probability), Monty shows the first goat, and the car is behind the other unopened door.  Only if the player picks the car (1/3 probability) does the other unopened door contain a goat. -- Antaeus Feldspar 20:27, 25 December 2006 (UTC)
thread_title:  I may sound stupid, but... 

message: This is a question that has already been asked and answered but it seems it needs to be addressed again -- if Monty has some particular pattern or method by which he picks a goat to show, and the player knows this and can distinguish between the goats, does it ever make some strategy other than "always switch" an optimal strategy?
The answer is "no".  To prove that this is so, we will assume the opposite.  We will assume that one of the goats is black and one is white, and that Monty has a bag with B black marbles and W white marbles; when he picks a black marble, he shows the black goat and when he picks a white marble he shows the white goat.  B and W may be 0 but they cannot, of course, be negative numbers.
B+W represents the total number of times Monty chooses between the two goats, which he only does when the player initially picks the car.  The player's chance of picking the black goat is equal to his chance of picking the white goat is equal to his chance of picking the car; therefore B+W is also the total number of times that the player sees a particular goat because he chose the other goat.
Therefore:
* B+W+B times, the player sees the black goat (B+W times because he chose the white goat, and B times because Monty had a choice and chose to show the black goat)
* B+W+W times, the player sees the white goat (B+W times because he chose the black goat, and W times because Monty had a choice and chose to show the white goat)
Now, let us assume that we can find values for B and W such that seeing a particular goat means the player should stay, and not switch.  If there is such a goat, we can devise a strategy in the form "if you see this goat, stay, and otherwise switch" that beats the strategy of "always switch".  If however the optimal strategy for each individual goat under all values of B and W is "switch" it means that the optimal strategy for the game is "always switch".  So, we assume that for some goat (say the black goat) the player is actually more likely to have picked the car and therefore maximizes his chances by staying, rather than switching. 
But here we run into a problem.  Out of the B+W+B times the player sees the black goat, B is the number of times the player picked the car and B+W is the number of times the player picked the white goat.  For staying to be an optimal strategy, B must be larger than B+W.  W would have to be negative to fulfill this condition but we noted at the beginning, W represents a number of marbles and clearly cannot be negative.  Even choosing a value of 0 for W only makes it possible to encounter a situation where switching provides no particular advantage, but: 1) no strategy in that situation can make the player's chances greater or less than 50%; 2) for every two times the player faces that situation, he gets a situation where switching pays off 100% of the time. 
Can we even pick any values for B and W such that the overall success of a strategy of always switching even becomes something other than 2/3?  No, we cannot.  What is the proof?  The proof is that staying always pays off when the player originally picked the car; switching always pays off when the player originally picked a goat.  The ratio of times the player picks the car to times the player picks one of the two goats is constant, and is not affected by how Monty chooses which goat Monty chooses to show in those situations where he has a choice of goats. -- Antaeus Feldspar 02:27, 31 December 2006 (UTC)
replies: text: Not to confuse matters (I agree with the analysis above), but there are "host choice" protocols for which there are better strategies even with indistinguishable goats.  For example, if the host is known to always open the highest numbered door containing a goat the strategy of "initially pick door 1, stay if the host opens door 3, switch if the host opens door 2" always wins.  The point that there are many variants of the problem depending on the exact host behavior is well covered in the paper by Mueser and Granberg.  -- Rick Block (talk) 03:24, 31 December 2006 (UTC)

text: Perhaps an easier way to show that (in the standard host choice protocol) being able to distinguish the goats does not alter the result is given in the new "Bayes Theorem" section. Notice, in particular, that no goats appear in the expression for the conditional probability P(Hij | Ck, I). The proposition "Ck = the car is behind door k" and its negation sufice.The Glopk 16:52, 2 February 2007 (UTC)
thread_title:  Does being able to distinguish the goats make some other strategy optimal? 

message: Monty Hall problem has been nominated for a featured article review. Articles are typically reviewed for two weeks. Please leave your comments and help us to return the article to featured quality. If concerns are not addressed during the review period, articles are moved onto the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Remove" the article from featured status. The instructions for the review process are here. Reviewers' concerns are here.
Gzkn 10:57, 7 January 2007 (UTC)
thread_title:  [[Wikipedia:Featured article review/Monty Hall problem|FAR nomination]] 

message: I wrote a flash simulation of the Monty Hall problem.  Is there a way for me to upload it to wikipedia? —The preceding unsigned comment was added by Lax4mike (talk • contribs) 03:22, 9 January 2007 (UTC)
thread_title:  Flash simulation 

message: These aren't Venn diagrams in the strict modern sense, but I'm not sure what else to call them. Venn might have disagreed.  Septentrionalis PMAnderson 04:18, 9 January 2007 (UTC)
thread_title: Venn diagrams

message: Abscissa brings up a point worth discussing. Much of this article consists of different explanations of the same result, and they really are themselves quite similar. 
*Do we need all of them? 
**We may; one reader will understand one, and another reader the next.
*If not, which do we keep?
Septentrionalis PMAnderson 03:36, 10 January 2007 (UTC)
replies: text: I would advise moving the "Simulation" section upwards, since we have a citation available (Howard Margolis Wason, Monty Hall, and Adverse Defaults, page 17) specifically identifying it as a successful method for inducing understanding -- as specifically contrasted with verbal explanations, actually.  "If subjects actually play
the MH game a few times (handling the cards themselves: watching someone else is not
very effective), that physical sense of the situation easily switches the intuition. After a
few plays where you handle the cards yourself, it will become obvious that it pays to
switch. But mere verbal instructions or even merely watching someone else handle the
cards will easily fail. So a person in doubt about whether it really pays to switch ought to
take a couple of minutes and deal the game a few times." -- Antaeus Feldspar 05:55, 14 January 2007 (UTC)
thread_title: Repetition

message: Is this picture helpful to anyone?  When I first started to understand the problem this hindered more than helped.  I understand that some people might have different ways of understanding the solution, but I believe this image is peddling a bad explaination on how to arrive at the solution.  This problem has absolutly nothing to do with what is suggested in the picture.  I move for its deletion, or at least a recreation which explains the solution better. This is not a case of just having 2 seperate guesses at the correct door (and thus 2/3 probability) 202.10.86.59 20:50, 13 January 2007 (UTC)
thread_title: MontyHallProblemMadeEasy.jpg

message: Because of the very nature of the paradox, the usual 50:50 response and the amount of debate that it generates, I would like to see more text in the intro on the background leading into the analysis.  The analysis is so long and uses so many methods, without fully explicating the controversy that has been generated in the public sphere, that many readers will not bother with the analysis, and will write if off -- some people were prompting to take the page down as incorrect and a near-hoax, for instance.  I would suggest using text based on the following:
"When Marilyn vos Savant quoted this puzzle in the US a few years ago [citation, date], she received over 10,000 letters mostly telling her she was wrong. 
One was from Robert Sachs, a professor of mathematics at George Mason University in Fairfax, Va. who said "As a professional mathematician, I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error and, in the future, being more careful." 
However a week later and Dr. Sachs wrote her another letter telling her that "after removing my foot from my mouth I'm now eating humble pie. I vowed as penance to answer all the people who wrote to castigate me. It's been an intense professional embarrassment." 
Well, we said it was counter-intuitive. Even professional mathematicians get it wrong."
(http://www.grand-illusions.com/monty.htm)
That is just a framework suggestion, not suggesting direct plagiarism of the text.  Or similar words around what has driven the controversy most recently, being the 'Marilyn vos Savant' article.  The so-called Marilyn vos Savant character is presumably a pen name and may represent a number of contributors [verify].
Also, it would be good to include links to online simulators in a separate section, or make reference in the current heading to them. (examples also found at the same site: http://www.grand-illusions.com/monty2.htm)
--Sean01 07:37, 15 January 2007 (UTC)
thread_title: About the Introduction, and online simulators

message: I think this is an excellent article, I like the formal discussion and and also the artwork, even the goofy one at the top. You might want to consider moving the history section up a bit and add to it the above posting (on this talk page) about why this has caused confusion. Maybe a good place would be just before the "understanding aids", especially if the above information is added then the reader will be even more interested to read the excellent analysis. But I mean, even as it currently stands, it's awesome, simply awesome! --Merzul 02:28, 17 January 2007 (UTC)
thread_title:  Awesome article 

message: Is the extended Bayesian analysis recently added from some particular source?  If so, can someone please add a reference?  The article is currently undergong a featured article review, which includes making sure that everything that should be, is referenced.  I fear some folks might view this extended analysis as approaching original research, which is prohibited (see WP:NOR).  -- Rick Block (talk) 14:24, 17 January 2007 (UTC)
replies: text: No particular source, and definitely not original research. It is a very straightforward application of basic probability theorems and concepts (Bayes theorem, marginals and conditionals, normalization). This is the kind of problem I may have given to my students as an exercise after the second lecture of an undergraduate class on probability back when I used to teach. I don't think any references are necessary other than the Wikipedia articles already linked to - it's really plain algebra. The Glopk 20:17, 17 January 2007 (UTC)

text: BTW, I hope that extended does not mean too long. I could have compacted the whole proof in about half the lenght, but I assume that the average reader is somewhat familiar with concepts of probability, but not too well versed in the formalism (especially the Bayesian kind). So I took some care in spelling out every step as clearly and simply as I thought proper. The previous version of this section, which mine replaced entirely, was defective in this respect, I think. But I haven't contributed much to Wikipedia yet, so I'd welcome some feedback on this regard.The Glopk 20:32, 17 January 2007 (UTC)
replies: text: "Straightforward application of basic probability theorems and concepts" sounds arguably like original research (I wouldn't argue this, but given the current level of scrutiny on this article I'm not sure no one else would).  My understanding is that this problem is actually used as an example in a variety of probability texts - if you could find it (even as an exercise, with the answer in the back of the book) it would be clearly not original (I know it's not in the probability text I used).  I don't mean "too long" by "extended", just that it now is much more formal (and longer) than the previous section.  It has a math textbook sort of tone ("we denote ...", "we can state ..." ), which I'm not sure is appropriate.  I haven't had a chance to look at any other math-related featured articles to compare the tone.  If you're interested in doing this yourself, the articles that are featured-class are listed at Wikipedia:Featured articles.  These are meant to be the very best Wikipedia has to offer, satisfying the criteria listed at Wikipedia:Featured article criteria.  The Monty Hall problem article was nominated as a featured article in July of 2005 (it looked like this at the time).  Since then, it's suffered a bit.  IMO, the current FA review is meant to goad the folks who care about it into spending some time fixing up some of the problems that have accumulated in the intervening year and a half (FA review comes with a threat that if the concerns are not addressed the article will be removed from featured status).  -- Rick Block (talk) 04:01, 18 January 2007 (UTC)
replies: text: Done some googling around - easy now that we can look at books. Here is one with an analysis similar to the one I wrote up: . Can we point to Google Books previews from Wikipedia references? Here is another web page with a similar one: . And yes, it is given as an exercise to undergraduate students of probability theory - see here: . Notice that it is at page 31, right at the end of the first chapter, because it really is an easy application of first principles and definitions. There isn't much in there, at least from a mathematician's point of view, but it's a cute enough problem, maybe because so many non-mathematicians find it so hard (there's a reason why so many social scientists have tested how people respond to it). There is only one way to do a correct Bayesian analysis of this problem, the difference is only in the symbols, and I tried to write it up in a way that would be at the same time correct, complete and easy to follow for a curious non-mathematician. I checked the July 2005 nominated version, and its Bayes Theorem section is almost identical to the one I replaced. The reason I replaced it is that it wasn't easy to read, even for a specialist like me. The reasoning was quite abbreviated and hard to follow, and it didn't really do justice to the insight that a Bayesian treatment of the problem provides. Besides, I don't see references for it there either. I believe the author had the correct intuition, but just couldn't formulate it well, IMHO. As for the tone, well, I should think that a section with a mathematical title should have some mathematical flavor too - what's the point of having one if the content is mathematically unappealing? ;-)  The Glopk 05:49, 18 January 2007 (UTC)

text: As I feared, there's now an objection to this section (others as well) as being "original research".  The Google Books references shouldn't be directly used since it's a "signup" site.  Assuming you're on a campus someplace, if you could find one of these references in the library and add a direct citation (e.g. ) that'd be perfect. -- Rick Block (talk) 04:08, 26 January 2007 (UTC)
replies: text: Done. Also removed two dead references to probability theory textbooks.The Glopk 17:30, 26 January 2007 (UTC)
thread_title:  Bayesian analysis 

message: I removed this addition by an IP from aids to understanding - not sure if it's needed or a repeat:
Another way of thinking of this is:  If I initially choose the car, he will show either one of the goats, in this case it is best to stay.  If I initially choose the first goat, he will show the second goat, it is best to switch.  If I initially choose the second goat, he will show the first goat, it is best to switch.  Notice that even after he exposes a goat you don't know if your door has a goat or car.  Since ⅔ of the time it is best to switch, switch!  Thus, simply put, your first choice was likely a goat (a ⅔ chance), so when he shows you where the other goat is, it is in your best interest to choose the other door.
SandyGeorgia (Talk) 04:03, 26 January 2007 (UTC)
replies: text: But... some proofs are more difficult for the average reader to understand than others, and my point was to draw the close parallel between the Bayesian proof and the decision tree proof - since the average reader will find the Bayesian argument more complex and confusing than the decision tree argument.  And, I add with a grin, is it necessary to use the word "proper" in "proper proofs"?  Finally, you haven't defined what "equivalent" is for proofs, but I can assure you that there are theorems in mathematics that have widely different proofs that many mathematicians would hardly call "equivalent".  In the situation at hand, I was trying to point out that, except for wording, the two arguments (proofs) proceed almost identically.  I've used both proofs in my own probability classes for years, and students often find the observation about parallel reasoning helpful.  Chuck 17:40, 26 January 2007 (UTC)
replies: text: But I could write a similar argument pointing out the equivalence of the Bayesian argument to the Venn diagram one, or of the latter one to the door combination one, and so on for all the pairs, directly and inversely. Where does it stop? The fact that different people may find the proofs more or less difficult to understand is addressed in this article by having many proofs, in the hope that the reader will "get the clue" from at least one of them, without an expectation that she will understand all of them. Say, the Venn diagram argument, which is often cited ans the most "intuitive", would likely be rather meaningless for a blind person, who may instead find the purely verbal/symbolic Bayesian argument quite easy to follow. That some person would not gain much by knowing that the argument she understands is "equivalent" (in whatever sense of the word you care to choose) to one she can't even conceptualize.The Glopk 18:13, 26 January 2007 (UTC)
thread_title: Aids to understanding

message: I undid change 104755257 by user David Eppstein, who had changed some of the "inline" fractions in the equations of the Bayes Theorem sections into LaTeX \frac{}{} forms. The result of this change was a marked inconsistency in the equations that looked visually unpleasant. In particular, the multi-line formula evaluating the normalizing constant mixed fractions of the two types, probably because having the final result in a \frac form made for a confusing read next to the previous line.. Also, the line spacing on my monitor became quite "jumpy".
Something needs to be done to improve the rendering of math in Wikipoedia, but until it is I think we should edit conservatively....The Glopk 15:24, 1 February 2007 (UTC)
replies: text: I can't believe that you think "1/6/1/2" is an appropriate way to render math. If you want the vertical fractions bigger, throw \displaystyle into the formula. But I'm not repeating my edit, someone else will have to do it. —David Eppstein 16:36, 1 February 2007 (UTC)
replies: text: I can't believe your eyes could tolerate the inconsistency in line spacing your edit caused. If you change the style of the formulae, be at least consistent and change them throughout. Or rather, don't, I already did the work for you. For the next time, please consider cooling your kindergarten-style antics before crash-landing on your keyboard. You know, everlasting records, embarassments and all that.The Glopk 17:12, 1 February 2007 (UTC)
replies: text: Deliberately avoiding getting into an edit war is kindergarten-style antics? *rolls eyes* Anyway, thanks for the fixup. —David Eppstein 17:40, 1 February 2007 (UTC)
thread_title:  Small Fractions Again 

message: The lead paragraph should state the problem in a simple and low-drama way. In particular, I think that the mention to any elements of "Let's Make a Deal" should be minimized because this is not about a game show, it is about a logic problem.  We should stick to the correct problem statement, the answer, and then mention that some find it non-intuitive. Unless somebody is going to have a heart attack over this, I will attempt to do so.--199.33.32.40 00:17, 2 February 2007 (UTC)
replies: text: We just completed a major revision of the article in which one of the changes we decided on was moving the problem statement and the answer out of the lead.  I would highly advise against deciding, on your own, to reverse that move.  Similarly, I cannot see what would be gained by minimizing any mention of "Let's Make A Deal"; the mention is already as minimal as we can get without removing it entirely and it seems to me that if we remove that because "this is not about a game show, it is about a logic problem" then we might as well remove from the lead of Albert Einstein the two words indicating that he was born in Germany because the article isn't "about" how he was born in Germany. -- Antaeus Feldspar 01:42, 2 February 2007 (UTC)

text: Well, I see that you waited only 45 minutes to see if "somebody is going to have a heart attack over this" before going right ahead.  I also see that you didn't care much that the only comment you did get in the short amount of time you waited was against your proposed changes, not for them.  Quite frankly, this isn't the kind of cavalier attitude you should take to editing Wikipedia, and also quite frankly, edit summaries such as "The problem is not that to state in the lead Section. State it. Correctly. Wikipedia is not a game show. It is an encyclopedia." are condescending and will not contribute to productive discussion. -- Antaeus Feldspar 01:42, 2 February 2007 (UTC)

text: Your condescension is really doing nothing for your case. Accusing your fellow editors of placing "some pretty face" above everything else is quite insulting. Meanwhile, the irony of you claiming to present "the adult ... version of the problem ... without the doors, the klieg lights, pretty girls, prizes etc." when in fact your proposed version of the lead incorporates more detail about the game show than the previous lead does not give us any reason to think that your complaints about the article are the results of an unbiased, acute appraisal. -- Antaeus Feldspar 01:42, 2 February 2007 (UTC)

text: If you want to propose a change, please feel free.  If you'd like, we could analyze the lead you added, here on the talk page (IMO, it has quite a few problems).  As Anteaus mentions, removing the problem (and solution) from the lead was a recent change in response to a Wikipedia:Featured article review.  All articles are subject to improvement, but making significant changes without prior discussion (and particularly despite unaddressed objections) is not how things are done here. -- Rick Block (talk) 02:46, 2 February 2007 (UTC)

text: I disagree with 199.33.32.40's apparent conviction that the article should be only about the problem and its solution and not about its history. This is an encyclopedia article, not a maths textbook. We are here to present all notable information pertaining to the problem, and its cultural significance is an important part of that. Maelin (Talk | Contribs) 03:13, 2 February 2007 (UTC)
thread_title:  Lead paragraph 

message: That some female who did little but cause more confusion gets into the lead section while the problem statement itself does not might be entertaining, but it is not educational. Does this really belong in the "Media" group rather than the "Math" group of FA articles? Well, if it does not belong in the "Math" group, then here is what was tried as the problem statement in the lead section:
:The problem presents a guessing game with a finite number, N, of possible discrete responses and only one right answer, such as guessing a number between one and ten where the problem poser has secretly selected one such number as the correct answer. The guesser is forced to make the guess at random. The poser then must then inform the gueser of N-2 wrong responses, which the poser does, and then the poser offers to the guesser the option to switch to the remaining response or stick with the orignal guess. The guesser's best approach is to switch because the guesser, in having had N-2 wrong answer(s) eliminated, has learned more information than what was presented at the beginning of the game.
At least this is about Math rather than about some entertaining "savant". BTW: Once a decent, subject-oriented version of this article is created, I strongly suspect that it will become more obvious that it deserves the "Low" importance rating that it gets from the Math WikiProject and that it is an unworthy subject of a "Math" FA. I actually want this to remain in Math and get permanantly demoted. --64.9.233.132 03:15, 2 February 2007 (UTC)
replies: text: This is not a statement of the "Monty Hall problem", but a generalized version of it (which is discussed in the section "Increasing the number of doors").  As the article is primarily about the Monty Hall problem, posing this variant in the lead is not appropriate.  FA has nothing to do with "mathematical significance".  -- Rick Block (talk) 03:28, 2 February 2007 (UTC)
replies: text: Look, it is a lot of fun to watch some contestants get it wrong we when insist that N=3, but it is ludicrous to suggest that we avoid a clear statement of the problem right up front. Again, if this is about Media, then let's just have whoever maintains Wikipedia:Featured articles move the aricle from "Math" to "Media". --64.9.233.132 04:13, 2 February 2007 (UTC)
replies: text: Anyone else feel it's become obvious that 199.33.32.40/64.9.233.132/Farever is just trolling? -- Antaeus Feldspar 04:18, 2 February 2007 (UTC)
replies: text: I am trying to improve the quality of the FA "Math" bin. Evicting this article one way or the other for the mid-to-long term would be an improvement to that quality, at least as far as anyone with a college education would be concerned.--64.9.233.132 04:34, 2 February 2007 (UTC)

text: I don't understand your view that simply being in the Math category means it must be only about math. Can you explain what, exactly, you want changed about the article and why you think this will improve the article for readers? Maelin (Talk | Contribs) 05:03, 2 February 2007 (UTC)

text: Re the first sentence of the proposed replacement problem statement: "The problem presents a guessing game with a finite number, N, of possible discrete responses..." It is not usually the case that starting a math article with the most formal, precise, and mathematically general statement of the problem is a good way to make the article readable. You'll lose readers on "finite number", "N", and "discrete responses", which make the statement unnecessarily technical compared to "three doors". The generalized version is presented later, to be sure, but it's the wrong way to start. And, like Maelin above, I fail to see how eliminating the story of how the problem came to be famous is an improvement; there isn't and shouldn't be a rule that mathematical articles must be purified of all non-mathematical content that might make them more interesting. —David Eppstein 05:13, 2 February 2007 (UTC)
replies: text: This is still showmanship. Before you know it, we will be putting  on the section with the explanation.--68.127.162.111 04:31, 4 February 2007 (UTC)
replies: text: 68:You are too late. They already use . Before you know it, we will have articles with puzzles like "What does mc2 equal?" Then there will be a big, lecturing, knowing display and, ta da! "It equals E!" Much applause.--64.9.237.152 04:29, 5 February 2007 (UTC)
replies: text: Please stop having your sockpuppets talk to each other. -- Antaeus Feldspar 13:59, 6 February 2007 (UTC)
thread_title:  Problem statement 

message: The References section contains entries that are not cited anywhere in the article body. One was added today, presumably by its author. What is the policy or custom about such references? Leave them alone? In academic papers (at least in my field), having such "dangling" references is highly frowned upon.The Glopk 17:19, 3 February 2007 (UTC)
replies: text: I removed it.  IMO, adding it was a pretty clear violation of WP:NOT#SOAPBOX. -- Rick Block (talk) 18:25, 3 February 2007 (UTC)
thread_title:  Uncited References 

message: I've been away for a couple of weeks. In the intervening period, this article seems to have morphed into a dusty old text book. That's very sad, given that Wikipedia has the opportunity to be so accessible and so different. I say: delete things that are wrong, not things that are simply not to your liking. De gustibus non est disputandum, after all! StuFifeScotland 13:18, 12 February 2007 (UTC)
replies: text: Ehr, could you make some specific examples of "dusty text book"-style text in the article?The Glopk 17:40, 12 February 2007 (UTC)
thread_title:  What A Pity 

message: #It is inherently text, not graphical, which means it can't be used directly by other language versions.
#:Nonsense, it is clearly graphical. See the little face, see the thought bubbles, see the order of the thought bubbles...Davkal 04:41, 21 February 2007 (UTC)
replies: text: I'm not sure who this comment is addressing, but I don't see anyone here who is commenting in bad faith.  -- Rick Block (talk) 05:36, 21 February 2007 (UTC)

text: Actually, it's your edits that are getting impossible to believe are serious good-faith edits.  "See the little face, see the thought bubbles, see the order of the thought bubbles..."?  That is supposed to be a good-faith response? -- Antaeus Feldspar 06:14, 21 February 2007 (UTC)
thread_title: Reasons against

message: In case anyone failed to notice, there is an issue with the copyright of :Image:MontyHallProblemMadeEasy.jpg (which I have asked the originator to address, see User talk:StuFifeScotland).  Pending resolution of this issue, this image must not be put on this or any other page.  I suspect this will be seen by some as a bad faith preemption of the above discussion.   This is not my intent.  Discuss away.  But don't put the image back.  I also strongly urge everyone commenting about this issue to refrain from further incivilities.  -- Rick Block (talk) 06:02, 24 February 2007 (UTC)
thread_title:  About the image 

message: The reasoning in the text box is fallacious. It has been oversimplified to the point that it is not accurate. As it is currently worded, it makes it seem as if switching is the winning move EVERY time, which it isn't. NipokNek 12:42, 24 February 2007 (UTC)
replies: text: I can't even understand the reasoning now. It doesn't make sense. "If I only knew which one, I'd certainly switch." Only knew which what? I'm going to remove the boxes, if anybody puts them back please make sure they actually make sense. Maelin (Talk | Contribs) 13:06, 24 February 2007 (UTC)
thread_title:  ...and the text box that replaced it 

message: I have moved here this paragraph, added as an introduction to the "Aids to understanding" section. While I think it may be useful to have some mnemonicals, they should probably come after more thorough explanations. Otherwise, for example, it is not clear at all that the "Bet on it!" of mantra (1) is anything but an arbitrary choice.The Glopk 23:30, 17 March 2007 (UTC)
replies: text: Here are some simple mantras that can help in understanding the Monty Hall problem, or in explaining it to others: (1) Switching means betting you were wrong the first time. Bet on it. (2) In offering the switch, Monty Hall is giving you two doors for the price of one. (3) You, not knowing anything, chose door 1; Monty Hall, knowing where the jeep is, chose not to reveal door 2. Whose choice do you think is more interesting? (4) Yet another way to think about it: If A and B are both at home watching the show on TV, and player A always stays, and player B always switches, then A wins whenever B loses, and vice versa. But player A only wins a third of the time, so that means player B wins two-thirds of the time.
There are more problems than simply the placement.  Addressing the reader is discouraged by the Manual of Style, and the tone is very informal.  Perhaps these issues can be fixed, but I'm not sure how.  I've reverted another addition of this same text.  -- Rick Block (talk) 03:24, 20 March 2007 (UTC)

text: I completely agree with the removal of this aprticular addition. But still I think the writer expressed a real need, i.e. that there would be some value in adding one or more "mnemonicals". By this I mean a one-liner, correct and intuitive explanation of the solution. Something along the lines of: "Short summary: the player should stick with their initial choice when that choice happens to be the lucky one, but the odds of this happening are 2 to one against, so switching is a better strategy". If a good "mantra" can be formulated, it could be placed at the beginning of the "Aids to understanding" section, and could be satisfactory for the readers in a hurry, while enticing the more interested ones to read the rest of the "Aids to understanding" section. Alternatively (but I think less usefully), one could be placed at the end of the section, as an easy-to-remember summary. The "cartoon" that was unfortunately at the center of so much controversy weeks ago was meant to serve this "menomonical" goal, after all, and while I agreed with the criticism directed at it, the goal was probably worthwhile.The Glopk 14:55, 21 March 2007 (UTC)
thread_title:  Simple Mantras 

message: The assumes, without explicitly stating, that the car is preferable to the goat. This might be so obvious that it goes without saying, but it may help clarify.--Blackmagicfish 05:37, 20 March 2007 (UTC)
thread_title:  Unstated Assumption