User talk:Martin Hogbin/Archive 3

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 1

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Archive 10

As requested...

"Guy, perhaps you could explain to me on your (or my) talk page what you think is going on and how it conforms to WP policy. I really do not understand it."

Glad to do what I can. DISCLAIMER: I am by no means an expert on Wikipedia policies, but I have read a lot of them and wached as they are applied.

Thanks, it is good of you to discuss this with me.

"The indefinite ban in Glkanter was made not by Arbcom but by a single admin."

Nope. Blocks are not bans. Bans are not blocks.

WP:BLOCKBANDIFF

explains the difference.

Fine but from the point of view of the person blocked a block is worse, they are physically prevented from editing WP. I see no point in making this distinction

BTW, I am guessing that you might think "indefinite" means "permanent." It does not. In this case, the indefinite block (blocks are not bans) will almost certainly be lifted when the arbcom makes its final decision.

I though that may be the case but it is still very unpleasant for the receiver. Indefinite prison sentences are genralyy considered bad, by much of society and the prisoners themselves.

"My understanding is that admins are not police or arbitrators but people carrying out administrative work on behalf of the WP community."

Nope. Not only is it true that admins are police, but it is also true that all editors are police. Many police powers (revert) are given to everybody including IP editors who are here for the first time. Other police powers (rollback) are given to editors who have shown some trustworthiness (I have rollback privileges). Other police powers are given only to admins, others only to the arbcon, and a few (deleting the main page, deleting everything and shutting down Wikipedia permanently) are only given to Jimbo Wales.

"They have the right, indeed the duty, to ban people as a result of a community consensus, but in the case of Glkanter there was no such consensus, there was not even a discussion."

Nope. There are things that are basically police actions (you or me reverting edits, any admin applying a block) that require no prior consensus. The reason they require no prior consensus is because they can be undone with a single mouse click by another editor or another administrator. In such cases you are free to seek consensus after the fact that the action was wrong and should be undone, but no prior consensus is required.

I guess a prisoner can be freed with only a key click. Martin Hogbin (talk) 19:22, 23 March 2011 (UTC)

"It is my belief that Elen acted completely beyond her powers and contrary to the spirit and policies of Wikipedia."

I, the 14 admins on the arbcon. and 3 uninvolved admins all disagree. Do you have any specific quotes from specific policies that you believe were violated? If so, I will be glad to examine each one and give my opinion.

"Glkanter's comments were relatively mild and made in his own user space about a WP editor who had brought the Arbcom action against him."

I, the 14 admins on the arbcon. and 3 uninvolved admins all disagree. I strongly disagree. Such behavior is totally unacceptable by any Wikipedia editor. He cannot plead ignorance; he was blocked twice before. I personally told him that he should be on his best behavior during arbcom. There is a pattern here. The 1000 word limit does not apply to him. The rules about not editing another user's evidence section do not apply to him. The warnings attached to his two earlier blocks (see his talk page) do not apply to him. And now the rules about civility and personal attacks do not apply to him.

"and made in his own user space"

Irrelevant. Show me a policy that says personal attacks are allowed on user pages.

"about a WP editor who had brought the Arbcom action against him."

Irrelevant. Show me a policy that says personal attacks are allowed in retaliation for bringing a dispute to arbcon.

Seriously. The above is not just empty words used for emotional impact. You are the one claiming that certain things are allowed and certain others are not allowed. The burden is on you to supply specific quotes from policy documents supporting your claims.

"It may well be that, had the matter been pursued through the proper channels, Glkanter would have ended up with a ban (although I doubt an indefinite one from the whole of WP) but this is no excuse for not following the proper procedure."

Proper procedures were followed. Name one that wasn't.

(In response to "the block imposed on Glkanter is not a ban") "Sorry that I got the terminology wrong but the fact is that he cannot edit due to the action of an admin."

If you had bothered to read

you would have read this:

"Banning should not be confused with blocking, which is a technical mechanism used to prevent an account or IP address from editing Wikipedia. While blocks are one mechanism used to enforce bans, they are most often used to deal with vandalism and violations of the three-revert rule. A ban does not, in itself, disable an editor's ability to edit any page. However, editors who violate a ban may have their account access blocked entirely, as a way of enforcing the ban."

May I gently suggest that you read the policies before accusing people of violating them?

) 16:55, 23 March 2011 (UTC)

Martin, excuse me for butting in, but both you and Gill need to reconsider your "allegiance" to Glkanter. You probably see Glkanter as "on your side", but from my brief interaction with him just before he was blocked, he was not acting like someone who is here to collaborate, and even assuming that was temporary lapse in his judgment, Glkanter has some

WP:AE... Tijfo098 (talk

) 21:04, 23 March 2011 (UTC)

Tijfo098, perhaps you should assume good faith on the part of myself and Gill. I have not questioned Glkanter's block because he is 'on my side' as you put it, I have questioned it because it is, in my opinion wrong, and I believe that Gill takes the same view. In his professional life he has acted in court cases where much more serious injustices have taken place and has a strong interest in miscarriages of justice in general. Martin Hogbin (talk) 21:47, 23 March 2011 (UTC)

I am just disappointed that, after specifically asking for my input, Martin ignored it except for making the one comment above.

talk

) 21:26, 23 March 2011 (UTC)

Guy, I do not understand. In what sense have I ignored your input? Martin Hogbin (talk) 21:47, 23 March 2011 (UTC)

If you think the rules of Wikipedia are unjust, then direct your arrows against these rules, and try to get them changed. If you feel that in this case the rules were wrongly applied, then explain which rule was applied wrongly how. If you can't do that, then do not blame the people who enforce the rules while exculpating someone who consistently refuses to pay attention to them.  --Lambiam 23:26, 23 March 2011 (UTC)

Lambiam, you may recall that you left the MHP article in disgust because of the iron grip over the page by a small group of editors. It is only because of the persistence of Glkanter that you and others are now free to improve the article. Martin Hogbin (talk) 00:24, 24 March 2011 (UTC)

I can only interpret this reaction by assuming you think the block was punitive and meant to be long-lasting. I don't see how or why you would think it is punitive, and Glkanter could have had it lifted in an instant by promising to stop his ranting (which he did all over Wikipedia) and become a good editor. Instead he just went on and on even after having been blocked.  --Lambiam 18:47, 24 March 2011 (UTC)

Martin, rest assured, I do assume good faith on behalf of both of you and Gill. But there is such thing as

) 23:33, 23 March 2011 (UTC)

Perhaps you all read

WP:BLOCK

differently from me. This is what I see:

...blocking is a serious matter, and administrators should avoid imposing blocks that are unlikely to be preventative in the reviewable circumstances.

Blocks should not be punitive

Blocks should not be used:

1. in retaliation against users; 3. as punishment against users,

Blocks should be preventative

Blocks intended solely to "cool down" an angry user should not be used, as they often have the opposite effect. However, an angry user who is also being disruptive can be blocked to prevent further disruption.

Those are the bits which tell you not to block him. Under which part of the policy was Glkanter blocked? Martin Hogbin (talk) 00:08, 24 March 2011 (UTC)

They prevented him from annoying (almost) everyone any further—wikijargon for that is

WP:DE. Isn't that obvious? Tijfo098 (talk

) 00:19, 24 March 2011 (UTC)

The quoted reason for his block was text on his talk page. From what I know of it it was a relatively polite criticism of Rick but unfortunately we cannot see what he wrote now. Martin Hogbin (talk) 00:24, 24 March 2011 (UTC)

He was warned by a couple of Arbs to stop that several times, e.g. (and the next diff from Glk is another giant rant about Rick). Since you like legalisms so much, do yo expect to spit a judge in the face in the courtroom and walk out? Or a more appropriate one: spit your boss in the face and not be fired? Tijfo098 (talk) 00:43, 24 March 2011 (UTC)

Re: "I guess a prisoner can be freed with only a key click", such melodramatic language is not helpful. The correct analogy isn't someone being put in prison, but rather someone being denied admittance to a privately-owned business because of repeated disruptive behavior. We don't own Wikipedia and we are here as guests of the owners. Anyone can start an online encyclopedia, and Wikipedia will even give you the software needed to run it for free. Many have tried to start alternative encyclopedias with different sets of rules, including at least one that was based upon giving disruptive editors like Glkanter free reign. All have failed. Please consider that perhap the nasty old rules are not as bad as you think they are.

Re: "Under which part of the policy was Glkanter blocked?",

WP:BLOCK

says "A user may be blocked when his or her conduct severely disrupts the project; that is, when his or her conduct is inconsistent with a civil, collegial atmosphere and interferes with the process of editors working together harmoniously to create an encyclopedia." If this longstanding pattern of disruptive behavior doesn't qualify, I don't know what does. Obviously you disagree, but just as obviously a bunch of people who don't know each other are telling you that you are wrong. There are few things more disruptive than personal attack on arbitrators during an arbcom.

Re: "Blocks should be preventative" and "Blocks intended solely to 'cool down' an angry user should not be used, as they often have the opposite effect. However, an angry user who is also being disruptive can be blocked to prevent further disruption.", nobody even hinted that Glkanter needed to cool down. Quite the contrary, actually; many have noted that warnings and blocks have no apparent effect on his behavior.

Re: "Blocks should not be punitive", "Blocks should not be used in retaliation against users" and "Blocks should not be used as punishment against users", Nobody but you seems to think they are in this case. I have been monitoring arbcon cases (without commenting) for a long time, and it is my observation that arbitrators are hypersensitive to any hint of such behavior by other arbitrators, and do not hesitate to say so.

Re: "The quoted reason for his block was text on his talk page. From what I know of it it was a relatively polite criticism of Rick but unfortunately we cannot see what he wrote now", not even close. The quoted reason for his block is still there, and was an attack on an arbitrator after repeated warnings not to attack anyone. The following (from the diff Tijfo098 posted above) couldn't have been more clear:

"If you have something to say about him or anything else to say to the arbitrators, present it calmly and neutrally, otherwise your talk page access will be removed so that arbitrators don't need to keep reading your posts here. If that happens, you will still be able to communicate with the arbitration committee via email, however you will be put on moderation and rants will be rejected."

So, in summary, you have failed to show a single policy that was not followed.

talk

) 04:41, 24 March 2011 (UTC)

Thanks for coming to my talk page to explain things to me I understand very well now. Martin Hogbin (talk) 21:17, 24 March 2011 (UTC)

Hello Martin, as you know, I was not involved in the process at all, other than being named in arbitration and being at the receiving end of a somewhat unkind and (IMHO) undeserved comment from you. Lack of time and (mostly) of interest. Now that it is coming to an end, and with a fairly predictable conclusion, I just want to point you to a short WP essay: I hope that reflecting upon it may be useful to you as a WP editor and to the project as a whole. It's Wikipedia:Randy's enablers. Cheers glopk (talk) 03:18, 24 March 2011 (UTC)

Glopk, you have made some unkind remarks about me in the past. Let us call that quits.

I read your essay. I guess the main reason that I have supported Glkanter is justice. This is a very fragile concept that is easily eroded by convenience. Those enforcing rules need to maintain higher standards than those breaking them. 'He had it coming' and similar arguments must not be accepted.

Today's heros were yesterday's troublemakers. There is agreement amongst the arbitrators that there was a degree of page ownership and tendentious editing by some editors. As I have pointed out to Lambiam above, it is thanks to the action of Glkanter the many editors who were driven away from the page by those factors can now return and edit the page.

Finally let me make clear that I do not agree with the way that Glkanter has dealt with this arbitration and I have told him so. Martin Hogbin (talk) 09:16, 24 March 2011 (UTC)

Re "I would also point out that it is often because of people like Glkanter that things get done" my rebuttal consist of the following arguments:

Wikipedia, which does not tolerate such behavior, is a huge success. Every online encyclopedia - in fact just about every online forum of any kind - that does tolerate such behavior has been a resounding failure.

You are in a very small minority that believes that people like Glkanter get things done. Many people from highly experienced administrators to totally uninvolved editors have told you that his behavior hurts Wikipedia.

Re "it is thanks to the action of Glkanter the many editors who were driven away from the page by those factors can now return and edit the page". highly debatable, almost certainly not true, and even if it were true, two wrongs don't make a right. Justice means that everybody has to play by the same rules. Even Jimbo Wales must follow the rules. See http://en.wikipedia.org/wiki/Jimmy_Wales#Controversy There is no exception for someone who does what you describe, and what you describe is not a credible claim.

Re: "I guess the main reason that I have supported Glkanter is justice", I take great offense to the implication that I am not supporting the consensus view of Glkanter's behavior because of justice. Give me a real example of someone being treated unfairly and I will be the first to defend that person. This is clearly not such a case.

In summary, your assertion that Glkanter has been treated unfairly and your assertion that Glkanter has been a force for good are, in the opinion of pretty much everybody who has examines them, totally without merit. Glkanter has been treated fairly and within the rules. This is a fact, and you are simply wrong if you think otherwise. If you think the rules are unfair, try to change them. Go ahead and introduce a proposal to the effect that "getting things done" excuses an editor from the rules concerning civility and personal attacks. But until the rules are changed to accommodate you, live by the current rules and admit that you have no case when you claim that the rules were not followed.

talk

) 11:59, 24 March 2011 (UTC)

Martin fighting Arbcom and the people who regularly go there is much akin to pissing in the wind, you may good and valid reasons that are perrfectly valid and make sense and they the wind will only blow them back in your face. It's a pointless debate that only ends in frustration.

talk

) 14:16, 24 March 2011 (UTC)

True, but in this case the reasons are neither good nor valid.

talk

) 14:28, 24 March 2011 (UTC)

I think there are plenty of very good and valid reasons. You have to carefully observe the whole history and you have to have some understanding of the content, before you are able to make a good judgement on this, I think. Appearances can be deceptive. You can't judge behaviour without any sensitivity to the content. Richard Gill (talk) 14:48, 24 March 2011 (UTC)

Hell In A Bucket, you are right, of course. Martin Hogbin (talk

) 14:59, 24 March 2011 (UTC)

One Arbcom member (John Vandenberg) did "carefully observe the whole history" and commented: "I have had the joy of reading all the archives; I tried to poke out my eyes afterwards." Some others of us have had the joy opportunity to observe the history in realtime and have no quarrel with the apparent outcome. hydnjo (talk) 18:23, 24 March 2011 (UTC)

I, on the other hand, have been careful not to read the MHP page, the MHP talk page, or any sections of user pages covering MHP content. That is because I categorically reject the assertion that "You can't judge behaviour without any sensitivity to the content." Bad behavior is bad behavior, and no possible content (or bad behavior by others) can turn bad behavior into good behavior. I have avoided MHP content because of a simple principle: either evidence of bad behavior is presented in the diffs or it isn't. If it isn't, no sanctions are allowed and anyone who tried to impose sanctions without someone posting diffs showing bad behavior would have a dispute with me and we would be going through the dispute resolution process. On the other hand, if the diffs do show misbehavior, ignoring that misbehavior based upon content is not allowed

It seems clear that some here are setting themselves up so they can conclude that the arbitration committee - every one of them - is wrong, that I am wrong, that Hydnjo is wrong, etc. I am going to predict that despite claiming that we are all wrong, there will be no attempt to go through the various steps of dispute resolution, because that would require evidence rather than assertions.

talk

) 20:53, 24 March 2011 (UTC)

'Some here'. That is not a personal attack I trust. Martin Hogbin (talk) 21:19, 24 March 2011 (UTC)

Yes, Guy, but John learned Tsirelson's theorem, and you haven't! ;-) Tijfo098 (talk) 00:24, 25 March 2011 (UTC)

I'm not saying everybody was wrong, nor am I saying that anybody in particular was wrong. I'm saying that something fishy has happened. I'm not surprised and I'm not complaining. I'm analyzing and commenting.

A wikipedia admin gets a minor penalty for ownership issues. A newcomer editor who strongly fought those ownership issues, because he was confronted by them on his very first day on wikipedia, gets a very heavy sanction. Whereas it seems that his most serious crime was to carefully document said ownership issues on his talk page. OK, so everyone superficially can see that he is breaking wikipedia rules that you mustn't say things about other editors, which can be interpreted as personal. But if you objectively document behaviour of another editor and say that it comes across to you as unfair, ownership, and so on .. I don't think that that is a personal attack.

Please also remember that it was said admin who requested the arbitration because in his opinion said newby editor was the cause that mediation was failing.

Please also recall that said newby who got this heavy punishment said ugly things about yours truly, and yours truly reciprocated in the same spirit, without either of us reporting the other to the authorities. Please also recall that said newby complained about other editors' OR and other editors' lack of respect for Verifiability, and these findings were confirmed by the arbitration. Richard Gill (talk) 15:53, 25 March 2011 (UTC)

OK, I know I'll regret this - and make no promises to continue this conversation, but this is really too much. Richard, I do think you too should read Wikipedia:Randy's enablers and meditate upon it. Let's take it point by point:

A wikipedia admin gets a minor penalty for ownership issues -- Could it be because the documented issues were found to be minor? And occurring in the course of a neverending effort to reach consensus by offering practical solutions in the form of actual and proposed edits, rather than rants and venting and personal attacks?

A newcomer editor who strongly fought [...] gets a very heavy sanction -- Under what definition of "newcomer" would Glkanter fall? Have you any idea of the size of his own diffs? It's large. Did he not participate in this MHP debate for near two years? He did. Did he not go through rounds if RfC, mediation and - finally - arbitration? Ditto. Is it a fair expectation that after all that he should have learned the rules of the WP house and, if he had a case, prevailed? It is. But not only he did not learn the rules, he actually managed to follow nearly to the letter points 1,3,4,6,7,8,10 and 11 of the

BGD

template, with a predictable result.

OK everyone superficially can see that he is breaking wikipedia rules [...] But if you objectively document behaviour of another editor [...] I don't think that that is a personal attack -- That is an interesting notion of justice. Let's see how it may apply in real life: if I publish nasty and entirely unfounded smears about you, and you sue me for libel in the Crown's Courts to protect your reputation, and all the available objective evidence indicates that you would indeed prevail, do you think that your barrister would advise you that, by all means, you jolly ought to go every day to Court and rant and personally attack me, the jury, the clerks, and the judge?

Remember that it was said admin who requested the arbitration because in his opinion said newby editor was the cause that mediation was failing -- Entirely irrelevant to the conclusion - please re-read carefully Guy's comments above: arbitration and mediation cover separate problem areas. In fact, it was Glkanter inability or unwillingness to understand this fact that caused the first scuffle between him and the arb clerks. Glkanter was named in arb by Rick because of his behavior, not his opinions regarding the MHP article.

Recall that [Glkanter] said ugly things about yours truly, and yours truly reciprocated in the same spirit, without either of us reporting the other to the authorities -- That was between you and him. Does it imply that everybody else should put up with such behavior?

Other editors' lack of respect for Verifiability [...] confirmed by the arbitration -- And how does that excuse Glkanter's own behavior?

Regards, glopk (talk) 17:29, 25 March 2011 (UTC)

An arbitration case regarding Monty Hall problem has now closed and the final decision is viewable at the link above. The following is a summary of the sanctions that were enacted:

• Standard discretionary sanctions are enacted for all articles related to Monty Hall problem
  (broadly interpreted)
• Glkanter is banned from Wikipedia for one year, and is further subject to an indefinite topic ban on subjects related to the Monty Hall Problem.
• Nijdam is topic banned from the subject of the Monty Hall problem for a period of one year.
• 1RR
  on the Monty Hall article for a period of one year.

For the Arbitration Committee, NW (Talk) 00:47, 25 March 2011 (UTC)

Discuss this

SilkTork, as you will see, Blackash continues to exert a strong opinion on the talk page on issues with a strong commercial and personal COI. I think it is essential for Blackash to be banned from the Tree shaping talk page so that editors with no commercial interest or personal involvement can discuss the issues of article name and current practitioners without continual interference.

This argument has gone on for years now. Several editors who came long ago in response to an RfC in this subject have been unable to make any progress because of continual interference from COI editors. Slowart obviously also has a COI but at least seems willing to withdraw from certain discussions if Blackash does the same. Something needs to be done. Martin Hogbin (talk) 08:52, 31 March 2011 (UTC)

I did consider suggesting that the topic ban should include discussion of the topic anywhere on or linked to Wikipedia as I felt that the matter would not die simply with a ban on directly editing the article. I'll take a look. SilkTork *^YES! 10:31, 31 March 2011 (UTC)

Thanks for that. Martin Hogbin (talk) 11:14, 31 March 2011 (UTC)

[comment deleted; issue was resolved]

) 13:53, 9 April 2011 (UTC)

I have struck out my original intro and replaced it with a more appropriate one. Martin Hogbin (talk) 08:23, 9 April 2011 (UTC)

Hi Martin, I don't want to come across as being overly picky, but I really do not approve of copying my signature into a reply post as you did at

09:36, 10 April 2011 (UTC)

No problem, I will attend to the matter. I sometimes copy sigs as an easy way of referring to or addressing an editor but I also object when this causes confusion as to who said what. I will be more careful about copying sigs in the future. Martin Hogbin (talk) 09:41, 10 April 2011 (UTC)

Thanks, I have no problem with linking to my page but an exact copy of my signature does cause confusion - especially to me. I have now withdrawn the RfC, it does seem pointless if Samurai is going to work on the article. SpinningSpark 10:11, 10 April 2011 (UTC)

You are involved in a recently filed request for arbitration. Please review the request at Wikipedia:Arbitration/Requests#Tree shaping and, if you wish to do so, enter your statement and any other material you wish to submit to the Arbitration Committee. Additionally, the following resources may be of use—

• Wikipedia:Arbitration/Requests#Requests for Arbitration;
• Wikipedia:Arbitration guide
  .

Thanks,

An Arbitration case involving you has been opened, and is located here. Please add any evidence you may wish the Arbitrators to consider to the evidence sub-page, Wikipedia:Arbitration/Requests/Case/Tree shaping/Evidence. Please submit your evidence within one week, if possible. You may also contribute to the case on the workshop sub-page, Wikipedia:Arbitration/Requests/Case/Tree shaping/Workshop.

On behalf of the Arbitration Committee, Salvio ^{Let's talk about it!} 10:40, 28 April 2011 (UTC)

Greetings,

I happened to find a paper yesterday which briefly mentions Edwards' transformations.

Malykin, G. B. (2009). Classical optical experiments and special relativity: A review. Optics & Spectroscopy, 107(4), 592-608.

I'm not posting this to the "one-way" talk page because I'm not suggesting it be included. It does contradict the wiki article, but I strongly suspect Malykin is incorrect in his conclusion. I thought you might be interested.

It's a three-sentence subsection within a section titled incorrect para-Lorentz transformations. Malykin lists quite a few of these, followed by a section with "correct" para-Lorentz transformations, of which he lists just two: Tangherlini and Sjödin transformations. Below is the section.

Edwards Transformations

In 1963, W. F. Edwards proposed the following transformations:

${\displaystyle x'=\left(1+2v/c\right)^{-1}\left(x-vt\right),\quad y'=y,\quad z'=z,}$

${\displaystyle t'=\left(1+2v/c\right)t.}$

It follows from these that

${\displaystyle c'_{x}=\left(c-v\right)\left(1+2v/c\right)^{-2},\quad c'_{y,z}=c\left(1+2v/c\right)^{-1}.}$

It is clear that these transformations cannot explain the results of the Kennedy–Thorndike experiments.

<end of article section>

It seems likely from the quote cited to Edwards in the "one-way" article and from other discussions of Zhang elsewhere, that Malykin's analysis didn't properly take into account that these transformations are anisotropic for the outbound and return legs.

Also, to answer your query from ten months ago, Tom's contact information can be found from the FNAL Phone Book (a web search will find it). He mentions that at the top of the "experimental basis of SR" faq. You may or may not want to contact him at this point, but in case you do for any reason that ought to work. Tim Shuba (talk) 20:24, 4 June 2011 (UTC)

Good to hear from you. I would certainly prefer Zhang's, and even Tom's, analysis over Malykin's. Thanks for the contact info. Martin Hogbin (talk) 22:12, 4 June 2011 (UTC)

Undo what you did on 2011 wimbeldon for the following reasons. You have not followed a single MOS guidline, didn't discuss with the user and then locked it for the anon so that you can do your own thing. An encyclopedia must be fullfilling and state everything. Your edit is so wrong undo it now. — Preceding unsigned comment added by Rageing Bull (talk • contribs) 20:05, 6 July 2011 (UTC)

There is no place in WP for advertising. It is an encyclopedia not a billboard. Martin Hogbin (talk) 20:50, 6 July 2011 (UTC)

That's not an answer that's a POV. Plus you removed the reference which was being used else where. Well done for fine work of incompetence— Preceding unsigned comment added by 78.147.179.68 (talk) 22:50, 6 July 2011 (UTC)

The above post is by banned sockpuppet user:KnowIG Fyunck(click) (talk) 23:37, 6 July 2011 (UTC)

An arbitration case regarding Tree shaping has now closed and the final decision is viewable at the link above. The following remedies have been enacted:

1. The topic covered by the article currently located at
   discretionary sanctions
   .
2. User:Blackash is topic banned from all discussion on the correct name for the tree shaping/arborsculpture/pooktre topic for one year. The topic ban includes talk pages, wikipedia space and userspace, but only covers discussion of what name should be given to the practice, and what title should be used for any articles on the subject.
3. User:Sydney Bluegum is topic banned from the subject of tree shaping/arborsculpture/pooktre widely construed for one year. The topic ban includes talk pages, wikipedia space and userspace.
4. User:Slowart is topic banned from all discussion on the correct name for the tree shaping/arborsculpture/pooktre topic for one year. The topic ban includes talk pages, wikipedia space and userspace, but only covers discussion of what name should be given to the practice, and what title should be used for any articles on the subject.
5. The community is urged to open up a discussion, by way of request for comment, on the article currently located at Tree shaping to determine the consensus name and scope for the subject matter, whether it should stand alone or whether it is best upmerged to a parent article. To gain a broad consensus, naming and scope proposals should be adequately laid out and outside comments invited to gain a community-based consensus. This should be resolved within two months of the closing of this case. Parties that are otherwise topic banned are allowed to outlay proposals and background rationale at the commencement of the discussion, and to answer specific queries addressed to them or their proposals. This concession is made due to their experience and familiarity with the area.
6. Within seven days of the conclusion of this case, all parties must either delete evidence sub-pages in their user space or request deletion of them using the {{
   db-self
   }} template.

For the Arbitration Committee,

) 15:48, 15 July 2011 (UTC)

hi mate, from previous discussions I recall you might be of more of a philosophical than mathematical bent. If you're interested I would like to play the two envelopes problem with you, to illustrate the fallacy in the switching argument.... If you're not interested, no worries. To kick it off, there is $1 in one envelope and $2 in another. You are holding an envelope. Now - what is A? Dilaudid (talk) 17:45, 21 July 2011 (UTC)

I get the impression that you are going to tell me something I already know. Have you seen the new section that I added called, 'Introduction to resolutions of the paradox'? In that, I point out that for a finite distribution step 6 fails. Martin Hogbin (talk) 20:19, 21 July 2011 (UTC)

Well apologies for patronising your math skills. But what I'm trying to point out is that for any proper distribution, step 6 fails. There is nothing in the switching argument that distinguishes between a finite or infinite distribution. Therefore if it is not valid for one, it is not a valid argument for either. This is what happens when one defines A sloppily. Dilaudid (talk) 05:16, 22 July 2011 (UTC)

Let me start with where I think we agree:

• For a finite distribution, step 6 always fails.

• A distribution such as 'chance that the smaller of the two envelopes contains an amount between 2n and 2n + 1 is p(n), where n is any whole number' is improper and this leads to a non-sequitur regarding step 6.

However, if you look at the second variant, you will see that, 'examples can still easily be found of proper probability distributions, such that the expected value of the amount in the second envelope given that in the first does exceed the amount in the first, whatever it might be'. Here, step 6 holds good, but the expectation is infinite for both envelopes. This essentially invalidates step 8. I do not see anything about a sloppy definition of A. Martin Hogbin (talk) 08:49, 22 July 2011 (UTC)

Can I suggest moving this conversation to the talk page, where others can join in. Martin Hogbin (talk) 08:50, 22 July 2011 (UTC)

The sloppy definition of A that I was worried about is whether it's a random variable ${\displaystyle A}$ (and we are frequentists) or it's a positive real number ${\displaystyle x}$ (and we are bayesians). It's clear we are talking about a Bayesian approach, which means that the probabilies of ${\displaystyle x}$ being the greater or lesser are functions of ${\displaystyle x}$, and a prior distribution. While you are correct that you can have a proper prior with infinite expectation, you cannot have a proper prior where the probabilities are 1⁄2 for all ${\displaystyle x}$, so either step 6 fails or the prior is improper. And it is true if you allow an improper prior the infinite expectation means that step 8 fails (although I hadn't realised that until you explained it) this means irrespective of the prior we choose, the argument is fallacious. Let's take this back to the main talk page when we are in agreement, if that's ok with you. Dilaudid (talk) 10:30, 24 July 2011 (UTC)

Just to clarify - I think the quote you have there is from Chalmers paper. I was interested and confused by that point for a little while after I read his paper, you just explained its resolution rather well (infinite expectations mean that it *doesn't matter*). This isn't relevant to what we are interested in, which is the precise flaw in the switching argument (which is using an infinite uniform prior, an improper prior). It's more relevant to the St Petersberg Paradox. I think we need to be careful not to start mixing our paradoxes, that leads to madness. Dilaudid (talk) 10:39, 24 July 2011 (UTC)

Dilaudid, I seem to be having a related conversation on the 'arguments' page. Let us continue there. Martin Hogbin (talk) 08:31, 26 July 2011 (UTC)

Ok will take a look at the talk Dilaudid (talk) 07:28, 27 July 2011 (UTC)

The best ref, IMO is Horticultural Reviews, Volume 35 [1] Horticultural Reviews, Volume 35 Edited by Jules Janick Copyright & 2009 John Wiley & Sons, Inc. Page 442. section 4. Creation of Unusual Growth Forms. In the ornamental nursery trade, it is a common practice to graft a scion from dwarf or weeping cultivar onto a tall straight stem of a compatible understock to mimic an arborescent growth habit. Tree roses can be formed by double working using a shrubby garden rose scion, a Multuflora de la Grifferaie interstock, to form a straight trunk, and ‘Dr. Huey’ rootstock. Grafting to create unusual growth forms in a practice called arborsculpture involves intertwining and grafting together the stems of two or more plants in order to create domes, chairs, ladders, and other fanciful sculptures (Fig. 9.2)" Thanks for asking. Slowart (talk) 21:31, 29 July 2011 (UTC) Martin Slowart is Richard Reames Arborsculpture him self.?oygul (talk) 01:43, 2 August 2011 (UTC)

Yes, I know, why are you telling me this? Martin Hogbin (talk) 08:07, 2 August 2011 (UTC)

	The Civility Barnstar
	For polite and sensible discourse in an RfC at Tree shaping. Noleander (talk) 19:26, 4 August 2011 (UTC)

From an observer at the north pole of the earth looking straight up, all the stars appear to be orbiting and affected by a fictitious centripetal (not centrifugal) force. Why is this type of fictitious force not included in the wiki articles about the various types of fictitious forces? Rcgldr (talk) 17:49, 12 August 2011 (UTC)

It is! In the rotating reference frame of the Earth, the stars are subject to a (outwards) centrifugal force and a greater (inwards) Coriolis force. The net result is the required centripetal force that holds them in orbit. But why are you asking me? Martin Hogbin (talk) 19:04, 12 August 2011 (UTC)

Yes, I later realized the apparent coriolis force has double the magnitude and opposite direction of the apparent centrifugal force giving the appearance of an apparent fictitious centripetal force, but one that is covered by the existing coriolis and centrifugal forces. I asked you about this since you posted on the dicussion page for centrifugal force. Rcgldr (talk) 15:52, 13 August 2011 (UTC)

I am glad that is resolved. Martin Hogbin (talk) 17:42, 13 August 2011 (UTC)

I read what you wrote on the MHP talk page about levels of the problem. Maybe you yourself do believe such levels exist. Rather then just mentioning them it would give more insight to formulate what you mean. Just mention what the problem should be on the different levels. Nijdam (talk) 17:22, 13 August 2011 (UTC)

Hiya, when you file a checkuser request on an account, please consider notifying the related users about the request, thanks. --Elonka 00:33, 14 August 2011 (UTC)

The SPI instructions state that there is no requirement to notify suspected sockpuppets of a pending investigation. This is in contrast to most other WP processes (ANI, Arbitration, etc) where notification of involved persons is required. I suppose that SPI notification may seem like the polite thing to do, and in some cases it may be desirable, but there are situations where it may increase drama and should be avoided. --Noleander (talk) 01:50, 14 August 2011 (UTC)

True, notification is optional according to SPI instructions. But in this situation, related to Tree shaping, I am asking Martin Hogbin to make the notifications. Since they are on public pages anyway, I do not see any compelling reason why they should be kept quiet, and filing the requests without informing other parties is tending to just add confusion to an already confusing situation. --Elonka 02:11, 14 August 2011 (UTC)

I have never used SPI before and, after reading that notification was not a requirement, I actually forgot to notify those involved. I am happy to do so if yo wish, if I can work out how to do it. Martin Hogbin (talk) 08:27, 14 August 2011 (UTC)

Done! Martin Hogbin (talk) 08:31, 14 August 2011 (UTC)

I do comment here on your point 1 - 6. Concerning point 2. it is not necessary to assume the contestant chooses uniformly. Concerning the symmetry with respect to the door numbers: this means that for every combination of door numbers the decision will be the same, based on the different conditional probabilities, having the same value for every combination. Nijdam (talk) 12:34, 14 August 2011 (UTC)

Nijdam, it might be best to continue these discussions by email, or are you allowed to discuss the subject in user space? Martin Hogbin (talk) 21:45, 14 August 2011 (UTC)

I'm only banned from pages typically about the MHP itself. Nijdam (talk) 03:48, 15 August 2011 (UTC)

OK. Let me start with the term 'conditional'. I do not find this term particularly helpful but, nevertheless, let use the convention that events which occur with certainty in our scenario (those required by the game rules) are not considered conditions.

One immediate problem we encounter is that the game rules are not very well described in the Whitaker/vos Savant statement. In fact we have to make many of them up. Iet us make the normal assumptions, that the host always offers the swap, for example, even though the question only tells us that in this particular instance the host offers the swap we choose to assume that the host always offers the swap. You might note at this stage that the same applies to the words spoken by the host. We take it that the host is required to say exactly the same words each time he offers the swap. If we do not make this decision we should consider every word that the host uses to be a condition of the problem. Alternatively we could make the assumption that the words spoken are of no significance or, more specifically, that the position of the car after the host has spoken is independent of the words he says. Do you agree so far? Martin Hogbin (talk) 08:30, 15 August 2011 (UTC)

Concerning the term conditional. what do you mean by "not finding it helpful"? If it is just the word, you know, as Rick end I have often said, it is easy to avoid the word, and use some understandable terminology. But in this discussion it is easier to use this word, as we know exactly what it means. And in this discussion we cannot avoid it, because is crucial in the solution.

Do not try to confuse the discussion again with words said by the host, audience coughing, wind blowing etc. No source ever takes such thing into account. Neither do I. No one, except you, does. Any source, even the less reliable, describe the MHP in terms of the door with the car, the chosen door and the door opened by the host. So, just start from there. Nijdam (talk) 21:48, 15 August 2011 (UTC)

I am not confusing the discussion, I am clarifying it. before we can answer the question at all we need to decide exactly what it means. This means deciding on the game rules and on what aspects of the question are significant. We have to make a decision that the words spoken by the host are not important. The question itself does not tell us that. Martin Hogbin (talk) 17:34, 16 August 2011 (UTC)

May be it clarifies thing for you. Nowhere in the problem statement it says that the way things go, depends on something else than the aspects I mentioned. Nijdam (talk) 22:13, 16 August 2011 (UTC)

You are quite right, but then the problem statement does not tell us anything at all about the way that things go. We have to decide for ourselves what events are significant before we can address the problem.

It is quite possible in a game show that the host would try to give clues as to what action the player should take by means of the language that he used. If we consider that this might be a possibility we must take it as a condition of our problem. In fact, this scenario seems more likely than that of a host having a bizarre and inexplicable preference for one door over another. Martin Hogbin (talk) 22:35, 16 August 2011 (UTC)

In this discussion I'm not interested in all kind of diversities. What do you think the average reader will (have to) understand as the MHP? Nijdam (talk) 07:02, 17 August 2011 (UTC)

To answer you question first, the average reader clearly understands the MHP as a problem where door numbers have no significance. In view of the fact that vos Savant added the door numbers to the problem it also seems clear that this was how Whitaker intended the problem to be understood. Of the thousands of letters from readers that vos Savant received there is no evidence that even one of them considered the door numbers, and more specifically the number of the door opened by the host, to be relevant. They may not all have used this language to describe their intuitive understanding but the average reader clearly understands the probability that the car is behind the originally chosen door to be independent of the door numbers in general and specifically of the door number opened by the host. It was some months before anyone (Morgan et al) proposed this dependence.

Regarding your interest, if you are going to arbitrarily ignore information in the problem statement then you cannot regard yourself as tackling the problem properly. The statement clearly tells us that the host says the word 'pick' before the player makes the decision on whether to swap or not. The statement does not tell us that the host always says this word so we must consider that case that the host might use another word or at least we must give a rationale for not doing so.

If course, I am being a little perverse, but so were Morgan et al. As a simple puzzle we regard the probability that the car is behind the originally chosen door to be independent of the door numbers and the specific door opened by the host, the words spoken by the host, and many other things. This is a perfectly reasonable and intuitive interpretation of the problem and it is the one that Whitaker intended and vos Savant responded to.

If you want to use this problem as a test for your students that is fine but it is unfair to expect them all to make the same decisions that you do. Most important is to make clear the decisions that have been made. Martin Hogbin (talk) 08:14, 17 August 2011 (UTC)

You seem to know the average reader well. And even then, what do you mean by: "have no significance"? It will be easily understood by the average reader that (with quite natural assumptions) that any aspect of the solution will be invariant under permutation of the door numbers. So what? Where does this lead us?

The probability distribution of the position of the car is NOT independent of the door opened by the host. And hence it is not obvious that the probability for the chosen door to hide the car has initially the same value as after the host opened the goat door. Notice that I'm very careful in formulating this. That's where the simple solution fails as a solution to the full MHP, as you have admitted yourself.

So again: please formulate the version of the MHP as you think the average reader will understand it. And add if you also think this is the MHP as you understand it. Nijdam (talk) 15:52, 17 August 2011 (UTC)

In the standard version of the problem the host chooses a goat-hiding door uniformly at random. The host's choice of door is therefore independent of the position of the car. Martin Hogbin (talk) 19:10, 17 August 2011 (UTC)

Do you mean to say that, if one introduces random variables for the position of the car and the door the host opens, these two variables are statistically independent? Nijdam (talk) 21:34, 17 August 2011 (UTC)

No, I mean that which of the goat-hiding doors the host opens is independent of the position of the car. Martin Hogbin (talk) 21:38, 17 August 2011 (UTC)

What then do you mean by "independent"?Nijdam (talk) 08:39, 18 August 2011 (UTC) Any chance on an answer? Nijdam (talk) 09:59, 19 August 2011 (UTC)

You are correct and I am wrong here. let me try to reformulate exactly what I mean. Martin Hogbin (talk) 10:34, 9 November 2011 (UTC)

(Editing)

"t will be easily understood by the average reader that (with quite natural assumptions) that any aspect of the solution will be invariant under permutation of the door numbers". Where does this leave us? It gives us the statement "Prob(other door hides car| numbers of doors chosen and opened) = Prob(other door hides car) = 2/3". It tells us to switch and that the probability of winning by switching is 2/3. It tells us that the specific door numbers can be ignored from the outset. Richard Gill (talk) 08:31, 6 November 2011 (UTC)

You finally admit, it is the conditional probability that counts? Nijdam (talk) 08:40, 6 November 2011 (UTC)

As I have said before, Nijdam, I have no objection to the use of the word 'conditional' if that makes you happy. We wish to calculate the probability of winning the car given all the significant conditions of the problem. It is a problem in conditional probability, as is every problem in Bayesian probability. However, as Richard say above we can easily deduce that the number of the door opened by the host is insignificant, along with many other things, and therefore we can ignore it in our calculations.

As I have said before, Martin, I have no objection not using the word 'conditional' if that makes you happy. As long as we wish to calculate the probability that governs the situation after we know which door is initially chosen and which one opened. The way this probability is calculated is irrelevant. Nijdam (talk) 17:01, 6 November 2011 (UTC)

Yes of course. That is the (conditional) probability that the player will win if they choose to swap. Ther are no other significant conditions. 17:32, 6 November 2011 (UTC)

No!!Nijdam (talk) 21:54, 6 November 2011 (UTC)

The host must open a door to reveal a goat. The sample space cannot be conditioned on this event, neither does it need to be. We knew at the start this would happen. Martin Hogbin (talk) 22:23, 6 November 2011 (UTC)

A sample space is never conditioned, so what do you mean? Of course we know at the start what is going to happen in general, but we do not know which door will be chosen and which will be opened. Nijdam (talk) 09:55, 7 November 2011 (UTC)

The urn again

If you remember, I have proposed a simple urn problem where you agree that you would do exactly the same thing, that is to say you would ignore unimportant facts and calculate the answer in the simplest manner possible.

I do remember, and also there he probability at stake was the conditional probability. Nijdam (talk) 17:01, 6 November 2011 (UTC)

Yes, but you were happy to calculated it in a simple manner, ignoring irrelevant conditions. Why will you not do the same for the MHP? Martin Hogbin (talk) 17:32, 6 November 2011 (UTC)

I also do with the MHP. But the way of calculation bears no significance, so why bother?Nijdam (talk) 21:54, 6 November 2011 (UTC)

I do not understand what you mean. I repeat a slightly modified version of the problem below. Perhaps you could answer my questions.

The urn problem restated

There are nine white balls in an urn numbered 1 to 9 and one black ball. Normal urn conventions apply. The first person takes a ball, which proves to be the white 5. The second person takes a ball which proves to be the white 7.

The third person is about to take a ball. How do you calculate the probability that they will take the black ball? What sample space do you start with. Do you need to explicitly calculate P(B3=R|B1=W5,B2=W7) or would you take an obvious short cut and just calculate P(B3=R|7 white balls and one red ball are left in the urn)?

The probability I have to calculate is P(B3=R|B1=W5,B2=W7), but I may reason it has the same value as P(B3=R|7 white balls and one red ball are left in the urn) (different experiment), and even simplify to reason that it is equivalent to an urn experiment with 7 white and 1 red ball. This only simplifies the calculation, but the relevant probability is the original P(B3=R|B1=W5,B2=W7). And it is obvious I can't say: it is the probability to draw the red ball, because this probability is 1/10 (in the experiment at stake). In this experiment it is clear that there is a difference between the probability to draw red in the original experiment and the conditioned experiment, because there is also a difference in numerical value. In the MHP however the values are the same, but as I explained several times, the nature of the probabilities differ. They also refer to different experiments. Nijdam (talk) 12:37, 7 November 2011 (UTC)

You say, 'the probability I have to calculate is P(B3=R|B1=W5,B2=W7)' but suppose now there are two urns containing identical sets of balls, a blue urn and a red urn. At the start you pick the blue urn. Do you now have to calculate P(B3=R|B1=W5,B2=W7,urn=blue)?

Of course. Also here, as in all the other situations, it is about the difference between the numerical value and the nature of the desired probability. As you understand, the reasoning is again, because of symmetry, or equivalence, the desired probability has the same value as a similar probability for one of the urns.Nijdam (talk) 22:30, 9 November 2011 (UTC)

What if your name was John? Would you now calculate P(B3=R|B1=W5,B2=W7,urn=blue,your name is John)? Martin Hogbin (talk) 00:27, 10 November 2011 (UTC)

Is my name in any way part of the experiment? If not, i.e. if my name is not relevant for any of the outcomes of the experiment, then my name does not have to appear in the sample space, and hence I can't condition on it. If, however, my name is part of the experiment, i.e. if for instance the experiment has to decide before the drawing is performed, which one of a set of people, among which I am, will do the drawing, and I'm the lucky one, then yes do I have to condition on my name. Nijdam (talk) 11:13, 10 November 2011 (UTC)

I agree with what you have written, especially, 'if my name is not relevant for any of the outcomes of the experiment, then my name does not have to appear in the sample space'. Would you not say the same is true for the host's choice of goat-door?

Well, you should know by now. The numbers of the doors are part of the problem. The player has a choice what door to pick, and the host in some cases also has a choice. Nijdam (talk) 15:14, 11 November 2011 (UTC)

Yes I do know, if you are interested in the the door number that hides the car or the number of the door that the player ends up with then the door number opened by the host is important but if you are only interested in whether the player ends up with the car or not the door number opened by the host is unimportant. Martin Hogbin (talk) 16:36, 11 November 2011 (UTC)

As elsewhere: unimportant for what? Nijdam (talk) 20:17, 11 November 2011 (UTC)

Answer??Nijdam (talk) 08:13, 13 November 2011 (UTC)

Unimportant for calculating the probability that a player who decides to swap will end up with the car or not. Martin Hogbin (talk) 09:37, 13 November 2011 (UTC)

A player always ends with the car or not, so this probability is 1. May be you mean something different. I suggest you specify the sample space and formulate exact what you mean. Nijdam (talk) 19:07, 13 November 2011 (UTC)

Yes, it was rather badly expressed, the probability of interest was the probability that a player who decides to swap will end up with the car. Martin Hogbin (talk) 10:05, 14 November 2011 (UTC)

On the other hand suppose you are presented with an urn containing one black ball and seven white balls marked 1,2,3,4,6,8,9. What probability would you now calculate? Martin Hogbin (talk) 10:21, 9 November 2011 (UTC)

Why should I calculate any probability? I might as well play some game with the balls. I mean, if I'm presented an urn without stating a probability problem, there is no need to do a probability calculation. Nijdam (talk) 22:30, 9 November 2011 (UTC)

As before, what is the probability that you will draw the black ball and how would you calculate it? Martin Hogbin (talk) 00:22, 10 November 2011 (UTC)

To make it instructive, I state the sample space, which is the urn itself, with a uniform probability law. Hence P(Black ball) = 1/8. No need for any calculation, as this probability is given. Nijdam (talk) 11:13, 10 November 2011 (UTC)

But is the uniform probabilty law (by virtue of the urn conventions) not equally applicable in the case where you have seen the W5 and W7 removed from the urn?

Conditionally yes. Nijdam (talk) 20:17, 11 November 2011 (UTC)

What do you mean by that? Martin Hogbin (talk) 01:09, 13 November 2011 (UTC)

In the case I've seen W5 and W7 being removed from the urn, this removal was part of the experiment. The original probability law, governing the urn, was a uniform distribution on the 10 possible outcomes. After the removal of W5 and W7, and stating that again a random draw has to be made, conditionally a uniform distribution governs this new situation. The point is not the uniform nature, but the conditional nature with respect to the original probability law. Nijdam (talk) 08:13, 13 November 2011 (UTC)

What would be your answer to the original urn problem stated at the top of this section if the balls were not numbered? Martin Hogbin (talk) 16:36, 11 November 2011 (UTC)

Then I calculate P(black | first draw was white and second draw was white). Nijdam (talk) 20:17, 11 November 2011 (UTC)

Just to be clear What sample space would you use? Are you saying that you would do the full conditional calculation? Martin Hogbin (talk) 01:09, 13 November 2011 (UTC)

You bring up an interesting question. Normally this is modelled by numbering the balls and taking the numbers as the outcomes. It raises a philosophical question about the distinguishability of the balls. Such problems play a role in physics as well. If the balls are indistinguishable, is it then possible to take one out, because it then is distinguished from the others? So my answer to your question will be, I number the balls. And then for the second part, you often ask about the calculation, which is unimportant. I just would point to - or prove - the equivalence with an urn with only one black and 7 white balls. Nijdam (talk) 08:27, 13 November 2011 (UTC)

It is an interesting point. Unlike bosons, which are fundamentally indistinguishable, all real macroscopic objects are distinguishable in principle. The question becomes one of whether we wish or need to distinguish between them and that depends on the question that we are asking and its context.

In the unnumbered ball urn question above I think you would agree that there is a strong case for treating them as indistinguishable. The interesting point is that there is a good case for treating the numbered balls as indistinguishable (even though we obviously can distinguish between them) because of the urn convention and the fact that we have no interest in the ball numbers in solving our problem. Martin Hogbin (talk) 11:12, 13 November 2011 (UTC)

Okay, indistinguishable of the white balls means, although we see different balls, once a ball has been drawn it is impossible to tell which one it was. The experiment consists of three successive draws of a ball without replacement. Possible outcomes are: BWW, WBW, WWB, WWW, as only the order of drawing and the colour matter. These four outcomes form the sample space. Probabilities are 1/10, 1/10, 1/10, 7/10, calculated in different ways. For instance; P(BWW)=P(WBW)=P(WWB)=P(The black ball is drawn)=1/10. Then P(3rd draw is B | 1st and 2nd draw are W)= P(WWB|WWB or WWW)=(1/10)/(1/10 + 7/10) = 1/8. Or equivalently by pointing to the remaining urn with 1 black and 7 white balls; P(3rd draw is B | 1st and 2nd draw are W)= 1/8. Nijdam (talk) 23:38, 13 November 2011 (UTC)

But the white balls are, in principle, distinguishable. Why have you chosen not to distinguish between then? Martin Hogbin (talk) 10:05, 14 November 2011 (UTC)

You asked what I would do if the balls weren't numbered, that's why. But it is irrelevant. The problem may be analyzed with or without numbering the balls. You're drifting away from the topic, which is the conditioning on what happened previously. Nijdam (talk) 11:43, 14 November 2011 (UTC)

A real problem

Nijdam, perhaps you would answer this question for me. Suppose you were employed as a probability consultant and a client came to you with a real-world version of the urn problem above.

9 white objects, numbered 1..9, and 1 black object are placed in an opaque container. You client has seen a person reach into the container without looking and remove white object number 5. They have then seen a second person do the same thing and end up with object number 7. Your client then asks you what the probability will be that they will end up with the black object if they reach into the container without looking and also how this probability should be calculated. What would you say to them? Martin Hogbin (talk) 16:48, 11 November 2011 (UTC)

Apparently he shows me an urn with 7 white and 1 black ball. The removal of the balls 5 and 7 were no part of the experiment. Piece of cake. Sample space {B,1,2,3,4,6,8,9}, random draw.Nijdam (talk) 20:31, 11 November 2011 (UTC)

This was meant to be a real-world problem. Is that what you would really say to your client? There are no urn conventions in the real world. Martin Hogbin (talk) 23:19, 11 November 2011 (UTC)

Well, I would have discussed all details with the client. But you gave me practically all the details, and as you said "urn problem", and asked for a probability, I assumed a random draw has to be made from the (remaining) content of the urn. Nijdam (talk) 17:11, 12 November 2011 (UTC)

I though I was being clear. This was meant to be an real-world version of the problem. The point I am making, however, is that there is a set of conventions that apply to urn problems that do not apply in the real world. In the real world you would have to discuss many things with your client, starting with asking exactly what they meant by 'the probability, and including many other things, such what the objects in the urn might be, whether thy might be distinguishable by touch, and many others that I am sure you could think of.

There are different conventions and rules for the same problem, depending on the context in which it is asked. In an examination question, for example, the student would be expected to assume that all the necessary information was given in the question and that all the information given was relevant to the answer in some way. But, as you have agreed above, in a real-world scenario you cannot assume that all the relevant information has been presented to you in the client's initial problem statement or that all the information given is relevant to computing the probability that the client actually wants to know. Would you not agree? Martin Hogbin (talk) 01:05, 13 November 2011 (UTC)

I thought I was being clear too. I said I would have discussed all details with the client. I did a lot of statistical consultation, and many times the client had to be helped in formulating what he wants. I.e. your client may just show me the urn and ask me "what is the probability of getting the black ball?" If I then would ask him if he would make a random draw from the urn, he may look puzzled at me, as he hardly understands what I mean. However if I ask him if he would shake the urn properly and then blindly takes out one of the balls - which by the way are all of the same weight and size and surface structure etc. - he would look at me and say "of course, what else could I do?" You see, for ordinary people such details are inherent connected to the situation with an urn, and implicitly assumed. Nijdam (talk) 07:58, 13 November 2011 (UTC)

Do you agree then that the way you would tackle a problem depends on the context in which it is presented? Martin Hogbin (talk) 10:43, 13 November 2011 (UTC)

This is too vague a question to be answered. Nijdam (talk) 23:46, 13 November 2011 (UTC)

Reduced probability space

To answer a question you ask elsewhere, my probability space would consist of two elements: the player initially chooses a car, the player initially chooses a goat, with probabilities 1/3 and 2/3 respectively. Everything else is certainty. Martin Hogbin (talk) 10:36, 6 November 2011 (UTC)

To repeat the question i asked several times: how do you describe the event door 1 is chosen and door 3 opened?Nijdam (talk) 17:01, 6 November 2011 (UTC)

I don't. There is no need to describe these events in the way you do. The player chooses a door and the host opens an unchosen goat-hiding door with certainty. Which doors these are are not important, just as the words used by the host are not important. The only question of importance is the whether the player swaps or not. This can be easily represented in my sample space. Martin Hogbin (talk) 17:32, 6 November 2011 (UTC)

You have to: the player knows which door she has chosen (I hope at least she does remember) and she sees the opened door. Or what? Nijdam (talk) 21:54, 6 November 2011 (UTC)

She may remember but she knows the door numbers make no difference, as do you. Martin Hogbin (talk) 22:23, 6 November 2011 (UTC)

No difference to what? Nijdam (talk) 10:08, 7 November 2011 (UTC)

To the probability that she will the car win by switching. Martin Hogbin (talk) 10:28, 9 November 2011 (UTC)

(outindented) Your sample space is (Car, Goat), with probabilities 1/3 and 2/3. What do you mean by the event "win the car by switching"?Nijdam (talk) 11:21, 10 November 2011 (UTC)

Exactly what I say, but I see what you are getting at. That event cannot be represented within my chosen sample space. On the other hand, is there any reason why it must be possible to represent that event within the sample space? Martin Hogbin (talk) 09:33, 11 November 2011 (UTC)

You're the one that brought it up.Nijdam (talk) 15:02, 11 November 2011 (UTC)

Yes, I do not doubt that the event occurred but why must it be represented in the sample space?

The occurrence of an event is nothing more than the occurrence of one of the outcomes, i.e. one of the elements of the sample space.Nijdam (talk) 11:23, 14 November 2011 (UTC)

If you want to by fussy then my sample space should really be Car-Stick,Car-Swap,Goat-Stick,Goat-Swap but we seem to have generally left out the swapping stage in out previous discussions. Martin Hogbin (talk) 23:28, 14 November 2011 (UTC)

Sorry Martin, you've lost me here. The extra aspect of swapping or not does not change a bit. And the whole discussion above applies as well.Nijdam (talk) 09:42, 15 November 2011 (UTC)

All I am saying is that my sample space should be (Car-Stick,Car-Swap,Goat-Stick,Goat-Swap) referring to the players initial choice and their subsequent action. This now allows all relevant events to be included. Nothing else makes a blind bit of difference. Whether the player sticks or swaps is important, whether the player initially chooses a car or a goat is important. We do not include the events that the host offers the player a swap or that the host opens a door to reveal a goat because these events occur with certainty. We do not include the door number that the player initially chooses, or the number of the door that the host opens or the name of the player or the name of the host because these events are not relevant to the probability of interest. Martin Hogbin (talk) 22:10, 15 November 2011 (UTC)

Just a question: What probabilities are assigned to the elements of your sample space? And another: Nothing else makes a blind bit of difference to what?? And a third: what is the probability of interest? Nijdam (talk) 22:32, 15 November 2011 (UTC)

See below

Nijdam, let me go back to my original sample space of just Car and Goat, I agree that the above space only works if we know the choice the player will make at the start. By "win the car by switching", I mean that the player will win the car if the choose the other available object. Martin Hogbin (talk) 21:05, 17 November 2011 (UTC)

I've no idea what this is about, But if you mean to perform an experiment with putcomes Car and Goat (probabilities ??), that's something different than the MHP. Nijdam (talk) 13:44, 23 November 2011 (UTC)

I guess that is where we disagree. If we mathematically formulate the MHP as a simple puzzle in which the number of the door originally chosen by the player and the door number opened by the host (within the rules of the game) are both considered independent of the probability that the player will win the car by switching then there is no reason not to use the simple (goat 2/3, car 1/3) sample space. We have no need in this interpretation of the problem to represent the event that the host opens an unchosen door to reveal a goat and the event that the player switches is represented by the player ending up with the opposite of their original choice. This makes the problem absurdly simple, which in fact it is when viewed properly.

If, on the other hand, you wish to treat the MHP as an examination question, where you will normally be expected to use all the information given but no other, then you must use the door numbers, because they are given to you. The sample space should therefore contain all possible combinations of producer door choice, initial player door choice and host door choice. For extra marks you might parametrise the producer's, player's, and host's door choice policies.

Finally, if you want to treat the MHP as a real world problem, you need to ask many questions before you can even start to answer it.

I prefer the first approach, you take the second to be the only one possible, and anyone who wants to make the problem absurdly complicated can choose the third. Martin Hogbin (talk) 13:06, 26 November 2011 (UTC)

As you're saying, you're just guessing. It's not a matter of disagreeing: you're just mistaken. If you want to describe and solve the MHP with a proper sample space you're not free to take whatever you like. And then, what do you mean by saying: the number of the door originally chosen by the player and the door number opened by the host (within the rules of the game) are both considered independent of the probability that the player will win the car by switching? Words are patient and easy said, but the exact meaning is unclear, not to say incomprehensible. What could be the meaning of the player's choice being dependent of the probability of getting the car by switching???

The probability of winning the car by switching is 2/3, whether the player initially chooses door 1,2, or 3. Do you disagree?

Either you refer to different probabilities of winning the car by switching, with the same value for all choices of door, and then this value is independent of the door numbers (and not the other way around), or you just mean only one probability and then it is pointless to say it does not depend on the number of the chosen door. So, what do you mean? Nijdam (talk) 11:11, 27 November 2011 (UTC)

The MHP is not different for ordinary people, students in probability theory, me or you. It could as well be considered to be a real world problem.

The only thing you can do is give an exact formulation - eventually in words, if formula's are too difficult - of the problem and the, or your supposed, solution. As you said yourself: formulate the MHP mathematically as a simple puzzle. I'm looking forward.

Nijdam (talk) 18:00, 26 November 2011 (UTC)

Ther is no such thing as 'an exact formulation'. What is not exact about formulating the problem with the sample space (goat, car)? It gives the exact answer, and not by chance. Martin Hogbin (talk) 01:20, 27 November 2011 (UTC)

It will be best you mathematically formulate the MHP as a simple puzzle (your words). Please do. Nijdam (talk) 11:11, 27 November 2011 (UTC)

Formulating a natural language problem mathematically

Nijdam, our disagreement occurs when we convert Whitaker's natural language statement into some form that is open to mathematical analysis. There is no standard algorithm or fixed procedure for doing this. If you know of one, please state it.

We both know Whitaker's question, it does not actually ask for a probability but let us agree that we shall attempt to give one. In natural language, we want to know the probability that the player will win the car if they decide to accept the host's offer to switch, made after a door has been opened. We cannot formulate this mathematically yet because we have not yet decided how to formulate the entire question. Are you happy to take my natural language statement as the question that we both wish to answer?

Would you prefer to take a frequentist or a Bayesian interpretation of 'probability'? I do not much mind which (although I slightly prefer Bayesian) but do insist that we take one interpretation and stick with it for this discussion. Martin Hogbin (talk) 12:09, 27 November 2011 (UTC)

I do prefer the frequentist iterpretation, as being (more) objective, and easier to interprete. Whitaker's question is not directly for a probability, but the answer "switch", will quite natural be followed by the question "why?". And the trick of the problem is of course the surprising 2/3 (conditional) probability of getting the car by switching. Nijdam (talk) 00:40, 28 November 2011 (UTC)

OK, let us be frequentists. This leaves many unanswered questions. With what probability is the car placed behind each door? With what probability does the player initially pick each door? With what probability does the host pick each legally available door, given doors previously chosen by the producer to place the car and the player? What is your rationale for these probabilities? Martin Hogbin (talk) 00:57, 28 November 2011 (UTC)

Being a frquentist I assume the play is repeated, or at least repeatable. I also assume the formulation of the problem is not meant for exact mathematicians, otherwise it would be phrased more exact. If common people is given a choice out of three things, one with a price, they quite naturally assume the price is hidden with equal chances and they are unaware of the position of the price. So, the car is hidden uniformly and the initial choice is independent of the position of the car. The distribution of the initial choice is unimportant, hence does not need to be specified. This leaves us with the strategy of the host. It seems reasonable to assume he always offers the switch, and only opens a door with a goat. Other scenarios may of course also be analyzed. But the assumed one offers all the interesting aspects of the problem. What if the host has a choice between two goat doors. I guess most people would say: he flips a (fair) coin. There we are: the standard MHP.

We shall take it that the car is initially hidden uniformly and the host chooses uniformly between unchosen goat-hiding doors. That is all fine with me, except for one thing.

You say that the initial choice of the player is unimportant. Are you suggesting therefore that, although we know the player might have chosen door 2 or door 3 we only consider the case stated in the question. We need to calculate the probability that the player will win the car by switching. Why do you not consider the possibility that the player might have chosen a different door? 2.102.214.196 (talk) 18:23, 28 November 2011 (UTC)

Forgot to log in? Anyway, the answer will be the same whatever the distribution of the initial choice may be. Nijdam (talk) 20:59, 28 November 2011 (UTC)

So you consider it acceptable to reduce the sample space because you can see a simplification of the problem that obviously will not affect the answer? A representative sample of the whole sample space you might say. Martin Hogbin (talk) 22:12, 28 November 2011 (UTC)

On the contrary. There is no reduction of the sample space, and there is no reduction of the possible distributions.Nijdam (talk) 10:17, 29 November 2011 (UTC)

The whole sample space should surely contain all the outcomes allowed by the rules of the game. The player might have initially chosen door 3. Martin Hogbin (talk) 18:31, 29 November 2011 (UTC)

I do not completely follow you in your last two comments. I suggest you list all the possible outcomes of the experiment.Nijdam (talk)

Surely the full sample space should include all possible outcomes that are permitted by the rules of the game. For example, that the player initially chooses door 3 and the host opens door 1 to reveal a goat. Martin Hogbin (talk) 18:50, 29 November 2011 (UTC)

The fact that you speak of the "full sample space" strongly suggest there is another sample space. There is however just one sample space, the full one, if that's what you like to call it. And, as we've been there before, it consists of 18 outcomes with positive probability. Agree? Nijdam (talk) 12:50, 30 November 2011 (UTC)

You talk as if the sample space somehow presents itself to us when we read a natural language description. This is not the case. Before we can even talk about a sample space we have to consider which events are relevant to the probability of interest (that the player will win the car by switching) and which events are not important. Martin Hogbin (talk) 14:55, 30 November 2011 (UTC)

It does indeed, as the sample space is no more than a mathematical formulation of the possible outcomes. That's why I asked you to list the possible outcomes. Although you mentioned an example of an outcome, you did not list them all. I described the outcomes more or less. Perhaps it clarifies things if you describe all outcomes. Do bear in mind, i.e. that you have to describe the uniform distribution of the car. Nijdam (talk) 00:41, 1 December 2011 (UTC)

I have copied the original statement here for easy reference.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

So what are the possible outcomes? We cannot even begin to answer that question without making assumptions about things that are not explicitly stated. For example, it says, You pick a door, say No. 1. It does not explicitly say that you might have picked door 2 or door 3. This is not an unnatural assumption considering it is a game show but it is an assumption.

The same is true of the host's choice of door. Must he always open door 2?

Now I agree that these two particular questions are answered by the 'standard' rules of the game that are assumed by most people and that we have agreed to assume here but I mention them to show that, right from the very start, we must make some assumptions about what is important and what is not when we propose a sample space.

The host says "Do you want to pick door No. 2?" We are not told that the host might have used different wording but logic tells us that normal speech often uses different words to mean the same thing. Maybe the host sometimes says "Do you want to switch to door No. 2?" The standard rules tell us nothing about the host's choice of words although we are clearly told of one possible wording in the problem statement. Our sample space should therefore include every possible form or words that the host might have used, just as it includes the doors that the player might have originally chosen. Why do we not do this? Because we have to decide which are the important events before we set up our probability space. There is no procedure or algorithm that tells us how to do this; it is a matter of interpretation. Martin Hogbin (talk) 21:04, 1 December 2011 (UTC)

You seem to run around in circles. Remember you somewhere above said: Surely the full sample space should include all possible outcomes that are permitted by the rules of the game. For example, that the player initially chooses door 3 and the host opens door 1 to reveal a goat. What then is the status of this remark?

Anyhow, the problem statement says: ...you're given the choice of three doors... And the sentence: You pick a door, say No. 1, indicates that as an example of the possible three choices, the choice of door No. 1 is given. Etc. Nothing in the problem formulation indicates any dependance of the words of the host, the words of the host are not a part of the experiment, but of the question to be asked. Before the host offers the switch, it is possible to calculate the relevant probabilities, but we do not know which probability is asked for. And then, the problem being a natural language problem, no one except apparently you will come to such thoughts. And, last of all, your simple sample space is completely inadequate for your supposed possible outcomes.

Thus I repeat: please list the possible outcomes, not as you think they might be, but as common people, with natural language, think they will be. Nijdam (talk) 13:32, 2 December 2011 (UTC)

I understand that I am being a little perverse but I am trying to make the point that the sample space is not defined precisely by the problem statement but requires some thought. You say that, 'the words of the host are not a part of the experiment' but what exactly tells you this? It is quite conceivable that the host would try to help the player by giving them a the player a clue in the language that they use. Martin Hogbin (talk) 16:44, 2 December 2011 (UTC)

You are, and that's no problem. as far as it brings new insight. But you can't dwell there forever. Of course a natural language problem needs some reflection when formalizing it. Some problems may even fail there because of insufficient description. The formulation of the MHP however leads to a unique (up to equivalence) sample space. Concerning the words of the host, much is conceivable, but when there is no indication whatsoever in the formulation, of any difference the words may induce, it is not up to us, to speculate. As I said above, the words of the host only tells you about the question asked, but nothing about a possible outcome of the game. If you have a different pinion, please show me how the words of the host influence (not how they may influence) the outcome of the game. Nijdam (talk) 18:00, 2 December 2011 (UTC)

Can you show me how the host's choice of door (within the rules of the game) influence (not how they may influence) the outcome of the game? Martin Hogbin (talk) 21:47, 2 December 2011 (UTC)

Yes, no problem. And then it is your turn. If the host opens door 1, we see door 1 opened, if he opens door 3, we see door 3 opened, two different outcomes. It's that simple. Nijdam (talk) 11:16, 3 December 2011 (UTC)

If the host the host says 'pick' we hear 'pick', if the host says 'choose' we hear 'choose', two different outcomes. As with the host's door choice neither affects the probability of interest. Martin Hogbin (talk) 12:28, 3 December 2011 (UTC)

Where in the problem statement did you read that the host says, or may say, "choose"? Nijdam (talk) 18:31, 3 December 2011 (UTC)

Where in the problem statement does it say that the host may open door 2? Martin Hogbin (talk) 22:58, 3 December 2011 (UTC

Here: " opens another door". And now your answer to my question, straightforward.Nijdam (talk) 21:02, 4 December 2011 (UTC)

There is no mention of door number 2 specifically, the only door mentioned is 3. Martin Hogbin (talk) 21:14, 4 December 2011 (UTC)

Why specifically? Do I have to spell it out for you? There are three (3) doors. Door 1 is chosen by the contestant. The host opens another door. Which door might that be? Not No. 1 as that is the same door. The other doors are door No. 2 and door No. 3. The host opens one of these other doors. He may open No. 2 or he may open No. 3. (As an example door No. 3 is chosen in this instance of the game.) Would you prefer a picture for easier understanding? Nijdam (talk) 23:53, 4 December 2011 (UTC)

You still seem to be viewing the problem like an exam question where information that is given is normally given because you are expected to use it and all the information required to solve the problem is given in the problem statement. In other situations it is quite possible that you might be given information that is not required to solve the problem and that some of the information required to solve the problem will not be given. I have given a fairground example at the end of this talk page for ease of editing. Martin Hogbin (talk) 12:53, 4 December 2011 (UTC)

It has nothing to do with an exam question. You keep mentioning this, as if you need to convince yourself. Nijdam (talk) 21:05, 4 December 2011 (UTC)

I an trying to convince you that the way a natural language statement is turned into a mathematical question and a sample space depends on the context. In an exam you assume that all the information you need to answer the question in the way intended by the examiner is contained within the question and that only necessary information is given.

You have already agreed that if this were a real life problem you would start by asking many questions. Do you not agree that in another context, such as the consultancy context we discussed earlier, you might want to enquire if there was any more relevant information and whether some information, such as the door numbers, was considered significant? Martin Hogbin (talk) 21:14, 4 December 2011 (UTC)

Some relevant info we deduced from the formulation. If it was a consultancy I would have asked my client to be sure. What more information do you want to know? And there we are again: to what should the door numbers be considered significant?? It's time you give a straightforward and precise answer. Nijdam (talk) 23:43, 4 December 2011 (UTC)

The way you put a question into mathematical terms depends on what question you think the questioner is asking. That is a basic point of statistics. In a real life situation we agree that you would need to ask many questions to find out what the questioner really wanted to know. In an exam question we would naturally assume that all information given was significant and necessary. However, the MHP was none of these it was a simple puzzle, proposed as a question to a column in a popular, general-interest magazine. We happen to know that the door numbers were never intended to be part of the question and that they were added by vos Savant to try to clarify the question. There is no doubt in my mind that Whitaker was not intending to distinguish between the 'conditional' and 'unconditional' interpretations of the problem and that it was intended to be a simple brain teaser in which the door number opened by the host played no part. Therefore, whenever the player makes their choice, {goat 2/3, car 1/3} is a perfectly adequate sample space to describe the intended question. Martin Hogbin (talk) 22:46, 7 December 2011 (UTC)

The MHP is a simple puzzle, a simple probability puzzle. I do not know who "we" are and how they happen to know something, but it is time, and I asked this several times, you clarify your ideas about the door numbers. This time you say they were not intended to be a part of the question. When the player chooses a door, will there be a number on that door, or if you hate numbers, will it be the left, the middle or the right door? And I have no idea about Whitaker's intentions; whatever they were, it is unavoidable to speak of conditional probabilities. To ease the discussion, answer the following question: Which door do you, as the player, choose? Nijdam (talk) 16:50, 8 December 2011 (UTC)

Let me start by supposing that Whitaker did not specify doors in his original question. The host opens any door not originally chosen by the player that hides a goat. We cannot identify the doors in any way. Martin Hogbin (talk) 21:03, 8 December 2011 (UTC)

This makes no sense. Whitaker does not explicitly speak about the numbers, but he mentions three doors. You're the player, you're on stage, do you see the three doors? Just answer yes or no.Nijdam (talk) 10:52, 9 December 2011 (UTC)

The problem statement does not tell me. I need to interpret the statement according to its context. I this was a real life situation I would see three doors along with many other things that might or might not be relevant. As this is a simple puzzle I do not see any doors, as I know they are irrelevant to the intended question. Martin Hogbin (talk) 17:39, 9 December 2011 (UTC)

Is this a yes or is this a no?Nijdam (talk) 18:02, 9 December 2011 (UTC)

That depends on the context, which is my whole point. I am not avoiding the question, just pointing out that your question is ambiguous. In reality, I can see nothing of the events. Do you mean:

Would I expect a person on a real game show to see which doors were opened? Yes.

Do I think Whitaker considered it important that I should imagine specific doors being opened? No. Martin Hogbin (talk) 18:19, 9 December 2011 (UTC)

You seem to know Whitaker well. I do not care what Whitaker might have considered important or not, fact is he introduced three doors, and no one doubts the fact that the player makes a choice from these doors. It is impossible for the host to open a door if not the choice of the player is made. I suggest you describe me how the game proceeds through the different stages. Nijdam (talk) 00:04, 10 December 2011 (UTC)

But you must care what Whitaker considered important if you are to answer his question properly. As Seymann said, Without a clear understanding of the precise intent of the questioner, there can be no single correct solution to any problem. Thus, with respect to the three door problem, the answer is dependent on the assumptions one makes about the intent of the one who originally posed the question. In this case, the intent of the questioner is made clear by the forum in which he chooses to ask it; a column on a popular magazine. Martin Hogbin (talk) 11:21, 10 December 2011 (UTC)

Yes, what he considered important, but not what he might have considered important. It is not up to us to speculate. Anyway, whatever he might have had in mind, he mentioned three doors to choose from. That's a fact, or do you have doubts? That's why (almost, I may have to exclude you) everyone pictures three doors, and for the sake of simplicity numbers them 1, 2 and 3. But again, and this time no other questions, remarks, etc., just describe how the game proceeds according to you. Nijdam (talk) 14:07, 10 December 2011 (UTC)

We have to use our consider, in Seymanns words, what the 'precise intent of the questioner' is before we can even formulate an answer. That is my main point.

Whitaker mentioned three doors but he did not distinguish between them.

Regarding how the game goes, the player chooses a door, which has either a car or a goat behind it. The host opens a different door to reveal a goat. The player then decides whether to swap or not. If he originally chose the car and swaps he gets a goat, if he originally chose a goat and swaps he gets the car, if he originally chose the car and sticks he gets the car, if he originally chose a goat and sticks he gets a goat. That is it.

We do not care what the number of the door is that the player originally chooses, which goat the host reveals or which door the host opens. Martin Hogbin (talk) 14:27, 10 December 2011 (UTC)

It suffices that you say: Whitaker mentioned three doors. I cannot imagine what you possibly could mean by saying: but he did not distinguish between them. Three doors are three doors. One door, another door and the third door. Does the player see three doors or what? If you have the idea the player does not see three doors, what then does she see?? Before continuing, just tell me what the player sees, and for the moment no more, just this. Nijdam (talk) 22:42, 10 December 2011 (UTC)

I'll make it easy for you. Logically, one of the following possibilities must be true.

1. She does not see any door
2. She just sees one door
3. She sees exactly two doors
4. She sees exactly three doors
5. She sees more than three doors

Just mention the number of the possibility you think is true. Nijdam (talk) 22:56, 10 December 2011 (UTC)

The problem statement does not tell us how many doors the player sees so I cannot answer your question. Martin Hogbin (talk) 00:05, 11 December 2011 (UTC)

Okay, then does she know how many doors there are? Nijdam (talk) 17:38, 11 December 2011 (UTC)

Yes. Martin Hogbin (talk) 12:49, 16 December 2011 (UTC)

How many? Nijdam (talk) 12:07, 20 December 2011 (UTC)

Three. Martin Hogbin (talk)

What difference would it have made, if you had said: she sees three doors?Nijdam (talk) 07:05, 21 December 2011 (UTC)

It might imply that the doors themselves might have some significance. The point is that if someone, before the start of the show, swapped all the door numbers (or any other identifying features) round it would not affect the outcome. Martin Hogbin (talk) 22:06, 24 December 2011 (UTC)

I can't follow you here. If the player knows there are three doors and she is on stage near the doors, she sees them (I do not consider her to be blind).Nijdam (talk) 09:44, 25 December 2011 (UTC)

Do you prefer to play the role of the player or of one of the audience?? Nijdam (talk) 19:19, 24 December 2011 (UTC)

Of course it is very reasonable to assume that the player could see the doors but it is, nevertheless, still an assumption. Martin Hogbin (talk) 10:59, 25 December 2011 (UTC)

I am answering based only on information given in the (Whitaker's) question. Martin Hogbin (talk) 22:06, 24 December 2011 (UTC)

In that case - read the problem formulation - you're the player. So, which door did you choose? Do not say something like: it doesn't matter which one, etc, just answer the question! I'm anxious to hear your answer. Nijdam (talk)

Whitaker's original question did not tell us which door the player chose. Vos Savant added 'say door 1' to the statement but this was just intended to be an example of one of the doors that the player might have chosen.

If you are asking me to follow Whitaker's suggestion and imagine that I am a player on a show then I have not imagined a door number, although I do wonder if there is a car or a goat behind my chosen door. Martin Hogbin (talk) 10:59, 25 December 2011 (UTC)

Doors

You choose to be the player. Following Whitaker's scenario, you're on stage now. Let us assume you're not blind. Because, as you said, you know there are three doors, you must be able to see them. Do you see them? Tell me how you like to distinguish them. A, B, C or 1,2,3 or left, middle right, anyway you like. You're asked to choose a door. As Whitaker wrote: "you pick a door" etc. See, nothing problematic. just tell me which door it is you've chosen?Nijdam (talk) 21:56, 28 December 2011 (UTC)

If this information is not given in the question we cannot use it in the solution. I pick a door. That is all. You may assume that I am not blind, that I see the door that I pick, that I can remember which one it was, and that I do not spot the obvious symmetry that makes it irrelevant but the information is not given in the question.

If you do not want to reveal which door you've chosen, you may solve the problem by calling it the door with the number x. And I presume you know very well how this continues.

It has nothing to do with my wishes. I am responding based only on the information given in the original question, as Morgan entreat us to do. The original question does not tell us which door was opened.

Let me ask you this question, 'Which goat does Monty reveal when he opens a door?'. Martin Hogbin (talk) 10:02, 29 December 2011 (UTC)

That's easy: The goat behind the door he opens. Nijdam (talk)

But which goat is this? Monty knows where the goats are, we presume that he can see them and that they are different goats, distinguishable in principle. Shall we call it goat number x?

You see my point? There is no more reason to include door numbers in our sample space than there is to include goat numbers. Martin Hogbin (talk) 11:55, 30 December 2011 (UTC)

Maybe the host always reveals the white goat (whichever door it is behind) when the player has initially chosen the car. Martin Hogbin (talk) 12:00, 30 December 2011 (UTC)

You're trying to make a point where there is none. If you would like to distinguish the goats, go ahead, it doubles your outcomes. However nowhere in the problem formulation anything is said about the difference of the goats, like "the host opens one of the closed doors and shows a goat, say goat nr. 1" or something like that. In fact anyone understands the goat doors could as well be empty. On the other hand it is said the player choose a door. And that means the chosen door is known. Nijdam (talk) 17:46, 1 January 2012 (UTC)

So, if the problem statement did say, 'the host opens a door to reveal the white goat', would it make any difference to your solution and sample space? Martin Hogbin (talk) 18:23, 1 January 2012 (UTC)

Yes, of course, it would mean another condition. Nijdam (talk) 19:11, 1 January 2012 (UTC)

What about if it said,'...and behind the other doors distinguishable goats'? Martin Hogbin (talk) 19:13, 1 January 2012 (UTC)

Well, it doesn't. And if, then look at what I said above. Nijdam (talk) 23:21, 1 January 2012 (UTC)

When must we distinguish?

A while back you were arguing that even if the doors were not numbered and the door numbers were not given in the problem statement it would still be necessary to include the door opened by the host as an event in our sample space. Your reasoning was that the player would undoubtedly be able to see the doors and distinguish between them.

Why then must the sample space not also include the ID of the goat that is revealed? We know that the host can see the goats and that goats are, in principle, distinguishable. Martin Hogbin (talk) 09:55, 2 January 2012 (UTC)

Would you be able to distinguish between two almost identically looking goats?Nijdam (talk) 11:42, 13 January 2012 (UTC)

I cannot say. I am not an expert on goats. Whether I or any specific person could actually distinguish between the two goats is not important. The goats are in principle distinguishable. There are two goats, not one goat moved from door to door. It is quite possible that the goat that Monty chooses to reveal depends on the location of the car. Must we include goat-number in our sample space? Martin Hogbin (talk) 12:05, 13 January 2012 (UTC)

Sorry, didn't know you were a layman with goats. Let's first solve a MHP with one door with a car and two empty ones. See where this leads us. Nijdam (talk) 20:01, 13 January 2012 (UTC)

But goats are an integral part of the MHP. The problem statement clearly tells us that there are two goats and the host reveals one of them. How can you ignore thee information in the specific goat that the host reveals? Martin Hogbin (talk) 20:05, 13 January 2012 (UTC)

Just do it. Nijdam (talk) 23:05, 14 January 2012 (UTC)

Of course you can ignore this information if you like but it is quite possible that the answer to the problem depends on it. It is possible to envisage a situation where the host prefers the white goat to the black goat and only reveals the black goat when he has to, just as Morgan envisage the situation where the host prefers door 3 and only opens door 2 when he has to. Neither possibility is stated in the problem statement so why do you insist on including door numbers in your sample space but not goat numbers? Martin Hogbin (talk) 00:42, 15 January 2012 (UTC)

Please Martin, do as I asked.Nijdam (talk) 10:47, 15 January 2012 (UTC)

Sorry, I am not sure what you want me to do when you say 'Just do it'. Martin Hogbin (talk) 18:59, 15 January 2012 (UTC)

Solve a MHP with one door with a car and two empty ones. See where this leads us. Nijdam (talk) 19:45, 15 January 2012 (UTC)

This leads me to one of the simple solutions but maybe it leads you to Morgan's solution. I do not see the point of this, the MHP has goats behind the loosing doors. One goat is revealed to the player but the other is not. Why do you not want to take this into account in your probability calculation. Martin Hogbin (talk) 16:40, 16 January 2012 (UTC)

Please Martin, spell it out. Nijdam (talk) 09:45, 20 January 2012 (UTC)

One car, two empty doors

My solution is to start with the sample space {C,E} so initially P(C)=1/3 P(E)=2/3.

A player who swaps gets the opposite of his original choice, so P(C|swap)= 2/3), a player who sticks gets his original choice, so P(C|stick)=1/3. Martin Hogbin (talk) 09:54, 20 January 2012 (UTC)

I think you will not be surprised when I ask: How do you describe the event "'the car is behind door No. 1'"? (That's where we started some while ago.) Nijdam (talk) 08:07, 25 January 2012 (UTC)

And I guess that you will not be surprised if I ask you in return how you would describe the event that the host says the word 'pick'. Both events undoubtedly occur but neither is relevant to the probability of interest (which is that the player wins the car given the conditions of the problem).

I think you do not realise that you are applying a set of rules or conventions to the way that you answer the problem. You know that the door numbers are important because a specific door number is mentioned in the (vos Savant's version of Whitakers's question) problem statement. You assume all the information given is important, so your sample space must include door numbers, and you assume information not given explicitly, such as the fact that there must be two different goats, is not relevant, so must not be included in your sample space. Would you agree? Martin Hogbin (talk) 09:42, 25 January 2012 (UTC)

First your answer, then other details. Nijdam (talk) 00:06, 26 January 2012 (UTC)

My answer is that I do not describe that event. Martin Hogbin (talk) 09:22, 26 January 2012 (UTC)

Seemingly too difficult for you. Then a simpler question: Which door did the player choose? Nijdam (talk) 00:13, 27 January 2012 (UTC)

We do not know. Vos Savant (but not Whitaker) superfluously gave door 1 as an example of a door that he might have chosen but it is pretty obvious that in makes no difference which door the player chooses if the car is hidden uniformly at random. Martin Hogbin (talk) 10:00, 27 January 2012 (UTC)

Difference to what?Nijdam (talk) 12:00, 27 January 2012 (UTC)

The probability that the player has originally chosen the car and the probability that a player who swaps will win the car. Martin Hogbin (talk) 15:13, 27 January 2012 (UTC)

Martin, you haven't learned much from our discussion. As I explained before, the probability that the player has originally chosen the car is 1/3. How in the world can anything make any difference to this?? And similarly, what difference could it make to the probability that a player who swaps will win the car? Normally your thoughts show more logic. Nijdam (talk) 23:03, 27 January 2012 (UTC)

Yes, you are quite right about the original probability but I cannot see what is wrong with 'the probability that a player who swaps will win the car'. Perhaps I should make it 'the probability that a player who participates in the game as described and who, after the host has revealed a goat, decides to swap will win the car'. Martin Hogbin (talk) 00:18, 28 January 2012 (UTC)

Well, try to formulate the event you mention "a player who swaps will win the car" in terms of your sample space. And then make clear where there is no difference. I'm lost actually. Nijdam (talk) 10:31, 30 January 2012 (UTC)

That is quite easy. The original sample space is {C,E} with probabilities 1/3 and 2/3 respectively. If the player's original choice is E (that is to say an empty door) and the player swaps they will end up with the car, so the probability that a player who swaps will win the car is 2/3. Whether the player initially chooses door 1, 2, or 3 does not alter this probability. The door number that the host opens, within the rules of the game, also makes no difference, neither does the name of the host or the words that he says.

Not as easy as you think. Indeed is E the event I asked for, with probability 1/3. Where could it make any difference which door the player chooses? There are only, in your model, the doors E (empty) and C (car), and it makes a considerable difference which one the player chooses. Please explain. Nijdam (talk) 10:54, 31 January 2012 (UTC)

The door number, or indeed any other distinguishing feature of the door, is irrelevant to the probability of interest which, as stated above is the probability that a player, who conforms to the rules of the game and who on being shown and empty door switches, will win the car.

Do you mean P(E)?? Show me how the door number is irrelevant to P(E)?

What do you mean by P(E)? Is it the probability that the player has chosen originally nothing? The door number is clearly irrelevant to this probability. Unless you think the player is more likely to have chosen nothing if they initially pick a specific door number, in which case perhaps you could tell me which door number. Martin Hogbin (talk) 22:22, 31 January 2012 (UTC)

You shouldn't ask me, it's your sample space. Indeed is it, as you stated, the probability the player's first choice is an empty door. In your sample space P(E)=2/3. In what way may a door number influence this? Please show me. Nijdam (talk) 11:45, 1 February 2012 (UTC)

The door number does not influence this. That is why I do not care about door numbers. Martin Hogbin (talk) 15:07, 1 February 2012 (UTC)

That's not an answer. Give me the correct formulation, best in formula, of your statement that the door number does not influence P(E). Nijdam (talk) 15:48, 2 February 2012 (UTC)

I cannot do that; it is done before the formal formulation of the problem. How do you show from your preferred sample space that the goat revealed or the words the host says is not relevant. Martin Hogbin (talk) 16:07, 2 February 2012 (UTC)

If you disagree, perhaps you can tell me which door is most likely to be a winner. Is it 1,2, or 3? We agree that the car is placed behind the doors uniformly at random.

What does it mean that the car is placed randomly? Use your sample space. Nijdam (talk) 22:09, 31 January 2012 (UTC)

The random placement of the car is used to assign the probabilities 1/3 and 2/3 to the elements in my sample space.

How do you know this? Nijdam (talk) 11:45, 1 February 2012 (UTC)

On car, two empty doors, uniform placement. Martin Hogbin (talk) 15:07, 1 February 2012 (UTC)

Can you show me in your sample space that the car is placed randomly? Nijdam (talk) 15:48, 2 February 2012 (UTC)

No, this is not necessary. See may answer aboveMartin Hogbin (talk) 16:07, 2 February 2012 (UTC)

You have not answered my question. Which door is most likely to be a winner. Martin Hogbin (talk) 22:22, 31 January 2012 (UTC)

You still seem to be missing my main point, which is that, on reading a natural language problem, a sample space does not automatically present itself to us. We have to decide what elements we need to include in our sample space in order to determine the probability of interest. Martin Hogbin (talk) 16:07, 2 February 2012 (UTC)

The doors do not need to form part of the problem, they are an irrelevance, a distraction. All that matters is what is behind the doors.

You have not (seriously) answered my question below. I agree that it is not exactly in the game show format but is clearly shows that the doors are not essential to the game; they merely play the role of the blindfold in my problem. Martin Hogbin (talk) 15:30, 31 January 2012 (UTC)

Ten doors, one car

Nijdam, I hope that by rational discussion we will eventually be able to come to a common understanding of this subject. In order to help clarify your views I would be interested to hear how you would deal with the following problem.

A car is placed uniformly at random behind one of ten doors, numbered 1 to 10. A player is allowed to pick any five doors. What is the probability that one of the chosen doors hides the car? How would you calculate this? Martin Hogbin (talk) 10:17, 2 February 2012 (UTC)

Firstly we have to assume the choice of the player is independent of the position of the car. Then we may reason that any choice of 5 doors will hide the car with probability 1/2, so all the conditional probabilities we're looking for have the value 1/2. This may also be calculated formally with sample space etc. We may also establish the equivalence with an urn with one black and 9 white balls and 5 successive drawings without replacement. To see clearly how this has to be solved, consider the car to be hidden with probabilities p1,p2,...p10. What then?Nijdam (talk) 16:07, 2 February 2012 (UTC)

I guess I should have mentioned that the random car placement was secret so, yes, the choice of the player is independent of the position of the car.

As you say, we could consider the car to be placed behind each door with probability 1/10 and then consider the large sample space in which the player picks every combination of 5 doors and eventually find the probability that the player will pick the car. On the other hand you say, 'we may reason that any choice of 5 doors will hide the car with probability 1/2'. You seem to be suggesting that we do not absolutely need to set up our vast sample space to do this and there I completely agree with you. Would you therefore agree with me that to assign the probability of picking a car from 3 doors we do not absolutely need to include the doors in our sample space? Martin Hogbin (talk) 00:19, 3 February 2012 (UTC)

No, I think you misinterpret me. My reasoning is just to ease the calculations, just as we may use symmetry in the MHP. Nijdam (talk) 17:06, 7 February 2012 (UTC)

So what sample space do you say is the minimum necessary to solve this problem. Martin Hogbin (talk) 17:12, 8 February 2012 (UTC)

To describe the experiment, the minimum sample space consists of the cartesian product of the numbers of the door with the car and the combinations of 5 door numbers out of 10. To solve the problem we may note the equivalence with respect to the question asked with a much simpler sample space. But we need to show this equivalence. Nijdam (talk) 23:26, 12 February 2012 (UTC)

So when does this equivalence become so obvious that we do not need to mention it? Suppose that the player has to walk through one of ten other doors to get to the room where the ten doors that might hide the care are to be found. What sample space is now required? Martin Hogbin (talk) 23:49, 12 February 2012 (UTC)

Never. Are the doors to walk through, part of the experiment? Nijdam (talk) 15:43, 13 February 2012 (UTC)

What do you mean exactly by 'part of the experiment'. Maybe this is where we might be able to agree. I assume that if I were to answer that the extra doors were part of the experiment you would want to include them in your sample space but if I said that they were not part of the experiment you would not. Are the words spoken by the host in the MHP 'part of the experiment' and how do you know?

Who is to say what is 'part of the experiment'? In a natural-language-worded statement it is not usually made clear what exactly is to be considered 'part of the experiment'. Should it be every fact that we are explicitly told? Should it be every fact that we might reasonable expect to be true? In my opinion it should be every fact that we consider might affect the probability of interest. Martin Hogbin (talk) 18:16, 13 February 2012 (UTC)

Gerhard's comment

pardon again, but the characteristic and specific feature of the MHP is the correct decision to be made, the correct answer to be given, and never any forever unknown supposable additional hint that  "(im)potentially  could eventually be expected",  arising from any peculiar behavior of the host or of the guests, the color of the doors or the illumination. You "can" suppose anything whatsoever you like, if you just like, but it is not necessary and not helpful for the correct decision, and it never will affect this correct decision to be made and the correct answer to be given. As you do and forever will know nothing about any such influence, all of this is a pure mathematical issue for undergraduates, that's where it belongs, not affecting the only correct answer to be given in the MHP.  Gerhardvalentin (talk) 15:32, 10 December 2011 (UTC)

One car, two goats

Now one for you, Nijdam.

The player is blindfolded and asked to point at the stage, where there are there are two goats and a car. The object closest to where the player is pointing is then removed from the stage and put in another room as the players original choice. The host then takes the player to a different room and then brings the white goat, from the stage, into that room with the player. The player is then given the choice between having their original choice or taking the item left on the stage. How would you answer that one? Martin Hogbin (talk) 10:03, 20 January 2012 (UTC)

With the help of a friend the player manages to climb on to the stage, and stumbles over the black goat, which in anger, pushes the player off the stage. The host then removes the black goat from the stage and puts it in a chair amongst the audience. The player then enters the stage again, and points to the white goat, making the black goat furious. The black goat rushes from his seat on to the stage and stumbles over the player, who in anger shoves the black goat from the stage. The host the removes the player from the stage and puts het in a chair among the audience where she becomes at rest finally. For her cooperation she receives the car. Nijdam (talk) 08:16, 25 January 2012 (UTC)

I guess that is why the goats are kept behind closed doors. But do the doors really make such a difference to the probability calculation? Martin Hogbin (talk) 09:30, 25 January 2012 (UTC)

You speak of "the white goat". what does this mean?Nijdam (talk) 11:48, 1 February 2012 (UTC)

It means that goat is revealed and that it is white. We do not know the colour of the other goat but we can surely assume that it is not the same one as the one that has been shown. We are therefore free to refer to it as the black goat, purely for our own convenience. Martin Hogbin (talk) 14:42, 1 February 2012 (UTC)

The problem statement did not mention a white goat, nor a black one. Do I have to add this? Nijdam (talk) 16:09, 2 February 2012 (UTC)

Yes is does, 'The host then takes the player to a different room and then brings the white goat'. Martin Hogbin (talk) 00:09, 3 February 2012 (UTC)

Well it just says: the white goat, from the stage, which leaves as interpretations: on the stage has remained a white goat and another one, not white, or a white goat and the car, leaving the colour of the other goat unexplained. Let me assume there is a white goat (W) and a black one (B).The original choice then takes the values C(ar), W or B, and for good reasons with equal probabilities. As we are informed that W is still on stage, the first choice wasn't W. The question now is about the conditional probabilities, given the first choice wasn't W, which are P(CW|first not W) and P(BW|first not W), being both equal to 1/2. Nijdam (talk) 16:56, 7 February 2012 (UTC)

I should have made clear that the player and the host know what is on the stage at the start and that the host will always reveal one of the goats to the player. Martin Hogbin (talk) 18:26, 13 February 2012 (UTC)

Summing up: On stage are a car a black goat and a white goat. The player picks at random one of the three, without seeing it, and happens not to choose the white goat. We now want to know what in this situation the probability is that the car is still on stage. Just as with the MHP, but even stronger, there is the suggestion this conditional (!) probability is 1/2. But:

P(C on stage|first C or first B) = P(first B)/(P(first C and show W)+P(first B))=1/3 / (1/6 + 1/3) = 2/3. Nijdam (talk) 19:18, 14 February 2012 (UTC)

Exactly! This is the MHP without doors. Suppose now we have the same three items on the stage but in darkness. The player points to the stage and the item nearest to where he is pointing is secretly marked as his first choice. The host then turns a spotlight into one of the goats (which he must do under the rules). The player now has the option of keeping his original object or swapping. Is this the same game as above? Would you use the same sample space? Martin Hogbin (talk) 21:23, 14 February 2012 (UTC)

Well, I wouldn't say THE MHP, but similar to the MHP. Further I hope you really mean your exclamation: exactly! Because it would mean your recognition of the use of a conditional probability. That's what counts, not all the variants you come up with. Anyway: of course I have to use the same sample space. I have to distinguish between the occurences of the black goat being spotted and the white one. I calculate for both cases the desired conditional probability, and will notice they are equal in value (Or use symmetry to establish this). What would you do? Nijdam (talk) 13:43, 17 February 2012 (UTC)

What would you do????? Nijdam (talk) 14:11, 18 February 2012 (UTC)

It would depend on the circumstances in which I was asked the question. If it was an exam I would take it that the goats were to be explicitly treated as relevant and us the same sample space as you. If it were a puzzle in a magazine I might reason that the the goat that was revealed was insignificant and use the sample space (CG} with the obvious initial probabilities of 1/3,2/3. Perhaps you could briefly answer the question below. What sample space would you use? Martin Hogbin (talk) 18:11, 18 February 2012 (UTC)

The circle is round: start reading here, Nijdam (talk) 00:50, 20 February 2012 (UTC)

Nijdam, sometimes your answers make me think, but not this time. You asked me what I would do and I told you.

You seem to be avoiding the point to which my argument below is inextricably moving. perhaps you could humour me and answer my question below. What is the correct sample space to use in that question? According to you that should be easy to answer. Martin Hogbin (talk) 10:19, 20 February 2012 (UTC)

So now the stage is now lit and car and goats are hidden behind curtains. Everything else is the same as above but, instead of turning on a spotlight, the host opens a curtain to reveal one of the goats. What is your sample space now? Martin Hogbin (talk) 00:19, 18 February 2012 (UTC)

Why curtains and not doors? Anyway: C = number of curtain with car, W = number white coat, X = chosen number, H number of curtain opened by host. Etc.

Nijdam (talk) 23:37, 23 February 2012 (UTC) You must surely see what I am getting at by now. In the example just above, where the goats were revealed by spotlights and one goat was white, your sample space included goat colour now your sample space does not include goat colour but it does include curtain number. Why did you not include spotlight number? Most likely the setup would include three spotlights, one trained on each object? Why now do you not include goat number? Although I have not specifically said that one goat is white, there are obviously two different goats. Martin Hogbin (talk) 09:41, 24 February 2012 (UTC)

I do include the colour of the goats, as you may notice, by the variable W. You told me about the curtains and the role they play in the different events, that's why I include them. The former experiment say nothing about different spotlights and any role they play. Satisfied? Nijdam (talk) 00:27, 26 February 2012 (UTC)

No, I am far from satisfied. I did not notice that you included W above. Even though the last version of the question does not specifically mention the goat colour I agree that it might be reasonable to include the identity of the goat revealed, if you consider that this might be relevant to the probability of interest. This, of course, raises the question of why you do not include the identity of the goat revealed by the host in your sample space for the standard MHP. You know there are two different goats and it is possible to imagine that the host has a preference for one of them. I see no reason to assume that a host door preference is any more likely than a host goat preference.

Regarding curtains and spotlights, I did not give my curtains numbers, they played exactly the same role in the game as the spotlights did in the earlier version. Their only function was to reveal one of the goats. Why curtain number but not spotlight number? Martin Hogbin (talk) 10:02, 26 February 2012 (UTC)

Well, you did not specifically mention the different colour of the goats, but you presented the problem as a continuation of the former one, and there you mentioned the host revealing the white goat, hence the colour seems to be important. As with the doors, it is meaningless to say "I did not give my curtains numbers". As soon as you mention the presence of three curtains, they may be numbered. Concerning the spotlight(s). you only mentioned a spotlight turned onto one of the goats. Nothing about other spotlights. So, what are you talking about? Nijdam (talk) 12:23, 26 February 2012 (UTC)

You say 'What are you talking about?' and that is a very good question. I have used natural language to describe a probability question. By it very nature natural language is vague. You must surely now accept my assertion that for a natural language decription of a probability problem there is no mathematical way, no algorithm, or no general method for turning it into a precise mathematical statement.

You say '...as you mention the presence of three curtains, they may be numbered'. Why then do you not number the goats in the standard MHP; we are told that there are two? Martin Hogbin (talk) 13:08, 26 February 2012 (UTC)

We discussed this last issue, and I explained that instead of showing goats the doors could be empty. Anyone will accept this is essentially the same problem. But I also said we may number the goats, no big deal. As for the "natural language": it is better to make a mathematical model, than just solve it in "natural language", as the latter may give rise to ambiguities. Nijdam (talk) 16:35, 27 February 2012 (UTC)

Of course it is better to use a mathematical model but in the MHP we are presented with a natural language problem in which there are two goats, one car, and three doors. We have to produce a mathematical model of the problem so that we can solve it. I would like you to tell me why you do not number the goats and include them in your sample space just as you do with the doors. Martin Hogbin (talk) 19:44, 27 February 2012 (UTC)

Nothing in the problem refers to a specific goat and as I already said: the problem would be the same when the goat doors were just empty doors. The door numbers however play a significant role. Nijdam (talk) 23:48, 27 February 2012 (UTC)

Nothing in my example above referred to a specific curtain but you said that they should be numbered and included in your sample space. In the MHP we should surely number the goats. Only one goat is revealed by the host but he might have revealed the other one, depending on his goat-preference. Surely we must include the goat numbers in our sample space. Martin Hogbin (talk) 00:00, 28 February 2012 (UTC)

I've no objection to number the goats, but notice what I say about the essential aspects of the MHP being present in a formulation without goats. Anyway includingbthe goat numbers clearly makes your idea of the appropriate sample space erroneous. Nijdam (talk) 10:52, 28 February 2012 (UTC)

You talk of the 'essential aspects of the MHP'. What exactly do you mean by this? Why are the doors part of the essential aspects of the MHP and the goats not? We can assume that Monty might have had a door preference which would affect the probability of interest. He might equally have had a goat preference, which also would have affected the probability of interest. Martin Hogbin (talk) 19:10, 28 February 2012 (UTC)

With the essential aspects I mean the presentation of the choice between two seemingly equally likely possibilities, and the surprising fact the odds are not equal but 1/3 to 2/3. For me the MHP is just another rewording of the three prisoners and Bertrand's box es. Nijdam (talk) 23:45, 28 February 2012 (UTC)

Neither the doors nor the goats are needed to arrive at the surprising fact that the odds of winning if you swap are 2/3. In fact they are both distractions and irrelevances. The only thing that matters is whether the player initially picks the car or a goat. If the player picks a goat and swaps they will, with certainty, win the car.

You still have not explained why you consider that the doors must for part of your sample space but the goats need not.

What sample space do you advocate for the three prisoners and Bertrand's box?

You have also not said whether you agree with my statement below, which I have made into a new heading.

We must include in our sample space everything which we think might affect the probability of interest

You're right about the goats, but not about the doors as being relevant to the surprising effect of the problem. The fact that many people think the odds are 50:50 arrives especially from the remaining choice between the two closed doors. The goats are just for fun. Nijdam (talk) 09:47, 29 February 2012 (UTC)

Answer to your above question: yes. And what is your reaction to my statement that including goat numbers makes your sample space not applicable? Nijdam (talk) 09:53, 29 February 2012 (UTC)

The doors are not required to state the problem, as I have shown above where exactly the same problem was created without doors. The doors are simply a way of marking the players initial choice of object and of revealing the host's choice of object. The number of the door is completely unimportant, what is important is the object that is behind it.

No, you just replaced the doors by something equivalent.

No, when I used a spotlight, you did not include spotlight number in your sample space. Why? The spotlight served exactly the same purpose as the doors, to hide, reveal, and identify objects.

????Was there more than one spotlight???

Does it matter? In order to illuminate one of three possible objects there must have been either three spotlights or on spotlight capable of illuminating at least three different positions. What is the difference?

I didn't bring the issue up, so: how many spotlights were there?

Would it make any difference to the sample space that you chose? (To me remember the 'correct' sample space depends only on what is considered might affect the probability of interest) Martin Hogbin (talk) 21:44, 2 March 2012 (UTC)

Well, you asked me why I din't include the numbers of the spotlight in the sample space.

I do not have ' a sample space', I have several. Which one is appropriate depends on the context of the question. If it is a simple puzzle then the sample space {C,G} is fine, because, by convention, nothing else can possibly affect the probability of interest.

You may have 1000 sample spaces, most of them will not applicable.

If it were an exam I would use the sample space that I thought the examiner wanted me to use, so I would include door number because it is given (or at least suggested) in the question, thus I would end up with the Morgan sample space.

It should struck you as illogic that you consider Morgan's solution as correct, and also your solution, although not equivalent to Morgan's.

The simple solution gives exactly the same answer as Morgan's solution and not by chance but simply because it assumes a natural and obvious symmetry at the start. It therefore is equivalent to Morgan's solution for the symmetrical case. Martin Hogbin (talk) 09:30, 1 March 2012 (UTC)

No it doesn't. You should know this by now. The (too) simple explanation does not give the same answer as Morgan's solution. And I and also Rick and Richird have explained that the simple solution does not make use of the symmetry. Years ago I already formulated the solution with the use of symmetry. It is only another way of calculating the conditional probabilities, something the simple solution does not do.

By 'answer' I mean the numerical value of 'the probability that a player who swaps will win the car'. This is 2/3 in both cases. Martin Hogbin (talk) 09:19, 2 March 2012 (UTC)

The probability to get 2,3,4 or 5 with a fair die is also 2/3.

I fail to see the relevance of this. The fact that a different question can have the same numerical answer to the MHP does not make the value of 2/3 obtained by the simple solution wrong. It is correct, as you well know. Martin Hogbin (talk) 21:44, 2 March 2012 (UTC)

I fail to see what it means that the simple solution has the same numerical value as the conditional solution, as you brought up.

It means that both solutions give the correct answer, and not by chance (as with your die problem) but because of an obvious symmetry in the problem. (Boris said this years ago.)

What do you mean by THE correct answer that both solutions give?? Nijdam (talk) 11:54, 4 March 2012 (UTC)

If it were a real-world problem I might include any number of things, depending on whether, in the circumstances in question, I though that might affect the probability of interest (that a player who, after seeing a door opened to reveal a goat, swaps will win the car).

Well, as long as it pleases you.

Why is it not possible that the host has a preference for one of the goats and that he always reveals this goat when possible? Thus is just as likely (unlikely) as his having a preference for one of the doors. Martin Hogbin (talk) 09:30, 1 March 2012 (UTC)

A lot is possible. But your drifting away from the main issue. Your preferred "solution" also does not count for any strange behaviour of the host.

You seem to be avoiding the issue. Why do we consider that the host might have a door preference but not a goat preference? I will make this clearer in a new section below. Martin Hogbin (talk) 09:19, 2 March 2012 (UTC)

We do not consider the host to have a door preference. Where do you get this idea? Nijdam (talk) 10:02, 2 March 2012 (UTC)

If we do not consider this to be possible then the doors obviously make no difference and they can be ignored. All the matters is whether the player originally chooses the car or a goat. What else could possible affect the probability of interest? Martin Hogbin (talk) 21:44, 2 March 2012 (UTC)

There you go again "the doors make no difference; to what? I asked you several times. Please give me an analysis in exact formulas what you mean by this. It's a good method to bring order in one's thoughts. Nijdam (talk) 11:11, 3 March 2012 (UTC)

I have answered this before. The doors make no difference to the probability of interest, which is the probability that a player who, having seen a goat revealed and who decides to swap, will win the car. Martin Hogbin (talk) 14:25, 3 March 2012 (UTC)

I'll wait for the analysis. Nijdam (talk) 23:42, 3 March 2012 (UTC)

There is no 'single correct solution', it depends on exactly what is being asked, just as Seymann says. Martin Hogbin (talk) 15:42, 29 February 2012 (UTC)

Should I be surprised? Nijdam (talk) 00:06, 1 March 2012 (UTC)

No, you should be convinced, by myself, Seymann, and Richard. Martin Hogbin (talk) 09:30, 1 March 2012 (UTC)

Convinced of what?? Nijdam (talk) 21:50, 1 March 2012 (UTC)

You see Martin, all your reasoning has lead you nowhere. In the - let me call it - standard MHP the player has made her initial choice and the host has opened a door, and only then is she offered to switch. I will have written this a thousand times. Using the symmetry leads to the fact that any combination of doors will give the same numerical answer to the conditional probabilities of interest, which we may however easily calculate straightforward. Other formulation of similar problems may have the simple reasoning as their solution, but not the standard MHP.

You like to say that the door numbers make no difference. I formulated above what this means. If you think of something different, do not formulate this in words, but give a concise formulation and analysis. Then may be it becomes clear what you mean by this. Nijdam (talk) 15:24, 5 March 2012 (UTC)

The question without door numbers

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, and the host, who knows what's behind the doors, opens another door, which has a goat. He then says to you, "Do you want to pick the other door that is still closed".

Nijdam, given this question, what do you assert is the correct sample space to use? The Morgan space? Martin Hogbin (talk) 09:24, 2 March 2012 (UTC)

It's exactly the same problem, we discussed this many times. The player is offered the switch when his choice and the door opened by the host are known. That's what counts, and that's what makes it necessary to calculate the conditional probability.

The model of the problem should count for the distribution of the car - randomly, resulting from the wording in "natural language" - the possible choices of the player, the choice of door tp be opened by he host and, due to indifference, the random choice if he has one. I do see three different doors, but the problem statement doesn't indicate anything to distinguish the goats. As I said: the goat doors could as well be empty, leading to the same (i.e. equivalent) problem Anyone (you too?) understands the goats as a gimmick. If, however, you like to number them: no problem; you still have to calculate the conditional probability.

Nijdam (talk) 10:19, 2 March 2012 (UTC)

In the problem statement above, there is just as much to distinguish the goats as there is the doors. We are told that there are three doors and that there are two goats. The only distinguishing feature of the door originally chosen is that it is the door originally chosen. The only distinguishing feature of the door opened by the host is that it is the door opened by the host (and that it hid a goat). Similarly, the distinguishing feature of the goat that has been revealed is that it has been revealed. There is no more reason to consider the doors, or the host's potential door preference to be important any more than there is to consider the goats or the host's potential goat preference to be important.

The doors are as much a gimmick as the goats for, as we have both seen above, exactly the same question can be posed without the use of doors. Martin Hogbin (talk) 21:38, 2 March 2012 (UTC)

No, definitely not. I said several times, the MHP may be formulated with no goats, but empty doors. It can't be formulated without doors, or, before you come up with spotlights, curtains, positions on the stage, etc, something equivalent. If you think you can, please try. Nijdam (talk) 23:53, 3 March 2012 (UTC)

I have already done this and you have already answered, you said:

Summing up: On stage are a car a black goat and a white goat. The player picks at random one of the three, without seeing it, and happens not to choose the white goat. We now want to know what in this situation the probability is that the car is still on stage. Just as with the MHP, but even stronger, there is the suggestion this conditional (!) probability is 1/2. But:

P(C on stage|first C or first B) = P(first B)/(P(first C and show W)+P(first B))=1/3 / (1/6 + 1/3) = 2/3.

You mention only C, B and W. There is no mention of stage position. You have solved the problem without mention of door number or its equivalent. Martin Hogbin (talk) 00:31, 4 March 2012 (UTC)

This is not the MHP or an equivalent formulation. Nijdam (talk) 11:51, 4 March 2012 (UTC)

If your requirement for a problem to be equivalent to the MHP is that it has doors then you are, of course, correct. I could be equally perverse and insist that to be equivalent to the MHP a problem must include goats. However, neither of these views makes much sense or is generally accepted. Both Bertrand's box and the three prisoners problem are generally considered to be equivalent to the MHP but neither contains either doors or goats.

I am sure that most statisticians and mathematicians will see my stage problem as a direct equivalent to the MHP. Martin Hogbin (talk) 16:01, 4 March 2012 (UTC)

Your "stage problem" is not equivalent to the MHP, as it distinguishes between a white and a black goat. If you have just two goats it becomes equivalent. Notice there are not three doors, but THREE different OBJECTS on stage. Nijdam (talk) 22:22, 4 March 2012 (UTC)

Notice you mention the equivalence of the MHP with the THREE prisoners, Bertrand's THREE boxes. Could you give me your solution to these problems without distinguishing between the prisoners or the boxes. That would be the day. Nijdam (talk) 22:17, 4 March 2012 (UTC)

Perhaps you misunderstood my stage problem. In it there were three objects, a car, a white goat, and a black goat. Martin Hogbin (talk) 23:46, 4 March 2012 (UTC)

What did I misunderstand?Nijdam (talk) 08:25, 5 March 2012 (UTC)

It must be your reasoning that I do not understand then. In my stage problem there are three objects involved, one car and two goats and in the MHP there are three objects involved, one car and two goats. In both cases we know there are two different goats and we can therefore distinguish between them, numbering them if you prefer. What makes the two problem not equivalent? Martin Hogbin (talk) 09:35, 5 March 2012 (UTC)

It is because you said: "he then shows THE white goat". If you just say: " he then shows a goat" it's okay. It's equivalent to the MHP, and with three "doors", being the position of the object on the stage. The position closest to the player is "door" No. 1 etc. It is logically impossible to define an equivalent problem without "doors", simply because the MHP itself has doors. Nijdam (talk) 15:02, 5 March 2012 (UTC)

The goats do not need to be different colours for us to distinguish between them. The doors are not numbered in the example above but you chose to number them. We can call the goat that is revealed number 1 if we wish; the other one, which we cannot see, will be number 2.

Do you not agree that it is possible to apply a Morgan type argument to the goats. Maybe the goat that is revealed is revealed because the host has a preference for that goat. Martin Hogbin (talk) 00:07, 6 March 2012 (UTC)

No problem, I already said we may distinguish the goats. It just complicates the problem a little. But I hope you agree, we may as well leave the goats out. And yes , we may apply a preference for one of the goes, why not, but let's stick to the problem with no door preference of the host and no goats. Nijdam (talk) 21:06, 6 March 2012 (UTC)

So we agree that it is possible that the host has a preference for a goat but that we should discount this possibility. What then is the correct sample space to use? Martin Hogbin (talk) 11:28, 7 March 2012 (UTC)

Why complicate things? Describe the sample space for the version I mentioned above. Nijdam (talk) 21:56, 8 March 2012 (UTC)

What I do not understand is why you can miss out the goats from your sample space but not the doors. We agree that the host could have a goat preference or a door preference but we will consider the case where he has no preference for goats or doors. The doors and the goats only complicate the problem unnecessarily. Martin Hogbin (talk) 23:45, 8 March 2012 (UTC)

It's not because of the lack of preference that we may leave something out. I repeat: the player knows which door she has chosen and which door the host has opened. Nijdam (talk) 08:33, 10 March 2012 (UTC)

What the player knows

In the version above the player knows that there are three doors, one car, and two goats. The player knows that the host opens one of the unchosen doors to reveal one of the goats and then says the words, "Do you want to pick the other door that is still closed".

The player sees the door that is opened by the host, sees the goat that is revealed by the host, and hears the word spoken by the host. Why then are the doors more important than the goats or the words spoken by the host? Martin Hogbin (talk) 09:28, 10 March 2012 (UTC)

You keep hammering on this. The problem says there are three doors, the problem does not say anything about the distinguishability of the goats, and as I indicated, the goats could as well be left out. Also the only thing the host says is "Do you want to pick the other door that is still closed". I may give free way to my fantasy and think of an host saying "pick" when the car is at door 1, saying "change to" when the car is at door 2, and "swap to" for door 3, but t only complicate things, not simplifies them, there is nothing in the formulation supporting this, and finally it does not bring any desirable aspect to the problem. The standard formulation is sort of minimum. All that is mentioned in the formulation of the problem is included, and nothing not mentioned.Nijdam (talk) 08:06, 11 March 2012 (UTC)

Time now has come you make clear what you mean by saying that the numbers of the doors does not make any difference etc. And be very precise! Nijdam (talk) 08:06, 11 March 2012 (UTC)

The formulation that I am referring to does not mention any door numbers. Here it is again: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, and the host, who knows what's behind the doors, opens another door, which has a goat. He then says to you, "Do you want to pick the other door that is still closed".

You will see that there are three doors, one car, and two goats. The goats are, of course, distinguishable, as are all goats. I am not aware of any goats that are

.

The probability that I wish to calculate is the probability that the player who swaps will win the car after the procedure above is followed according to the standard game rules and given that the player sees one of the doors opened to reveal one of the goats and hears the host say the words, "Do you want to pick the other door that is still closed".

The problem cannot be expressed any more precisely that this until we decide how we are going to formulate the problem mathematically. Please tell me how, from the wording above, we can deduce that the door is important but the goat and words spoken by the host are not. Martin Hogbin (talk) 09:38, 11 March 2012 (UTC)

Not the door numbers itself are important, I thought you would be aware of that, but the distinguishability. And as I said we may distinguish the goats as well, although this it not necessary and nothing in the problem indicates how we should do so. For the last time: the host says nothing else than what's in the problem formulation.

You will know my question: which door did the player choose and which door is opened by the host? Of course you are free to think of any problem resembling the MHP, and one of such problems is where we, the audience are asked before the player made her choice to decide what she has to do, And we have to say either switch or stick. Then your arguments form a solution.

You have still failed to explain why we must distinguish between the doors but we may distinguish between the goats. What in the problem statement given above tells you this? Martin Hogbin (talk) 18:02, 12 March 2012 (UTC)

I explained that the simple fact that the doors are distinguishable means there identification is part of the problem. Nowhere it says the goats are distinguishable, and I said anyone understands they just are a gimmick and could as well br left out. Now I want to know from you which good the player has chosen.

Then show me how in your sample space the event: "swapping will give the car" is defined. Andfurthermore at last answer my question about the meaning of the door numbers making no difference to something. And be strict logical in this. Good luck.Nijdam (talk) 14:25, 12 March 2012 (UTC)

Easy. The simplest possible sample space that will give the correct answer (Note this is not my sample space just the simplest) is {G,C}, with probabilities 2/3 and 1/3. A player who initially picks a goat and then swaps gets the car. Always.

You pertain in saying "will give the correct answer" what on its own is a meaningless statement. I fail to see what swapping means in "your" sample space. In the MHP the player swaps doors! Nijdam (talk) 23:06, 19 March 2012 (UTC)

An alternative possible sample space, relevant to our discussion above, is {C,G1,G2}. If the player initially picks, say, G1, the host must reveal G2, and if the player swaps they get C.

On the other hand, if the player initially picks C, it can be argued that we need to know the probability that the host will pick each goat before we can answer the question.

The door numbers (obviously) make no difference to the probability of interest, which is, as explained above, is 'the probability that the player who swaps will win the car after the procedure above is followed according to the standard game rules and given that the player sees one of the doors opened to reveal one of the goats and hears the host say the words, "Do you want to pick the other door that is still closed"'. Martin Hogbin (talk) 18:02, 12 March 2012 (UTC)

Could you show me a case where the door numbers could make a difference to the probability of interest? May be I might then understand what you mean.Nijdam (talk) 23:06, 19 March 2012 (UTC)

Cases where the door numbers do matter

This is an example where the door numbers are important

Suppose you're on a game show, and you're given the choice of three doors, numbered 1 to 3: Behind one door is a car; behind the others, goats. You pick door 1, and the host, who knows what's behind the doors, opens door 3, which has a goat. He then says to you, "Do you want to pick door 2?". The host always opens door 3 when the (standard) rules allow. What is the probability that you will win the car if you swap to door 2?

Here is another example:

Suppose you're on a game show, and you're given the choice of three doors, numbered 1 to 3: Behind one door is a car; behind the others, goats, the car being placed behind door 1 with probability 1/2. You pick door 1, and the host, who knows what's behind the doors, opens door 3, which has a goat. He then says to you, "Do you want to pick door 2?". What is the probability that you will win the car if you swap to door 2?

The probability of interest is clearly different from the example above in the case below:

Suppose you're on a game show, and you're given the choice of three doors, numbered 1 to 3: Behind one door is a car; behind the others, goats, the car being placed behind door 1 with probability 1/2. You pick door 2, and the host, who knows what's behind the doors, opens door 3, which has a goat. He then says to you, "Do you want to pick door 1?". What is the probability that you will win the car if you swap to door 2? Martin Hogbin (talk) 18:53, 20 March 2012 (UTC)

Different problems, different solutions, no big deal.Nijdam (talk) 10:25, 21 March 2012 (UTC)

Cases where the door numbers do not matter

These are examples where the door numbers are not important

Suppose you're on a game show, and you're given the choice of three doors, numbered 1 to 3: Behind one door is a car; behind the others, goats, the car being placed randomly (uniformly). You pick door 1, and the host, who knows what's behind the doors, opens door 3, which has a goat. He then says to you, "Do you want to pick door 2?". The host always chooses randomly (uniformly) between doors allowed by the rules. What is the probability that you will win the car if you swap to door 2?

Suppose you're on a game show, and you're given the choice of three doors, numbered 1 to 3: Behind one door is a car; behind the others, goats, the car being placed randomly (uniformly). You pick door 2, and the host, who knows what's behind the doors, opens door 3, which has a goat. He then says to you, "Do you want to pick door 1?". The host always chooses randomly (uniformly) between doors allowed by the rules. What is the probability that you will win the car if you swap to door 1?

Suppose you're on a game show, and you're given the choice of three doors, numbered 1 to 3: Behind one door is a car; behind the others, goats, the car being placed randomly (uniformly). You pick door 3, and the host, who knows what's behind the doors, opens door 1, which has a goat. He then says to you, "Do you want to pick door 2?". The host always chooses randomly (uniformly) between doors allowed by the rules. What is the probability that you will win the car if you swap to door 2?

Here the probability of interest (that the player will win the car if he swaps) is obviously the same in all cases. Martin Hogbin (talk) 18:59, 20 March 2012 (UTC)

Explain the meaning of THE probability of interest being the same in all cases. What cases of you mean? See: THE probability is always and in all cases and forever and ever the same. Nijdam (talk) 10:28, 21 March 2012 (UTC)

The probability that the player will win the car if he swaps is obviously the same in all the above examples. Martin Hogbin (talk) 00:49, 22 March 2012 (UTC)

The same as what?? Guard your logic. Nijdam (talk) 00:03, 23 March 2012 (UTC)

What is the probability that the toss of a fair coin will be head? Answer, 1/2.

When I ask 'What is the probability of x?', I am asking for a number, from 0 to 1, not a philosophical discussion. So when I ask, 'What is the probability that the player will win the car if he swaps?' I am asking for number. This number is 2/3 in each case above, thus the probability is the same in each case. Is this not what people want to know? If I swap what are the chances that I will win the car? Martin Hogbin (talk) 01:10, 24 March 2012 (UTC)

You're mixing up things. I'm not interested in all the different ways you formulated similar problems. Just concentrate on our main point of discussion. You stated: The door numbers (obviously) make no difference to the probability of interest, which is, as explained above, is 'the probability that the player who swaps will win the car after the procedure above is followed according to the standard game rules and given that the player sees one of the doors opened to reveal one of the goats and hears the host say the words, "Do you want to pick the other door that is still closed"'.

And I asked you to show me what you mean by: the door numbers make no difference. You just say: it is obvious, well: show me. Nijdam (talk) 21:39, 25 March 2012 (UTC)

I am not sure what you are asking. Is it not obvious to you that the probability of interest has the same vale in the three examples I have given above? Martin Hogbin (talk) 08:36, 26 March 2012 (UTC)

What on earth could be the relation of your remark with door numbers????? Just concentrate, I repeat, on my quote of what you've written. From your own words I deduce the doors have numbers, let us number them 1,2 and 3. You defined 'the probability of interest', call it p. What do you mean by saying that the numbers 1,2 and 3 make no difference to p???? Nijdam (talk) 09:05, 26 March 2012 (UTC)

I mean that the door numbers can, at the start of the problem, be arbitrarily changed without affecting the probability of interest. Martin Hogbin (talk) 09:20, 26 March 2012 (UTC)

Does your sample space have door numbers at the start of the problem? Nijdam (talk) 16:15, 26 March 2012 (UTC)

I do not have a sample space. It is, of course, possible to set up a sample space based on door numbers but, as it is quite obvious from the start that the door numbers are irrelevant, it is also possible to use a sample space that does not include door numbers, such as (G,C} or {G1,G2,C}. As the goat number is also quite obviously irrelevant, I see no reason not to start with the sample space {G,C}. It can only give the correct answer to the problem and it is therefore perfectly valid. Martin Hogbin (talk) 17:28, 26 March 2012 (UTC)

Either you give an informal reasoning in which you have to include the alleged irrelevance of the door numbers, or you build a formal model with a sample space where you also have to include the door numbers in order to proof their 'irrelevance'. Nijdam (talk) 07:57, 27 March 2012 (UTC)

It depends on how obvious you think the irrelevance of the door numbers is. After all, do you think it necessary to explain why the specific goat that is revealed is irrelevant or why the fact that the host says the word 'pick' is unimportant?

In turning any natural language statement into a precise mathematical question it is generally necessary to make some quick, informal, and often unmentioned, assessment of which events are significant for calculating the probability of interest. Martin Hogbin (talk) 17:17, 27 March 2012 (UTC)

You're permanently overlooking the logical aspect of your term 'irrelevant'. In your simple solution, door numbers are not involved. But that's something different than not relevant. You just choose to solve the problem in such a way that the door numbers are not involved. You still didn't show the irrelevance of the door numbers. Please, only answer what you consider the irrelevance to be. Try to be as precise as possible. Nijdam (talk) 21:50, 27 March 2012 (UTC)

I am not quite sure what you mean. By 'irrelevant' I mean what I have demonstrated above; that the probability of interest is not changed by a change in door number thus it is not necessary to include the doors in our sample space.

You're running around in circles. You do not include door numbers; then you conclude some probability does not depend on them (how on earth could it), and finally syiu ay: see, the numbers are irrelevant. Where is your logic? Nijdam (talk) 07:30, 28 March 2012 (UTC)

The doors are not really part of the problem at all. They merely serve to hide the objects behind them so that someone can choose an object without knowing what it is. The 'natural' sample space is {C G1,G2} for they are the objects which are chosen by the player and the host and the objects one of which the player will eventually win. The MHP can be rephrased without doors at all, as in my spotlight version. Martin Hogbin (talk) 22:19, 27 March 2012 (UTC)

No you keep saying this, as to convince yourself, but for instance your spotlight version is not a version without "door numbers". Nijdam (talk) 07:30, 28 March 2012 (UTC)

Problems equivalent to the MHP

Here is your statement of a problem that does not involve doors:

On stage are a car a black goat and a white goat. The player picks at random one of the three, without seeing it, and happens not to choose the white goat. We now want to know what in this situation the probability is that the car is still on stage.

Let me restate it slightly thus:

On stage are a car a black goat and a white goat. The player picks at random one of the three, without seeing it. It is then revealed to the player that they have not chosen the white goat and the white goat is removed from the stage. The player is then given the option of switching their choice to the other object remaining on the stage. What is the probability that a player who decides to switch will choose the car?

What is the correct sample space for this problem?

Is it equivalent to the MHP? Why? Martin Hogbin (talk) 08:32, 28 March 2012 (UTC)

No, it isn't. Unless we say on stage are 3 objects,. a car. and two goats. The player mention his choice by saying: I choose object nr x, etc. How does in your formulation the player reveal their choice? Nijdam (talk) 22:30, 28 March 2012 (UTC)

That is an interesting question and my whole point is that there is no clear distinction between the two problem. Suppose the player points randomly at an unlit stage, suppose the objects are in hidden is some kind of revolving door in which the compartments are visually identical? However the player chooses we are free to number the objects if we wish; we know there are three different objects. We can also choose to number the goats if we wish; we know there are two different goats. The only way in which we can objectively decide on which events we should include in our sample space is to ask ourselves the question 'Could this event possibly affect the probability of interest?'. Martin Hogbin (talk) 09:43, 30 March 2012 (UTC)

To answer your direct question about how the player reveals their choice this is really the question of how they indicate their original choice, which I discuss above. Once the original choice is made the player need only say 'stick' or 'swap'. Martin Hogbin (talk) 17:26, 31 March 2012 (UTC)

You may come up with any ingenious formulated problem, as long as it doesn't have the equivalent of the 3 doors, it will not be equivalent to the MHP.Nijdam (talk) 22:12, 3 April 2012 (UTC)

But what exactly is the 'equivalent of the 3 doors'? How do I know if my setup has the 'equivalent of the 3 doors'?

Also, why do I need the doors at all for the problem to be equivalent to the MHP? We are always free to number the objects 1 to 3.

Suppose I change my question to: On stage are three objects numbered 1 to 3. They are a car a black goat and a white goat but we do not know which object has which number. The player picks at random one of the three, without seeing it. It is then revealed to the player that they have not chosen the white goat and the white goat is removed from the stage. The player is then given the option of switching their choice to the other object remaining on the stage. What is the probability that a player who decides to switch will choose the car?

Is this now equivalent to the MHP? Martin Hogbin (talk) 23:00, 3 April 2012 (UTC)

No, as in the MHP the goats are not distinguished. Furthermore the numbering of the objects should be at random, not fixed. Nijdam (talk) 09:10, 4 April 2012 (UTC)

What about this then? On stage are three objects randomly numbered 1 to 3. They are a car and two goats; we do not know which object has which number. The player picks at random one of the three, without seeing it. It is then 'revealed' to the player that at least one goat remains on stage and one goat is removed from the stage The player is then given the option of switching their choice to the other object remaining on the stage. What is the probability that a player who decides to switch will choose the car? Martin Hogbin (talk) 10:24, 4 April 2012 (UTC)

Neither is this one. In the MHP the host reveals more than just that one goat is removed. He also shows the object number of the removed goat. In your example above it is superfluous to say at least one goat remains on stage; it suffices to mention that just one goat is removed. To make it equivalent to the MHP the host should say: object number h (different from the chosen object) is a goat and will be removed from the stage.Nijdam (talk) 21:33, 6 April 2012 (UTC)

Sorry there was a mistake in that, which you pointed out. It should have read:
On stage are three objects randomly numbered 1 to 3. They are a car and two goats; we do not know which object has which number. The player picks at random one of the three, without seeing it. The host then says that from the two unchosen objects he will remove a goat and removes a goat from the stage The player is then given the option of switching their choice to the other object remaining on the stage. What is the probability that a player who decides to switch will choose the car?

Is this the same as the MHP?

What if the host then says the goat that he removed was object number 2?

What if, instead, the host tells the player that the goat that he removed was called zebedee? Martin Hogbin (talk) 21:50, 6 April 2012 (UTC)

My answer is mainly the same. Your first formulation is not equivalent to the MHP. The answer will be that for every combination of chosen object and revaeled one, assuming the host acts randomly if necessary, the conditional probability will be 2/3. Your second formulation is not complete, as from the formulation it follows the player didn't choose object nr. 2. But supposing the player did choose object nr. 1 (and the random acting of the host), it is equivalent to the MHP. Then for the case with the goat called Zebedee - show some respect to the goat and write her name capitalized - this is the same as with the black goat and the white goat. It's similar, but not equivalent to the MHP. Do not ask me what the situation will be if the goat wasn't called Zebedee, but Hollibee instead. Nijdam (talk) 08:02, 7 April 2012 (UTC)

First, my apologies to the goat.

So you are saying that if, in the above example, the host says that the number of the object that the player originally chose was 1 and the object number of the goat that he revealed this would be equivalent to the MHP? Martin Hogbin (talk) 08:47, 7 April 2012 (UTC)

Sorry. I mentioned 'door' instead of 'object', but did change it. And, in spite of the threatening sound of your question, yes, then it would be equivalent to the MHP; just read 'door' for 'object'. Nijdam (talk) 06:01, 8 April 2012 (UTC)

Would the question be equivalent if the object numbers were revealed at the end if the show?

a) What do you mean by an equivalent question? b) Revealed to whom? c) Howe does the player indicate her choice? Nijdam (talk)

What about if the object numbers numbers were assigned (randomly) to the objects after the show. Martin Hogbin (talk) 09:00, 8 April 2012 (UTC)

Or exactly one year thereafter?Nijdam (talk) 18:55, 8 April 2012 (UTC)