Wikipedia:Featured article review/Monty Hall problem/archive1


 * The following is an archived discussion of a featured article review. Please do not modify it. Further comments should be made on the article's talk page or at Wikipedia talk:Featured article review). No further edits should be made to this page.

The article was kept 06:14, 29 January 2007.

Monty Hall problem

 * Messages left at Antaeus Feldspar, Rick Block, and Mathematics. Gzkn 11:00, 7 January 2007 (UTC)

Has one inline citation. Mixed referencing style. Contains a trivia section disguised as Anecdotes. External links need pruning. Venn diagram images need captions. Weasel statements (for example: "It has been speculated that one reason the Monty Hall problem is so counterintuitive is that we expect deceit in situations like this.") Use of contractions, which should be avoided, and which leads to informality. Gzkn 10:52, 7 January 2007 (UTC)


 * On inline citations: First of all, this is not true. The following extracts from the text are all inline citations; they merely don't happen to be footnotes.
 * Craig F. Whitaker of Columbia, Maryland in a letter to Marilyn vos Savant's September 9, 1990, column in Parade Magazine (as quoted by Bohl, Liberatore, and Nydick). [BLN is duly explicated in the References]
 * In 1975, Steve Selvin wrote a pair of letters to the American Statistician (February and April issues) regarding the Monty Hall problem.
 * As Monty Hall wrote to Selvin:

"And if you ever get on my show, the rules hold fast for you &mdash; no trading boxes after the selection. &mdash;From the Let's Make a Deal website"
 * In the May-June, 1989 issue of Bridge Today magazine, Phillip Martin wrote an article entitled "The Monty Hall Trap."
 * including a front page story in the New York Times (July 21 1991)
 * I doubt I've listed all of them. Please read the article; don't just count footnotes. The genuine question is: is there any claim which is challenged, or likely to be challenged and which is not clearly sourced?


 * As for the bit about contractions: That section of MOS is an invitation to bad writing, and should be removed. Septentrionalis PMAnderson 22:38, 7 January 2007 (UTC)
 * You're right...I was on the lookout for Harvard referencing/footnotes instead. In any case the inconsistent referencing (mix of external jumps, in-text references, and footnotes) still needs to be cleaned up. Gzkn 00:51, 8 January 2007 (UTC)
 * In other words, this has now become a complaint that the solitary footnote has not been worked into the text, like the others. Please look at it. The content of the footnote is a long and cumbersome reference, which would be clumsy in text. This is what footnotes are for - to move references like that out of running text. Septentrionalis PMAnderson 04:15, 9 January 2007 (UTC)
 * You misunderstand me. I'm just saying the referencing should be consistent. If that would be clumsy in text, how are the other in text references not clumsy? The column of the footnote is already listed in the references. Why duplicate it? Gzkn 05:29, 9 January 2007 (UTC)
 * Because they do fit reasonably smoothly in text, and this won't. I came back here after looking at it. As for the referencing needing to be "consistent", for heaven's name, why? as long as it is clear and presentable? Wikipedia is inconsistent. Septentrionalis PMAnderson 06:12, 9 January 2007 (UTC)
 * "Because they do fit reasonably smoothly in text, and this won't" I would argue that stuff like A widely known statement of the problem is from Craig F. Whitaker of Columbia, Maryland in a letter to Marilyn vos Savant's September 9, 1990 column in Parade Magazine (as quoted by Bohl, Liberatore, and Nydick (1995)). (in the lead no less!) rebuts that argument. Gzkn 01:44, 15 January 2007 (UTC)
 * By "external jumps", do you mean "external links"? This would be a valid objection if the external link read [1] as many do; but it reads Let's make a Deal. Septentrionalis PMAnderson 04:15, 9 January 2007 (UTC)
 * There are plenty more external jumps than the Let's make a Deal one. And yes, there is even one that reads [1]: "The first appearance of the same general class of problem was probably the one presented in Joseph Bertrand's Calcul des probabilités (1889), known as Bertrand's Box Paradox [1]." And that link is now broken, so there's no source to back up the claim presented. Gzkn 05:29, 9 January 2007 (UTC)
 * That, at last, is a real problem, and I will see what I can do. Septentrionalis PMAnderson 06:10, 9 January 2007 (UTC)
 * Done. Septentrionalis PMAnderson 16:13, 9 January 2007 (UTC)


 * Regarding the example held up of "weasel statements", this appears to be supported by the Mueser and Granberg paper, which lists the perception of Monty as a "knowledgeable adversary", and any information given by Monty as information that he may be providing in an effort to deceive, as one of the "cues" that shape individuals' analyses of the problem and frequently lead them to incorrect assessments. This appears to be borne out in practice, as Cecil Adams discusses his initial analysis of the problem in terms of Monty trying to "bluff the contestants, then counterbluff them".  In short, it's not well-cited and not specific enough but calling it a "weasel statement" appears uncalled for. -- Antaeus Feldspar 00:40, 8 January 2007 (UTC)


 * I was just going by WP:WEASEL (see the Examples section)...please don't take it personally. "It has been speculated..." is a common beginning to a weasel statement. Again this could be corrected by just citing a source. Gzkn 00:51, 8 January 2007 (UTC)
 * I agree, it could definitely be vastly improved by citing the source and phrasing with more specificity (I made an attempt at doing this, actually, but found my editing skills not up to it while in the midst of a minor headache). I just think that "weasel statement" is a pretty strong term, and should really be reserved for those statements which could not be substantiated if they were phrased with more specificity.  Which are only a subset of "statements that could really benefit from more specificity." -- Antaeus Feldspar 01:37, 8 January 2007 (UTC)

The "Venn diagrams" are perfectly clear; they are explained by the paragraphs in which they sit. Making these into normal captions, with boxes, would make them worse. Septentrionalis PMAnderson 04:15, 9 January 2007 (UTC)
 * I think they might be a bit cryptic without a caption. I wish you wouldn't be so hostile though ("more careless objections")...no need for that. Gzkn 05:29, 9 January 2007 (UTC)
 * Perhaps I have been over-touchy. But I've just been through a long session with people who do simply count footnotes as their judgment on an article at Good Article Review. Septentrionalis PMAnderson 06:10, 9 January 2007 (UTC)
 * No, they are not perfectly clear; if you find them perfectly clear, I suggest a fresh set of eyes needs to copyedit the entire article. Sandy Georgia  (Talk) 19:20, 9 January 2007 (UTC)
 * I still find them clear; and I do have a fresh set of eyes. I do not remember editing this article at all before this discussion; and I certainly have nothing to do with these diagrams. Septentrionalis PMAnderson 20:13, 9 January 2007 (UTC)
 * I don't think a caption would make them clearer...for instance, the appropriate caption of the first picture would be the second sentence of the attached paragraph. I don't think that repeating this information would be very valuable. Christopher Parham (talk) 00:47, 10 January 2007 (UTC)


 * May I speak bluntly? I view this review with hostility and irritation, as the issues raised are either wrong or trivial. There is exactly one (1) use of the fancy new php footnote mechanism, introduced on 2006-11-27 by someone (Antaeus Feldspar) who obviously wasn't trying to be consistent with the perfectly valid style of referencing already used in the article. It is this new reference style that is the mistake, along with what I consider a review nomination based on not seeing a vast list of such "approved" references. Now we see an attempt to back away from the nomination reason, but the history is clear. This is a thinly disguised attack by the discredited inline citation squad. Nor is there a single other issue raised on this page that rises to the level of requiring a Good Article Review. Use the article talk page. End this absurdity now. --KSmrqT 06:45, 9 January 2007 (UTC)
 * Wow...I've never heard of this "inline citation squad" you speak of...I find it interesting that you hold me in so much contempt. Do I know you? I don't believe I've ever interacted with you before. "Thinly disguised attack"? Good Lord. What's with all this hostility? How is this helpful at all? Gzkn 06:56, 9 January 2007 (UTC)
 * You have trampled on a very sore corn among many editors, I'm afraid. See the talk page to WP:WIAGA for some of the history. But I must go. Septentrionalis PMAnderson 07:04, 9 January 2007 (UTC)

(edit conflict; mishandled by system, resulting in accidental removal): At any rate: the article has four different referencing styles, a problem which needs to be addressed, as well as the problem with trivia/anecdote and an External link farm. In terms of referencing, there is one cite.php footnote, some imbedded URL citations, some Harvard style inline refs, and numerous external jumps which should be either wikified or converted to refs. Any style is OK (once the external jumps are eliminated), but the article needs to pick one and stick with it. I'm not really keen on going through the article and looking at what still needs to be cited until the main editors decide which style they are going to use, and convert the imbedded links and external jumps so we can see where it stands. Last time I helped convert a math article, my work was reverted, so the rest of us can't help unless the editors decide which way they want to go. Is anyone going to work on it; if so, when do you expect to complete the first pass, so we can take a look at whether citation is lacking? There's no point in editors here trying to help - as we did at Featured article review/Regular polytope - if the bottom line is that no work is going to be done on the article anyway (as has occurred so far at Regular polytope). Sandy Georgia (Talk) 06:37, 9 January 2007 (UTC)
 * What do I expect?
 * Reviewers who have actually read the article with attention; counting footnotes is not enough. (If the present reviewers meet this, so much the better.)
 * Comments about citations which recognize that different forms of citations are useful for different purposes, even within the same article.
 * Complaints about lack of inline citation which cite instances of points which are both genuinely uncited and which are challenged or likely to be challenged. Septentrionalis PMAnderson 07:02, 9 January 2007 (UTC)
 * I'll be happy to read the article and provide a detailed list - as I did on Regular polytope - once the hostility subsides and you all decide if anyone is going to actually work on the article. In the meantime, four different referencing styles, the External link farm, the trivia, and jumps to external websites should be addressed:  it's not our concern which referencing style you use, or how many citations you count - this is not GAC.  It is our concern that the article is consistently referenced, and that text that needs to be cited, is cited.  Please contain your hostility towards Gzkn, who made a good faith nomination of an article that merits review, and leave your GA baggage where you found it.  Sandy Georgia  (Talk) 07:15, 9 January 2007 (UTC)
 * Gzkn began with a complaint which is, as he admits, factually false. That it was about inline citations raised more hackles; the stereotype of reviewers who insist on footnotes at every semicolon is less unfounded than it should be. This produced a certain level of hostility right off. Most of the rest of his complaints are either trivial, or blemishes which he perceives and others do not.
 * Heated rhetoric like "factually false" isn't necessary; the article needed review. Rather than dragging GAC baggage over here, let's focus on the work at hand.  Sandy Georgia  (Talk) 18:04, 9 January 2007 (UTC)
 * Sandy's complaints about Regular polytope are largely about a handful of speculative sentences, linking sourced archaeological finds. I spent a few minutes adjusting them, as she could have done herself; but I can see why she was ignored.
 * Incorrect on several counts. Most of the deficiencies there have not been addressed, you made a very minor edit to an article with a long list of problems, I hope regular polytope is not an example of what the Math Project considers compelling and brilliant, and I did start the work myself, but was reverted.  That's no problem (often FAs with so many issues have been abandoned, so we try to help out, but I'm happy to leave the work to others), but the editors who reverted should complete the work - there is a long list of work remaining on the article, including a thorough copyedit.  Sandy Georgia  (Talk) 18:04, 9 January 2007 (UTC)
 * There is a wider issue here, which should be addressed at WT:WIAFA: are citations a toolkit, or a shibboleth? If they are a toolkit, multiple forms of citation may be expected in a single article, as they are at Pericles; different tools serve different purposes. Septentrionalis PMAnderson 15:59, 9 January 2007 (UTC)
 * Comment Pericles does not cite different things in completely different ways, but the same things in two different ways. First, the entire reference is cited in the References section (i.e., # Kagan, Donald (1996). “Athenian Strategy in the Peloponnesian War”, The Making of Strategy: Rules, States and Wars by Williamson Murray, Alvin Bernstein, MacGregor Knox. Cambridge University Press. ISBN 0-521-56627-4.). The tiny part of this reference is then shoved between two ref tags and inserted next to the fact being cited (i.e., D. Kagan, Athenian Strategy in the Peloponnesial War, 54). The notes section, as you may or may not have noticed, is for footnotes, which are in turn given inline citations (i.e., "Pericles' date of birth is uncertain; he could not have been born later than 492-1 and been of age to present the Persae in 472. He is not recorded as having taken part in the Persian Wars of 480-479; some historians argue from this that he was unlikely to have been born before 498, but this argument ex silentio has also been dismissed.[142] [18]"). It's true that some sources contain external links and some do not, but that's generally because those sources are primary sources and are available on Wikisource, which has formatted things like this such that one can link to individual lines, saving people the time it takes to page down, risking paging down over it out of sheer impatience/boredom. It is cited using Ref_label because sticking footnotes in a section intended for references looks really stupid.--Rmky87 05:19, 13 January 2007 (UTC)
 * That would be an issue for WP:V; the issues with the math articles currently at FAR include but go beyond citation. This is not GAC, FAs are held to higher standard and more stringent, comprehensive review than the subjective GA process, and we don't just count citations on FAs.  Once you all have decided if you want to work on the article, I will thoroughly review it and provide a list if needed - but not eager to do that work if no one plans to address the problems, as has occurred at regular polytope.  Sandy Georgia  (Talk) 18:04, 9 January 2007 (UTC)
 * For the record, "uniformity" of citation appears nowhere in WP:WIAFA - or, as far as I can tell, anywhere else. Let us cut directly to what WP:CITE actually requires: "the most important thing is to provide all the information one would need to identify and find the source"; it would not be useful to invent requirements. Regular polytope could use a note to the effect that Coxeter's book contains all the non-controversial facts listed and not otherwise cited; but I see no corresponding difficulty here.  Septentrionalis PMAnderson 19:46, 9 January 2007 (UTC)
 * Many of the external jumps are valuable links and probably shouldn't be removed, so it would be wise to be careful about this. Christopher Parham (talk) 00:47, 10 January 2007 (UTC)
 * Removing external jumps doesn't necessarily imply removing the content. There are several ways to deal with external jumps.
 * Sometimes they're really intended as references, and can be converted to text with the external website as the citation.
 * Sometimes they are better listed as External links
 * It is never good prose to say, "For more information, see [1]"; that fails 1a. And, if it's just "for more information" that argues that the external jump belongs in External links.  If the content is important to the article's comprehensiveness, that argues against 1b.
 * Sometimes they indicate an article failing 1b, comprehensiveness. If an article links out to important information, it's not comprehensive - the subject of the external site could become a Wiki article, with a wikilink to the current article, or the text can be written in the current article, with the website used as a ref.
 * External jumps often indicate a lack of comprehensiveness or a failure to cite sources correctly. They often also get into the territory of WP:NOT; Wiki is not a webpage or a blog, with multiple links to external sites.  FAs should write their own content to the extent possible.  Once you all are finished massaging the article prose, its mixed referencing styles, and the external jumps, we can re-evaluate.  Sandy Georgia  (Talk) 15:14, 11 January 2007 (UTC)
 * "For more information, see [1]" fails 1a? I don't quite see why so. What phrasing would be better? I agree that an external jump might indicate a lack of comprehensiveness; that concern has to be weighed in each individual case (inlcuding here). But certainly an article can be comprehensive in the sense demanded by the FA criteria without providing all extant information on a subject. Finally, there is an argument that external links that elaborate on a specific segment of the article should be moved to the general EL section. IMO this does nothing but decrease the usefulness of the article. Christopher Parham (talk) 23:22, 11 January 2007 (UTC)


 * Comment Add 1a to the list of deficiencies, which like regular polytope, may be more significant than the other problems with 1b, and 1c. I had a glance at several sections to check the prose; it's not even necessary for Tony to have a look.  The article needs a serious prose check and thorough copy edit for things like basic grammar, tone, and typos.  If some of the math editors could move the article further along on the basics, a more thorough list and analysis might then be helpful. I am curious that so many editors are defending these articles without seeming to have read them (fallout from the GAC baggage?), and I wonder if the Math Project has a good copyeditor on board?  While I understand some of the math editors feel poked by GAC (I don't really understand why anyone even covets a subjective rating based on one editor's review anyway), FAs are held to higher standards, and there is work to be done on these articles. Sandy Georgia  (Talk) 18:44, 9 January 2007 (UTC)
 * It could use a copy-edit. I've seen recent FA's that were far worse, but I will do one. I shall not, however, be converting it into fake Edwardian; this is an encyclopedia, not an exercise in anachronism. Septentrionalis PMAnderson 19:46, 9 January 2007 (UTC)
 * Copy-edited about the first half; I do not claim to have caught everything even there. I found nothing positively ungrammatical; I hope this was not a reference to the split infinitives, which I retained: moving either always in the lead would produce the sort of journalese which Fowler condemns. Septentrionalis PMAnderson 20:29, 9 January 2007 (UTC)
 * Comment. The "History of the problem" section has an incomplete sentence. The "Combining doors" section should have "rather than" rather than "instead of", and I can't tell what "it" refers to. Actually, I'm not sure what this paragraph adds to the article, so maybe it could just be cut. The article seems a bit repetitive in other aspects and maybe could be shortened, but I don't really understand the complaints about the referencing. Gimmetrow 02:04, 10 January 2007 (UTC)
 * The article is repetitive, and has grown considerably since promotion. For reference, it was promoted July 7, 2005; the last version before promotion may be found here. Most of the "Variants" sections are new. The "Increasing the number of doors" section has prose issues now, but was only one paragraph in the original promoted version. Gimmetrow 03:37, 10 January 2007 (UTC)
 * Comment: I am of the opinion that the article could be cut in half, and its quality would dramatically improve. I am aware that not everyone shares this opinion. But in its current state, I find it overwhelming, directionless, and confusing. - Abscissa 02:49, 10 January 2007 (UTC)
 * Abscissa has a point. The article contains several explanations of the same result, and many of them could be struck. I suspect, however, that one will make sense to one reader, and another to another reader, so I'm not sure which ones, if any, to remove. This should be taken to the article talk page. Septentrionalis PMAnderson 03:07, 10 January 2007 (UTC)

List of random problems

 * Still contractions sprinkled around.
 * As is modern standard idiom. Septentrionalis PMAnderson 03:24, 10 January 2007 (UTC)
 * Fixed. --PresN 15:16, 11 January 2007 (UTC)
 * pronoun referring to the player changes randomly between "he" and "they" and "s/he"
 * Fixed. The gender is now never specified. -- Rick Block (talk) 23:58, 13 January 2007 (UTC)
 * Bold is used liberally for emphasis instead of italics
 * Fixed. -- Rick Block (talk) 00:03, 14 January 2007 (UTC)
 * These terms need wikilinks for those unfamiliar with mathematics: algorithm, decision tree
 * "The Monty Hall problem is a puzzle involving probability loosely based on the American game show Let's Make a Deal." involving probability loosely is quite awkward; ambiguous "loosely" comma duly inserted in first line. Septentrionalis PMAnderson 03:24, 10 January 2007 (UTC)
 * "Mueser and Granberg improved the phrasing;" Who? First time encountering these two names in the text...needs explication.
 * Clearly a reference. -- Rick Block (talk) 00:32, 14 January 2007 (UTC)
 * Well, it's clear to me as a regular Wikipedia editor that I should look down in the references section to find out who they are. Casual readers, though, will have no idea. Expanding a bit (University of Missouri-Columbia professors...) would be helpful. Gzkn 01:44, 15 January 2007 (UTC)
 * "The problem would be different if the game host were permitted to make the offer to switch more often (or only) depending on knowledge of the player's original choice or if the host does not know what is behind each door." Awkward and confusing
 * Changed to "more often (or only) if the player original chooses the car". -- Rick Block (talk) 00:32, 14 January 2007 (UTC)
 * "To drive the point home, one only has to imagine..." "To drive the point home" is hardly encyclopedic prose.
 * Fixed. -- Rick Block (talk) 00:51, 14 January 2007 (UTC)
 * "The player can then more easily appreciate the randomness of his first choice and the large amount of information he has gained since he made that choice and then see the wisdom in switching." winding snake
 * Deleted. -- Rick Block (talk) 00:51, 14 January 2007 (UTC)
 * "...if we increase the number of doors, why does this explanation assume the host would open 98 doors to make the problem similar to the original?" Why is first person being used in an encyclopedia?
 * Fixed. -- Rick Block (talk) 00:51, 14 January 2007 (UTC)
 * "It is correct to assume the host would open 98 doors in this alternate game; because in the 3 door game the player has only one switching option — and the player in the 100 door game must also be presented with a single switching option." Not exactly the correct use of the semicolon and mdash.
 * Reworded. -- Rick Block (talk) 01:43, 14 January 2007 (UTC)
 * Something needs to be done about the "Venn diagram" images. It's not clear upfront which image corresponds to which paragraph. Either refer to the image in text or use captions. Referenced in text. I hope it works for all computers. Septentrionalis PMAnderson 20:26, 10 January 2007 (UTC)
 * And now the Venn diagrams are centered, with text above clearly indicating diagram below. -- Rick Block (talk) 18:50, 14 January 2007 (UTC)
 * "There is a simple way for people to convince themselves that a switching strategy really does win two out of three times on the average, and that is to simulate the game with playing cards, playing Monty's role." Compelling prose?
 * Reworded. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "...he discards, should bring the point home" Compelling prose?
 * Reworded. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "Consider various possible host behaviors, in which his decision to switch may be based upon the accuracy of the contestant's initial guess:" Confusing way to have readers look at the table to the right. Just explicitly say so, instead of having a colon.
 * Fixed. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "With several minutes remaining in the game, the game host chose two players for the "Big Deal". Behind one of three doors was the grand prize. Each player was allowed to choose a door (not the same one)." Why the past tense all of a sudden? "remaining in the game"-->What game? What is the "Big Deal"?
 * Reworded. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "In this scenario, a variant of Selvin's problem can be stated." Who? First encounter needs explication.
 * Deleted. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "The game host eliminates a player with a goat behind his door..." ambiguous "his"
 * Reworded. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "How likely is that? 1/3." Compelling prose?
 * Reworded. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "The two player game, from the final player's point of view, resembles like the single player game:"
 * Reworded. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * "Actually, the two player game is exactly the same as the one player game, except in reverse."
 * Reworded. -- Rick Block (talk) 06:20, 14 January 2007 (UTC)
 * n doors section is full of second person. Not exactly encyclopedic.
 * Fixed. -- Rick Block (talk) 18:50, 14 January 2007 (UTC)
 * "which begins with 26 boxes (typically — it depends on the version of the show)" Compelling prose?
 * Changed to "which begins with a number of boxes (typically 26)". -- Rick Block (talk) 18:50, 14 January 2007 (UTC)
 * "the player's keeper is equally likely to be the winner" Player's keeper??
 * Reworded entire paragraph. -- Rick Block (talk) 18:50, 14 January 2007 (UTC)
 * "Another explanation is available at http://www.acbl-district13.org/artic003.htm". Why are we resorting to blog style here?
 * Deleted this sentence. -- Rick Block (talk) 18:50, 14 January 2007 (UTC)
 * "A similar problem appeared in Joseph Bertrand's Calcul des probabilités (1889), known as Bertrand's Box Paradox, which is the . In this you have three boxes, each with two drawers on opposite sides. Each drawer contains a coin; one has a gold coin on both sides, one a silver coin on both sides, and the third gold on one side and silver on the other. You open a drawer and find a gold coin; what is the chance of the other side being silver?" Something went wrong here. And why is second person being used now?
 * "you can't have picked the silver/silver box" Second person/contraction...compelling prose?
 * Compared to "the player cannot have chosen the silver/silver box"? Definitely. Septentrionalis PMAnderson 03:24, 10 January 2007 (UTC)
 * Both now moot; Bertand's box paradox is a separate article. Septentrionalis PMAnderson 20:26, 10 January 2007 (UTC)
 * "It went on to give examples..." compelling prose?
 * Changed to "Martin then gives examples ..." -- Rick Block (talk) 18:50, 14 January 2007 (UTC)
 * "Over 40 papers have been published about this problem in academic journals and the popular press." Citation? Where is this statistic from? Gzkn 02:18, 10 January 2007 (UTC)
 * It is from the Mueser and Granberg paper; I've added the citation. -- Antaeus Feldspar 05:10, 10 January 2007 (UTC)
 * I have three remarks for Gzkn:
 * If you are unfamiliar with the inline citation war, I apologize for casting you as a participant.
 * I still feel that all the issues I have seen here belong on the article talk page, and do not rise to the level of a review.
 * Thank you very much for your detailed critique of the writing. This level of attention and awareness is uncommon. Usually when I have that much to improve I find it easier to just edit the article! (Or, complain briefly and leave it.) Therefore, I will try to reward your attention with some of my own, as edits.
 * Many readers have strong, and often wrong, responses to this puzzle. I'm not sure why; this is not, say, "abortion". As you may be aware, whenever this happens the editing gets more challenging — both in fending off misguided alterations and in clearly and effectively addressing a diverse audience. For ordinary mathematics, we work hard to write prose that is clear, correct, and compelling; for extraordinary topics like this, we work twice as hard. And while I feel that most mathematicians write poor English, I also feel that most English majors write even worse mathematics.
 * Mathematics is inherently so formal that it drives many readers away; therefore good mathematics writers present the formal content in a more informal style. This is the opposite of the humanities, where personal opinions are often clothed in formal attire to lend them greater credibility. Guess which I prefer. --KSmrqT 07:08, 10 January 2007 (UTC)

Curiously silent
I apologize for not having participated in the discussion so far - I've been abroad on business for the past week. I'll read through all of the above and comment within the next few days (I am rather jet lagged at the moment). -- Rick Block (talk) 04:37, 13 January 2007 (UTC)
 * Since nominating this article for FA, I and others have watched the page to keep it mathematically correct. Many of the criticisms are more or less well founded, although as user:KSmrq notes above there is a difficult balance in mathematics articles in general, and this article in particular, between formal correctness and general understandability.  I will spend some time over the next few days addressing the  above.  -- Rick Block (talk) 20:15, 13 January 2007 (UTC)
 * I believe everything in the list has been taken care of. Good work! I still believe that the "In popular culture" is basically trivia that either can be worked into the text (the Erdos anecdote --> History) or is unnecessary and can be deleted (the NUMBERS episode). Are all the links in the External links section necessary? Some of the descriptions could probably be reworded too ("A Simulator that you can run in your web browser"). SandyGeorgia explained my view on the external jumps/referencing much more eloquently than I could have. Gzkn 01:44, 15 January 2007 (UTC)

Comments from SandyGeorgia
Note Please don't strike commentary from other reviewers: Gzkn provided his list (in addition to the commentary above it), but other editors are striking the items as if completed to Gzkn's satisfaction. Please request the original reviewer to strike if/when satisfied the concern has been addressed. Sandy Georgia (Talk) 15:04, 14 January 2007 (UTC)
 * OK. I believe I've unstruck all those that I struck, and I'll request Gzkn to rereview. -- Rick Block (talk) 16:39, 14 January 2007 (UTC)
 * Glad to see you so hard at work on it: please let us know when you've had time to get through Gzkn's list, as I'm still concerned about the way external jumps are employed, and how they contribute to 1a, 1b problems - I haven't read the entire article yet, and I haven't wanted to drop my list on you until I know you've had a chance to go through the article and finish your cleanup.  Also wondering why I see Venn diagram in the TOC, but no Venn diagrams in the article?  Also, I believe WP:MOS (or somewhere else) specifically deals with not using contractions - is that being addressed ?  Sandy Georgia  (Talk) 20:07, 14 January 2007 (UTC)


 * As far as I know, everything Gzkn has brought up has been addressed. I don't understand the external jump issue - can you explain?  The diagrams in the Venn diagram section show the universe of doors, divided into chosen and not chosen sets, with the probability of each door indicated.  These aren't quite traditional circular Venn diagrams, but they do show the probability relationship between the doors in the sets of "chosen" and "not chosen".  -- Rick Block (talk) 20:48, 14 January 2007 (UTC)
 * Forgot to mention - I don't think there are any more contractions. -- Rick Block (talk) 21:09, 14 January 2007 (UTC)

OK, if you're caught up with Gzkn, I'll give you a quick list of my concerns (I don't usually use Harvard inlines, so some of my suggestions may need to be adjusted to the correct formatting).

&mdash;From the Let's Make a Deal website That's a quick start - I still haven't thoroughly read the entire article, so these are just some directions of work. Sandy Georgia (Talk) 23:54, 14 January 2007 (UTC)
 * I'd like to see some adjustment to the lead if possible; the spoiler in the midst of it is distracting, and citations aren't usually provided in the lead (with some exceptions). Would it be possible to summarize the article, per WP:LEAD, without using the direct quotes, the citations, and the spoiler?  The lead should be a stand-alone summary of the entire article, without getting into too much detail in any one area.  There should be no text in the lead which isn't expanded in the article.  Rather than summarizing the article, the lead seems to be introducing the problem (with text that is not included elsewhere in the article).
 * Also, in some places I encounter too much text about the references which interferes with reading the article - example - this (followed by the quote) seems to be overburdening the lead with referenced detail - can the references and quotes be moved to the body, using the lead to summarize the article without getting into this level of detail?
 * A widely known statement of the problem is from Craig F. Whitaker of Columbia, Maryland in a letter to Marilyn vos Savant's September 9, 1990 column in Parade Magazine (as quoted by Bohl, Liberatore, and Nydick (1995)).
 * Whether this segment goes in the body or the lead, the prose seems to be more about the reference than about the problem. Does the reader really need to know the exact date, location, and author of the letter, for example, or can that be found in the Reference section for the reader who is interested in following up?  Is the date, location, and author of the letter central enough to the article to 1) be included in the text at all, and 2) be included in the lead?  Can you try something which introduces the quote, then simply provides an inline ref to the source, without the distraction of the extra detail?  The specifics on the source are already given in the References section, so it seems this could be reduced to one set of parentheses, pointing the reader to the ref.
 * This now reads "A widely known statement of the problem appeared in a letter to Marilyn vos Savant's Ask Marilyn column in Parade Magazine (Bohl et al. 1995)." Good enough? -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * Can the section heading, "The problem, with all constraints explicit" be shortened to just "The problem"?
 * Done. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * Prose - there is some prose redundancy which seems to make it harder for the non-mathmetician to read rather than easier -some examples:
 * The version of the problem popularized by Parade unfortunately leaves room for possible misunderstanding s ...
 * The reasoning of the solution is, at length: The chance of winning the car is doubled when the player switches from the original door to another door rather than sticking with the original choice.
 * The reason for this is that To win the car by sticking with the original choice, the player must choose ...
 * At the point w When the player is asked whether to switch, ...
 * By referring to "the problem as stated above", another chance to lose the mathmatically-challenged reader is introduced - maybe which statement can be somehow be clarified:
 * In the problem as stated above, it is because the host must reveal a goat and must make the offer to switch that the player has a ⅔ chance of winning by switching.
 * The most common objection to the solution is that, for various reasons, the past can be ignored when assessing the probability; thus ignoring the first choice of door, and the host's choice of which door to open.
 * These are all done. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * Those are just some samples from the top of the article of how prose might be tightened up to reduce redundancy and improve clarity - I didn't continue, but I doubt that the current prose is going to get past Tony: he is very good at re-working technical prose, and I'd consider begging him to help improve the clarity in some of these areas, considering there is still ample time left on review.
 * I've asked Tony1 for help. So far he's a done very light copyedit. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * Skipping now to the issues of the External jumps:
 * These kinds of external jumps raise several problems (see WP:NOT, WP:EL):
 * However, if the show host has not randomized the position of the prize in a fully quantum mechanical way, the player can do even better, and can sometimes even win the prize with certainty. There is an article explaining it and an applet demonstrating the effects.
 * If we have to jump to an external website to demonstate something, that argues against comprehensiveness (1b) of this article. External links almost never have a place in the text of the article (I've seen valid exceptions, but not to deviate from the topic - usually Geography articles that need to link to maps or daily weather - things we can't wikify).  And, this kind of prose is just not encyclopedic:  you wouldn't see it in Britannica, for example (argues against 1a).  Consider the reader reading this in hard print - does it make sense?  Is it comprehensive?  There are several general ways to resolve external jumps:
 * Write the Wiki article about the content of the External site, and link to the Wiki article.
 * Explain the content of the site, and reference it inline to the external site.
 * Or, if for coyright reasons, we really absolutely cannot write it or demonstrate it ourselves - via Wikified content or referenced content - then at least we should do an excellent job of prosifying the External jump. "There is an article" isn't excellent prose.
 * Sending our readers to an alternate site for an explanation - I can't see anything in the referenced site that we shouldn't be able to write ourselves, sourcing it to the original author. I don't see a rationale for the external jump; this argues against both 1a and 1b.
 * This external jump can easily be converted to an inline reference to the external website, which can be listed under References - the External jump is actually a reference - we shouldn't be sending Wiki readers outside of Wiki, unless absolutely necessary. External jumps almost always belong in External links or References (in this case, Refs):
 * It's now a reference. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * And if you ever get on my show, the rules hold fast for you &mdash; no trading boxes after the selection.
 * Also now a reference. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * Same situation here - what we have in this case is an entire sentence that is distracting from the text, and is actually an external jump which should be an inline reference:
 * In the May–June, 1989 issue of Bridge Today magazine, Phillip Martin wrote an article entitled "The Monty Hall Trap." The article presented Selvin's problem, with the correct solution, as an example of how one can fall into the trap of treating non-random information as if it were random.
 * Could become:
 * An example of how one can fall into ... is ... end of sentence(Martin, Phillip).
 * Then include Martin in the References section. By writing about the reference, the text becomes overburdened - the text need not be about the Reference - it can simply be inlined as a reference, avoiding sending Wiki readers jumping about the internet to external sites - we should internalize content as much as possible.
 * Also now a reference. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * Here is another example of an External jump that can be eliminated by prosifying the text, referencing it inline, and including the external jump in References:
 * The syndicated NPR program, Car Talk, featured this as one of their weekly "Puzzlers," and the answer they featured was quite clearly explained as the correct one. Transcript here. Also available in their book, Haircut in Horse Town (Magliozzi &amp; Magliozzi, 1998).
 * The syndicated NPR program, Car Talk featured the Monty Hall problem as a weekly "Puzzler", giving the correct answer (inline ref here pointing at the transcript and the book, which are included in References).
 * Now a reference. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * In some places, the article refers to Parade Magazine; others, vos Savant - by sticking to consistent references, the article will be easier for the non-mathmatical reader.
 * I think this is consistent now (refers to Parade). -- Rick Block (talk) 19:50, 16 January 2007 (UTC)
 * Eliminate parentheticals wherever possible - they are distracting and at times indicative of inattention to prose:
 * Consider various possible host behaviors, in which his decision to switch may be based upon the accuracy of the contestant's initial guess. (See table.)
 * The table shows various possible host behaviors, in which the decision to switch ...
 * All parentheticals are now gone, except in the Bayes Theorem section which is being actively edited. -- Rick Block (talk) 03:00, 17 January 2007 (UTC)
 * I don't speak Harvard inline, but this doesn't seem consistent:
 * The Parade column and its response received considerable attention in the press, including a front page story in the New York Times (July 21 1991) in which Monty Hall himself was interviewed.
 * If the reader wants to find the ref, what do they look for alphabetically in the References section? I think it's under Tierney, John (1991), so shouldn't that be the inline?  Again, the text is more about the reference, rather than text with a reference that doesn't interfere with the flow of the text.
 * Now a reference. -- Rick Block (talk) 19:50, 16 January 2007 (UTC)


 * Had a quick look, saw much improvement, but due to travel, request the review stay open until I can re-read the article. Sandy Georgia  (Talk) 20:27, 17 January 2007 (UTC)
 * Except for the comment about the lead, I believe all the specific concerns you've raised have been addressed. I've started a discussion about the lead on the article's talk page.  Please join the discussion there.  -- Rick Block (talk) 18:23, 21 January 2007 (UTC)

Second look from SG
Read the article last night; the improvements are significant, many of my concerns have been addressed, and I'd like to see us get this closed without moving to FARC. The prose flows better with the removal of the external jumps and extensive commentary about the references (as opposed to using the references), and prose redundancies have been reduced. I see a few minor issues remaining, but am still very concerned about the WP:LEAD.


 * Math notation problem: in the Bayes' theorem section, the math notation wraps off of my screen (I checked 3 different screens), and on printout, the longer formulations and text following formulas are chopped off.  Is there a way to decrease the size on the math formulas?
 * The longest one is now fixed, are the others problematic as well? -- Rick Block (talk) 03:37, 26 January 2007 (UTC)
 * The text under "subject to where the car is, i.e. conditioned on a proposition . Specifically, it is" is now wrapping correctly. There's still a problem with the formulas under "The denominator can be evaluated by expanding it using the definitions ..." and under "This can be proven using Bayes' theorem and the previous results:"  (On this computer - I can check laptop, larger screen, and a printout later.)  Is it possible to cut the formulas at a plus sign and manually wrap them to the next line?  Sandy Georgia  (Talk) 14:20, 26 January 2007 (UTC)
 * Yes. Done. -- Rick Block (talk) 05:34, 27 January 2007 (UTC)
 * Bertrand, Joseph (1889). Calcul des probabilites is listed in References - what is this, where do we find it?  Book, journal, paper?  More biblio info is needed.
 * I think this can be removed entirely. As far as I'm aware, it was there entirely because of the mention of Bertrand's Box Paradox, which was stated in an earlier version of the article to be the earliest known version of a Monty-Hall-like problem.  However, upon closer examination, Bertrand's Box Paradox turned out not to really be a Monty-Hall-like problem, despite some external similarities (such as the "intuitive" answer being 1/2 and the actual answer being 2/3.) -- Antaeus Feldspar 17:07, 25 January 2007 (UTC)
 * Deleted. -- Rick Block (talk) 03:37, 26 January 2007 (UTC)


 * I still see one place where a reference needn't be taking up "prose" space: in the Sequential doors section, rather than stating who proved what when as a separate sentence, we can remove that from the prose, and use it as a ref (also removing the colon and better prosifying the conclusion):
 * The best strategy is to stick with the first choice all the way through but then switch at the very end. With this strategy, the probability of winning is (n−1)/n (Bapeswara Rao and Rao, 1992).
 * Done. --Rick Block (talk) 03:37, 26 January 2007 (UTC)


 * Bridge principle section: a one sentence section ??  Also, wording is weasly.  This section needs to be somehow better incorporated into the whole.
 * Section deleted (there's a mention of related bridge problems in the History section). -- Rick Block (talk) 03:37, 26 January 2007 (UTC)


 * WP:MSH specifically addresses the word "The" in section headings: "The", "a" and "an" should be omitted from the beginning of heading titles. Thus "Mammals", not "The mammals".
 * Headings have been reworded so none start with "The". -- Rick Block (talk) 03:37, 26 January 2007 (UTC)


 * In the section labeled, "The general case", the first paragraph sounds weasly. "One common criticism" is unfortunate wording, as it invites a citation; criticism usually requires an "according to whom".  The second paragraph begins with the words, "In general", which also sounds weasly, and the generality isn't clarified.  There's also still some redundancy there - the entire section could be cleared up with tighter attention to the prose - also, the second paragraph is not at all clear.
 * One common criticism of the Monty Hall problem is that the host's behavior is not fully specified, such as the version published in Parade in 1990. In that instance, it was not specifically stated that the host would always open another door, or always offer a choice to switch, or even that the host must open a door containing a goat. The criticism is that without specifying these rules, the player does not have enough information to conclude switching is the best option.
 * In general, the best course of action depends on the behavior of the host and switching may not be successful two-thirds of the time. The table shows possible host behaviors and the impact on the success of switching.
 * A suggestion (perhaps not the best suggestion - just an idea):
 * In the version of the Monty Hall problem published in Parade in 1990, the host's behavior is not fully specified; in that instance, it was not specifically stated that the host would always open another door, or always offer a choice to switch, or even that the host must open a door containing a goat. Without specifying these rules, the player does not have enough information to conclude switching is the best option.  The best course of action depends on the behavior of the host; if the host's behavior varies from the version on the Monte Hall show, switching may not be successful two-thirds of the time. The table shows possible host behaviors and the impact on the success of switching.
 * Reworded. -- Rick Block (talk) 03:37, 26 January 2007 (UTC)


 * Now, to the bigger problem of the lead. If you go to the first section (The problem), you see that the problem is not introduced in the text, rather the lead.  The text of the article dives in to the middle of the problem.  The problem should not be introduced in the lead - it should be included in the text, with the lead summarizing the entire article. A summary need not include the solution or the spoiler; I believe if you'll restructure the first part of the article - so that the problem is introduced in the text - then a more general, summarizing lead can be written, without the necessity of getting into problem/solution detail in the lead. For an article this size, a shorter lead would be acceptable, discussing the problem in general terms.
 * Change proposed at talk:Monty Hall problem. -- Rick Block (talk) 03:37, 26 January 2007 (UTC)


 * And, finally, to the touchier subject of citations :-) I understand and have read numerous times the objections against citing math/science articles, and the comparisons made to medical articles such as the ones I usually edit.  I've seen the argument that standard mathmatical knowledge/info need not be cited, as it can be found in any textbook, and I agree that the math here is fairly standard to a math major.  On the other hand, I can also give dozens of examples of statements in Tourette syndrome that are common medical knowledge to a neurologist and that can be cited to dozens of different textbooks or journal articles:  so, I pick one.  A reputable one.  Doesn't matter which one, as long as I know it's an acknowledged, reputable source, to assure Wiki readers I'm not just making it up.  The fact that it is common knowledge, available in any textbook, doesn't mean I can't/shouldn't cite it.  I may accept the common knowledge math here, but not everyone is a student of math.  I can see that each step in the math formulations need not be cited, but I can equally see that there are numerous references and external links (already provided) which could be used to cite sections of the article, so that an interested party can refer to a source if they want to follow up or verify.  I don't see a reason not to put a general reference for each different mathmatical formulation - for example, any textbook or website where a reader can go to follow up on the Bayes' theorem formulation.  We simply can't present an entire formulation without somehow demonstrating that it's not original research.  Or, where can a reader find the Decision tree formulation (pls, no Ronald A. Howard - ).  These can be any textbook, or any number of the external links, references given at the bottom of the article.  It should be possible - with such common knowledge and such an oft-discussed problem - to give one general ref for each math formulation/section.
 * Added a reference for the Bayes Theorem formulation (Gill 2002).The Glopk 07:00, 27 January 2007 (UTC)

I am very close to Keep on this article, and hope the lead can be reworked, some general cites can be given for each formulation, and we can get this closed without FARC. Sandy Georgia (Talk) 19:55, 24 January 2007 (UTC)

Comments from ChuckHG
As a mathematician who has used the Monty Hall Problem in his probability classes, I offer these comments:
 * The paragraph The problem would be different... does not belong in the Solution section. It has nothing to do with the solution presented and should either be deleted or moved elsewhere, perhaps to The general case section.
 * Changed to "The solution would be different". This section is presenting the solution to what is generally meant by the "Monty Hall problem".  Qualifying that other solutions are possible given other host behaviors seems fair to me. -- Rick Block (talk) 02:26, 23 January 2007 (UTC)
 * There seems to be a somewhat laissez-faire use and interchangeability of the words probability, chance, and odds. In particular, probability and odds have a specific and different mathematical meaning/defintion; for example, a 2/3 probablility is 2:1 odds, and a 1/3 probability is 1:2 odds.  Chance is generally a loosely defined concept, probably most often taken to mean the same as probability (as in 1 out of 3 chance of winning).
 * Where it meant probability I've replaced "odds" with "probability". -- Rick Block (talk) 02:26, 23 January 2007 (UTC)
 * That the popular Parade statement of the problem is itself subject to misunderstanding through unstated assumptions (and is a significant contributing factor in the widespread disbelief in its solution) is omitted from the lead, in spite of the fact that a major part of the article is given over to addressing these issues. -- Chuck 17:09, 22 January 2007 (UTC)
 * I've added a sentence about this to the lead. -- Rick Block (talk) 02:26, 23 January 2007 (UTC)

Status: Anyone think we can close this? I've asked the nominator to look again. Marskell 21:07, 24 January 2007 (UTC)
 * No. I have a LONG list of outstanding concerns above.  Sandy Georgia  (Talk) 21:31, 24 January 2007 (UTC)
 * Gzkn's page indicates he's on a Wikibreak for personal reasons :-( Sandy Georgia  (Talk) 14:27, 26 January 2007 (UTC)

Concerns of Gzkn
Good work. I'm fairly confident we can avoid FARC once Sandy's and my concerns are addressed. Here are things I feel still need work:
 * I'm not too wild about the tone of the recent expansion of the "Bayes' theorem" section (informal "we" used throughout). If the other explanatory sections can do without the first person plural, this one can too. Also, some of the longer math notation scrolls off the screen for any monitor resolution smaller than 1024x768.
 * I, too, have reservations about the Bayes theorem section. There is a similar, less well written but mathematically more cogent, treatment of the Monty Hall problem on the Bayes's theorem (sic) page. Chuck 15:26, 25 January 2007 (UTC)
 * I am sorry to disagree with the above statement. That treatment is very verbose, and while I can see its usefulness in showing the role that different choices of priors play in the inference, it's really too contrived to count as a proof of the Monty Hall winning solution - unless we regard a "proof by making up lots of examples" as acceptable. In the ususal statement of the Monty Hall problem the solver has no freedom of choice of either priors or conditionals.
 * I agree that the informal "we" can be removed, but - given the limitations on math notation in Wikipedia, am a bit at loss on how to address the criticism on the length of the equations. The longest equations (the expansion of the normalization constant at the denominator of the Bayes expression) are aligned so that their three terms maintain the same position and meaning throughout. I think it makes it much easier to understand.The Glopk 18:35, 25 January 2007 (UTC)
 * The approach I'm exploring is using a table for the definition of the conditional probability of the Hij proposition using one table line per case and plain text for the description (rather than a "math" case expression and "math" generated text). This looks similar but doesn't end up forcing horizontal scrolling - although it doesn't preserve the meaning inside the "math" expression. -- Rick Block (talk) 20:01, 25 January 2007 (UTC)
 * I've eliminated the informal "we" from this description and am working on reducing the length ot the math notations. I'm not sure what the sense of Chuck's comment is - are you suggesting adding the bit about varying the probabilities of the door the host picks, as in Bayes's theorem?  -- Rick Block (talk) 18:23, 25 January 2007 (UTC)
 * Perhaps we can address Chuck's concern by adding at the end of the section a sentence or two to explain in qualitative terms the outcome of that Bayesian machinery. For example, something like: "Notice how the host's actions have no bearing on the probability of the door first picked by the user since its posterior probability remains equal to its prior value of 1/3. The effect of the host's opening of Door 3, on the other hand, is clearly shown by the last two equations: it is to cause the probability of that door to collapse from its prior value of 1/3 to 0, thus doubling the probability of the only remaining door.". Would that be acceptable? The Glopk 20:00, 25 January 2007 (UTC)


 * There's still the "In popular culture" which smacks to me of trivia. Is it truly necessary? Can the notable ones can be integrated into the History section? Gzkn 01:13, 25 January 2007 (UTC)
 * The pop culture references are now a paragraph in the History section. -- Rick Block (talk) 03:55, 26 January 2007 (UTC)

Status
There are good faith efforts underway to address the concerns that have been raised (including the most recent batch from SandyGeorgia posted at 19:55, 24 January 2007 (UTC) and Gzkn's immediately above). I suggest either the FAR be extended or the concerns be taken to the article's talk page and the FAR closed. -- Rick Block (talk) 20:10, 25 January 2007 (UTC)


 * Well, if there are still concerns we can't do option b and just close. Let's leave it here two or three more days and then move it to FARC to keep the page moving; it can always be closed if there are rapid keeps from the people involved. Marskell 14:39, 26 January 2007 (UTC)


 * Close without FARC - my concerns have been satisfied. (Gzkn is on a wikibreak, unfortunately, but by my read, his concerns have been met as well.)  The lead is much cleaner (short, but adequate), referencing has been attended to, and prose has been tightened up; I still get a wrap of the math formulas on one screen, but that could be my problem.  Hopefully the Math Project will find a way over time to reduce the size on math notation.  Nice work!  Sandy Georgia  (Talk) 14:33, 27 January 2007 (UTC)
 * The above discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article review. No further edits should be made to this page.