User talk:Glopk/Monty Hall Problem Archives

Bayesian analysis of Monty Hall problem

Hi - I've asked a question about the Bayesian analysis you've recently added. Please see Talk:Monty Hall problem (and reply there). Thanks. -- Rick Block (talk) 14:26, 17 January 2007 (UTC)

I hope you enjoy editing here and being a Wikipedian. Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page (I've been around quite a while and am very willing to help), or place {{helpme}} on this page (your talk page) and ask your question here. Again, welcome! -- Rick Block (talk) 14:38, 17 January 2007 (UTC)

Hi - Can you take a look at the Bayesian analysis section? I've changed the conditional probability definition of Hij to use a table (so the text is not rendered using the math markup). SandyGeorgia is asking for a reference as well. I've posted a comment about this on the talk page - the upshot is if you can find a book to directly reference that'd be great. BTW - I think the new section is much better than the original one. It is far more complete. Good job! -- Rick Block (talk) 04:17, 26 January 2007 (UTC)

FAR on Monty Hall problem

Monty Hall problem has been nominated for a featured article review. Articles are typically reviewed for two weeks. Please leave your comments and help us to return the article to featured quality. If concerns are not addressed during the review period, articles are moved onto the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Remove" the article from featured status. The instructions for the review process are here. Reviewers' concerns are here. - Chardish (talk) 06:11, 28 March 2008 (UTC)

MH madness

Hi - Have you been watching the madness at talk:Monty Hall problem? I've lately created an "arguments" subpage to try to help structure things (both the main talk page and the arguments subpage will have FAQs). You haven't commented in a while. There's actually a thread at Talk:Monty Hall problem/Arguments for which I suspect your expertise would be useful (currently the last thread). At this point, the subpage is far less ridiculous than the main talk page (to some extent, I hope this eventually flips). In any event, I noticed you still log on at least occasionally and mostly wanted to drop by and say hi. -- Rick Block (talk) 00:07, 19 February 2009 (UTC)

Hi Rick. Yep, seen the madness, but have abstained from the fray both for lack of time and because my supply of patience for the ignoramuses is very very much smaller than yours. Will take a look at the graph you mention.glopk (talk) 02:56, 19 February 2009 (UTC)

Thanks for the comment at Talk:Monty Hall problem/Arguments, although I suspect Martin will not be happy with this answer. I think he's actually questioning how we know the problem should be expressed as conditional with respect to the door that is opened. To a mathematician the problem is obviously a conditional probability problem - but why? I seem to be unable to explain this to him. -- Rick Block (talk) 05:35, 19 February 2009 (UTC)

Well, how do we know which questions to ask of a given universe I? Dropping the indices from the Bayesian MHP analysis, we know that P(C|I)? and P(C|H,I)? are both legitimate questions to ask. You (or Martin) ask: what makes the latter the relevant one to the MHP? I answer: because C|H,I is the simplest expression that captures all the facts at hand: there is a car (C), Monty opens a specific door (H) using a certain strategy (I), and he offers to switch (I). Why is it the simplest? Because it shoves under the carpet (I) everything else. Why is it relevant? Because if you remove H you go back to P(C|I), which is a three-faced coin rather than the MHP. Why does H condition C given I (i.e., why isn't C independent of H)? Because C conditions H under I: in the standard formulation Monty has to follow a rule in selecting which door to open that depends on where the car is. And if P(H|C,I) is not identical to P(H|I), it follows (from Bayes' theorem) that P(C|H,I) is not the same as P(C|I).

Interesting. To some mathematicians the problem is definitely a non-conditional problem. I think it largely depends on how one first meets the problem Gill110951 (talk) 05:37, 25 June 2010 (UTC)

Three prisoners

I asked for a comment on the Talk: Three Prisoners problem about the inserting of "the rules of the game". Will you please have a look there. Nijdam (talk) 10:45, 19 February 2009 (UTC)

Replacement section at MHP

Hi - Seems like you might be interested in this change. I've reverted it once already and commented at Talk:Monty Hall problem#Bayesian approach. -- Rick Block (talk) 14:02, 24 April 2009 (UTC)

Professor?

You made me curious, so I poked around in your old edits. I was probably thinking about comments like this one. Based on this and recent comments you evidently at least used to teach. I don't actually care and have tried to divulge little about my own real life identity (more from a "we're all equal editors here" than any privacy concerns - I generally don't make a point about being an admin either). -- Rick Block (talk) 00:28, 29 April 2009 (UTC)

Yes, of course - was just joking in response to your "you are both professors". I have been out of academia for many years now, and "do" prob. theory in rather mundane (but profitable) settings, rather than teach it.

On an unrelated note, how do I get the internal link to the MHP "Bayesian analysis" section to look like it was before, i.e. without the ugly '#'? glopk (talk) 18:00, 30 April 2009 (UTC)

Re the link - use the "pipe" syntax, i.e. [[#Bayesian analysis|Bayesian analysis]]. -- Rick Block (talk) 21:50, 30 April 2009 (UTC)

Thanks! Fixed.glopk (talk) 15:58, 1 May 2009 (UTC)

Martin Hogbin's complaints about Morgan et al.

Hi - Can you respond at Talk:Monty Hall problem/Arguments#Error in Morgan et al?? Martin has been attempting to discredit the Morgan et al. paper (for months). He claims to be a physicist, but has no probability expertise. The current issue is whether the Bayesian treatment, assuming a uniform distribution of q yielding a probability of winning by switching of ln(2), is correct. Looks like it to me. -- Rick Block (talk) 13:20, 6 May 2009 (UTC)

Sure, will take a look. glopk (talk) 03:23, 7 May 2009 (UTC)

Suggested changes to Monty Hall problem

You are invited to join the discussion at talk:Monty Hall problem#Changes suggested by JeffJor, Martin Hogbin, and Glkanter. Rick Block (talk) 04:08, 3 December 2009 (UTC) (Using {{Please see}})

We're now in informal mediation, see Talk:Monty Hall problem#Mediation. Feel free to participate (or not), time permitting. -- Rick Block (talk) 19:46, 29 December 2009 (UTC)

Recent edits at MHP

Hi !

I just wanted to thank for your recent changes and the effort to provide a detailed measure theoretic description. This was basically what I had in mind when talking about "frame/context" to rest of the article earlier. Unfortunately Nijdam reversed it right away. For what it's worth, I've added my comment on the discussion page and provided a source, that exactly matches your description (3 step modelling).--Kmhkmh (talk) 12:06, 11 March 2010 (UTC)

Thanks for your support. Will continue on the discussion page as you suggest. --glopk (talk) 15:08, 11 March 2010 (UTC)

Unfortunately the next round of edits regarding the formal solution has been opened. I'm not going to revert it again to avoid an edit war. Unfortunately this edits are even coming from a mathematician, who treats the article from the viewpoint of his personal interests only an insist on doing so. I asked him personally to refrain from such behaviour but to no avail.--Kmhkmh (talk) 13:49, 24 June 2010 (UTC)

Looks like a bit of a tag team. How about we discuss things on the talk page rather then revert first, ask questions afterwords. Martin Hogbin (talk) 15:15, 24 June 2010 (UTC)

I suggest you recommend that to Gill. The order here is rather clear, Gill made a large controversial change without consent and insisted on even it after having made aware of the controversial nature. Glopk merely resetted it to the state before the controversial edit.--Kmhkmh (talk) 15:25, 24 June 2010 (UTC)

Martin: tag off! :-) glopk (talk) 16:20, 24 June 2010 (UTC)

What is this nutty statement about wrecking an FA class article? I am trying to improve it and to introduce a neutral POV into its formulation. Gill110951 (talk) 19:44, 24 June 2010 (UTC)

I understand what you say you are trying to do. However, the fact is that you have done a large deletion and change in an FA-class article. When reverted, you have done it again. It is obvious that there isn't an editorial consensus about your changes, so your insistence in pursuing them after being reverted is "wrecking". I am not addressing here the issue of whether your changes are NPOV or not, the article's discussion page is the appropriate forum for that.glopk (talk) 23:04, 24 June 2010 (UTC)

And what is this nonsense about game theory being irrelevant and new? Read the literature, man. Nalebuff is before vos Savant. Talk to some economists. Gill110951 (talk) 05:33, 25 June 2010 (UTC)

"Man", I responded in the article's talk page. glopk (talk) 22:46, 25 June 2010 (UTC)

"reference"

Hello Glopk, tried to add the required reference (pigeons). Please can you help, result of my added ref differs from the rest of references in the article, don't know how to make that better. Btw: Gills adds underline that - in any given special case/situation that so happened - deviant odds can only be affected by any kind of typically "given" additional information concerning the actual present constellation (by opening one special door). Think it's of importance for readers to be in the know. Regards, --Gerhardvalentin (talk) 19:39, 25 June 2010 (UTC)

email

Hi - Do you pay attention to the email account registered with this login? Just curious. -- Rick Block (talk) 19:38, 14 July 2010 (UTC)

Not regularly, but I could check it for he next few days, if needed. glopk (talk) 22:50, 14 July 2010 (UTC)

Mediation

Perhaps not necessary, but you should probably also add yourself to those accepting mediation at Wikipedia:Requests for mediation/Monty Hall problem#Parties' agreement to mediation. -- Rick Block (talk) 21:58, 11 August 2010 (UTC)

 Done, thanks. glopk (talk) 22:03, 11 August 2010 (UTC)

Richard tries to cut the crap

Hi glopk, I have spent all day "doing my stuff" on the MH mediation page. In an effort to decrease my verbosity I put up some footnotes to some new mediation page contributions by me, on my own talk page. Still struggling with how to do links in wikipedia and how to get notifications when important things are changed. I hope you have time to take a look and do please comment, in whichever way you like. Gill110951 (talk) 13:43, 15 August 2010 (UTC)

Placeholders

1 2

MHP: the essential difference 1 : between the solutions

Do you see the difference between:

A: "the switcher wins twice as often as the stayer"

and

B: "the switcher wins twice as often as the stayer, whatever the player's initial choice or which door was opened by the host"

Do you agree that B implies A, but A does not imply B?

If both your answers are yes, you will agree that the conditional argument gives a stronger reason for switching than the simple solutions.

Some people might find the simple solution with the simple conclusion A good enough for them, but at least they ought to be able to see why many sources find the unconditional solution incomplete: B is definitely better.

A tells you "always switching beats always staying".

B tells you "nothing beats always switching".

It's not surprising that B beats A. To get A you only need to know that your initial choice is right with probability 1/3. To get B you have to know the whole list of "completely at random" assumptions.

From the point of view of scope, A is better than B: it is more likely to be true, since its "minimal assumptions" are more likely to be true. If all you want is A don't waste time arguing for assumptions which aren't needed in order to guarantee your desired conclusion.

Conversely, if you insist on limiting your scope by writing down all the standard assumptions, you should at least try to do something useful with them.

I think these are the essential mathematical truths behind all the fighting (such a waste of energy).

They can all be reliably sourced, too.

Gill110951 (talk) 15:04, 15 October 2010 (UTC)

My answers are: yes I see the difference, and no, B does not imply A, and neither does A imply B.

Proof: with the same variable definitions for C, S, H as in the Mathematical Formulation section in the article, and defining the proposition

W == "Win by switching" == (C ≠ S)

and denoting the background information with I, your assertion A is:

${\tfrac {2}{3}}=\sum _{c=1}^{3}\sum _{s=1}^{3}\sum _{h=1}^{3}P(W,C=c,S=s,H=h|I)$

whereas B is:

${\tfrac {2}{3}}=\sum _{s=1}^{3}\sum _{h=1}^{3}P(W,S=s,H=h|C,I)$

Notice the difference? glopk (talk) 00:24, 16 October 2010 (UTC)

I disagree with your translations of A and B into maths. I will drop the background information $I$ below. Recall, $C$ is door hiding car, $S$ is door selected by player, $H$ is door opened by host. Then A is:

$P(W)={\tfrac {2}{3}}$

and B is:

$P(W|S=s,H=h)={\tfrac {2}{3}}$ for every $s\neq h$.

By the law of total probability, since the six possibilities (6 pairs of different values of $S,H$) are mutually exclusive and exhaustive, we can rewrite $P(W)$ as

$P(W)=\sum _{s,h:s\neq h}P(W|S=s,H=h)P(S=s,H=h)$.

According to B, each of the 6 conditional probabilities in this expression equals 2/3. Again since the six possibilities are mutually exclusive and exhaustive their probabilities sum to 1:

$\sum _{s,h:s\neq h}P(S=s,H=h)=1$.

Together, this gives us $P(W)={\tfrac {2}{3}}$. From B we derived A. QED. Gill110951 (talk) 12:48, 17 October 2010 (UTC)

Where is C in your expression for proposition B? Also (but this is a meta-point) I find it amusing that you'd drop the "rules of the game" I, but then go through algebraic contorsions (s ≠h) in order to write your expressions: are you afraid of being seen as Bayesian? :-) If you drop it, than you must write: W == "Win by switching" == (C ≠ S) AND (C ≠ H) AND (S ≠ H), and carry all that on in your sums. Putting it in more mechanical terms: please rewrite your proof in a way that makes your expressions computable (by your peecee, in case you don't have a Turing machine handy). Until then I find it incomplete. glopk (talk) 17:10, 18 October 2010 (UTC)

I don't understand why you think that writing a sum over the six pairs s,h with s unequal to h is an algebraic contortion. We both agree that S and H are always different so the three pairs with s=h have probability zero, so what is the point of including them in summations? You'll end up with expressions that your peecee might find difficult to handle such as 0/0="undefined" and 0 x "undefined". You'll have to go into algebraic contortions by defining what a switcher should do in the situation that the host reveals a car and/or the host opens the door chosen by the player. We agree that these possibilities have probability zero so we needn't waste time on them.

I only dropped "conditional on I" because it is a waste of time to write it *everywhere*. If you want it back, please just replace every P( ... | ...) by P( ... | ... , I) and ever P( ... ) by P( ... |I). What does your peecee do with "conditioning on I"?

I don't understand why you insist on every expression being reduced to summations over "atomic events". Why do you need me to write formulas telling you how to compute every probability which I write down? Surely you know how to do that, without me telling you. But anywhere, here is the recipe. It has two parts. First part: the rule P( A | B ) = P( A & B ) / P(B) reduces every conditional probability to a ratio of unconditional probabilities. Second part: the rule P(A) = \sum_h\sum_s\sum_c P(A & C=c, S=s, H=h ) reduces every unconditional probability to a summation of probabilities of elementary events. For a given event A, you must just check which triples h,s,c, with h different from c and s, are compatible with A, which ones not. Then sum all the elementary probabilities of h,s,c compatible with A. I only discuss events which are expressible in terms of elementary events (outcomes, atomic events). Richard Gill (talk) 21:08, 18 October 2010 (UTC)

Eeeeh, I was in jest, didn't mean to irk you, sorry I did. OK, let's restart from your original question. I accept that, within your translation into math, B implies A. I also wrote as much in the MHP talk page at least two times, most recently about two months ago, and that was the last time I tried to have an intelligent conversation on math with Martin Hogbin. It didn't work. Indeed one might write the math in gold on plates of the finest Carrara marble, get them jointly blessed by the ghosts of Laplace and De Finetti, hung them on the wall of Gresham College, climb to the top of its roof, grab a bullhorn and scream till blue in the face that the simple solutions are computing marginals of the conditional solution, and still Martin would not believe you. Or rather, he would not understand you, and in the next four sentence would proclaim yet again (a) that it does not matter in the standard case (b) that your math is of limited interest to the average Wikipedia reader, (b) 7000 papers written by psychologists who could not for their life tell P(A|B) from a dachsund count as much as 10 papers written by mathematicians, (c) therefore all conditional solutions should be marginalized in an appendix with size 3 font and (d) the simple solution are correct, complete, divinely inspired and really all there is to the MHP, let's all go home and let Glkanter stand guard on the article henceforth. Now, do I sound frustrated enough? glopk (talk) 20:46, 19 October 2010 (UTC)

Nicely put, Glopk! I share your frustration! Richard Gill (talk) 08:37, 22 October 2010 (UTC)

MHP: the essential difference 2 : between the editors

MHP is a puzzle, a paradox. Usual intuition gives the wrong answer. One has to take a step back, think clearly and think out of the box in order to see that the player ought to switch. This means that at some point we have to suspend our direct intuitions and switch to careful conscious logical thinking. Later, we may develop an intuition which helps us give the right answer in similar situations in the future, but for newcomers to MHP that intuition is not there.

When we change mode and start using conscious rational thought instead of immediate intuition, we must distinguish in the original real world story between those elements which are important to keep in mind, and those which are merely ornamentation. I think that the disagreement between conditionalists and unconditionalists is actually not a disagreement between using conditional probability formalism or not, but is a disagreement whether the specific door-numbers are ornamentation or essential. After all, both are interested in the situation after a door has been opened, and clearly the probability that there is a car behind door 3 (or after "a door") after it is opened revealing a goat has indeed dramatically changed.

In a sense the disagreement is harmless, because under the usual supplementary assumptions about equal probabities all over the place, people who take the door-numbers on board, and work carefully through the more complicated problem do discover, after going to all that trouble, that whether or not you should switch does not depend on the specific door numbers in hand. However, what if we had discovered that the door numbers were relevant??? Admittedly you would have to change the problem a lot to make them relevant! See the paper by Jef Rosenthal. But please remember that a priori, the first time people hear about MHP, almost no-one thinks it is of any relevance that of the two doors closed after the host has opened Door 3 and revealed a goat: one was selected by the Player and the other (the other door left closed) was selected by the Host. To say it differently: newcomers to MHP see at this stage of the game two closed doors with numbers 1 and 2 on them and one opened door, Door 3, with a goat standing there; they don't "see" that the two closed doors got to be in that state of being still closed in a very asymmetric way. It's not the numbers and the open/closed which counts, it is the specific history which led up to that situation. It's important that Player chose 1 and Host left 2 closed, rather than Player chose 2 and Host left 1 closed. In fact: it's only important that Player chose A_DOOR, Host left AN_OTHER_DOOR closed.

Could we agree that the big difference of opinion is not conditional or unconditional, but whether the door numbers are taken care of outside or inside the formal analysis? The advantage of keeping them outside, in the informal, pre-processing stage (or as an afterthought, post-processing), is that newcomers to MHP are much more easily taken on board, and that the essence of MHP comes across to anyone. You don't have to have a PhD to understand that it's smart to switch. The point to taking them inside is that this does make the solution "more complete". Because, as I have said before, by taking explicit note in the logic/mathematics of the specific door numbers, one does rule out the possibility that some mixed strategy of switching or staying depending on the door numbers in the case at hand, is better still.

The big first step in enjoying MHP is to understand that switching beats staying. For the connoisseurs it is important to realise that these two are not the only options and that we can with just a bit more work say something better still. Clearly the editors are divided in the accent which needs to be put on the stuff for the connoisseurs. There is at least one editor who thinks the connoisseurs ought to be totally ignored, there is at least one editor who thinks that MHP is only for connoisseurs. Personally I find both of those two points of view not conducive to constructive editing of an important wikipedia page.

I realise that all this is a personal opinion. However it is a personal opinion which I have come to out of the challenge to find a synthesis of the different positions held by different editors here, which respects them all, does them all justice, and results in something richer.

Moreover it is strongly influenced by my professional-life-long experience consulting in statistics, with clients from law and medicine, psychology and linguistics, computer science and quantum physics. This has taught me that solving real world problems with mathematics and logic is an art. One must make choices which are a matter of taste. One has to balance degree of relevance to the actual problem, and amenability to formal solution. A solution to a problem in medicine or law which is absolutely correct from a scientific point of view but which one can't explain to a medical doctor or a lawyer is deeply unsatisfactory. We always have to compromise, and finding a beautiful compromise is a creative process. "The solution" depends not just on the problem but also on who asked the problem.

Wikipedia is an encyclopaedia, and people come from many backgrounds to learn about MHP. We want most everyone to be able to find "their" solution. That means that we do have to present different solutions in an unprejudiced way. I think that means that all editors working on the page have to work hard to try to understand all the main points of view which are out there. Richard Gill (talk) 12:30, 29 October 2010 (UTC)

MHP: the essential difference 3 : what does "complete" mean?

I think all editors, except myself, want the main part of the article to take on board all the standard assumptions of equal probabilities all over the place. I'm happy to abide with the majority on this as long as it is said *explicitly* near the beginning of the article that that is the point of view of many sources, but not all. That resolves my difference of opinion with everyone else: alternative assumption sets come later in specialist sections.

1. Can everyone agree that there is a conceptual difference between the statements: "2/3 of the time, the car is behind the other closed door", and "2/3 of the times that the player chose Door 1 and the host opened Door 3, the car is behind Door 2"?

2. Can everyone agree that whatever vos Savant and Whitaker might have intended, and whatever all the other sources might think or claim they are doing, the simple solutions (I refer to the reasoning in these solutions, not to their bottom line "switch") only directly tell us that the first statement is true, whereas the more complex conditional solutions directly tell us that the second statement is true?

3. Can everyone agree that for most people it is intuitively obvious that the relative frequency with which the car is behind the other closed door won't change when considered separately for any particular combination of initial door chosen and door opened by host? (I take it everyone does agree that this is true - what I am looking for consensus on, is the idea that most people will take this for granted).

4. Can everyone agree that if (counterfactually!) those relative frequencies could have been different, then we could have been more interested in the conditional probability than the unconditional probability, that switching gives the car?

5. Can everyone agree that because of the full symmetry of the fully specified standard problem, the second (conditional probability) statement follows logically from the first (unconditional)?

If so, then the difference between the "completeness" of the simple solutions and conditional solutions to the full or standard MHP, is merely in whether or not the "details" I have listed here as points 1 to 5 are mentioned explicitly or not. Some editors think strongly that a solution is not complete if you have not dealt explicitly with these issues, others think that bothering about those details is a total waste of time. But more importantly, some sources implicitly have the one opinion, others explicitly have the other.

It would be good if we could agree on the facts of the matter, so that finally all that remains is to agree on relative weight paid to different subtopics. Richard Gill (talk) 14:27, 3 November 2010 (UTC)

Starting points

Glopk, I'm trying to find out on which points editors do agree. Please see Wikipedia talk:Requests for mediation/Monty Hall problem/Starting points. Nijdam (talk) 14:13, 13 December 2010 (UTC)

arbitration case

You are involved in a recently-filed request for arbitration. Please review the request at Wikipedia:Arbitration/Requests#Monty Hall problem 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, Rick Block (talk) 06:39, 9 February 2011 (UTC)

Monty Hall problem opened

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/Monty Hall problem/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/Monty Hall problem/Workshop.

On behalf of the Arbitration Committee, (X! · talk)  · @144  ·  02:27, 12 February 2011 (UTC)

Timeline for evidence in Monty Hall case

Please see Wikipedia talk:Arbitration/Requests/Case/Monty Hall problem/Evidence#Timeline for Evidence, Proposed Decision. On behalf of the Arbitration Committee, Dougweller (talk) 16:41, 21 February 2011 (UTC)

Wikipedia:Arbitration/Requests/Case/Monty Hall problem closed

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.
• Rick Block is restricted to 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

Notation for Monty Hall Bayes theorem proof

Dear Glopk, in the interests of collegial collaborative editing I have written out the Bayes theorem formal proof of the conditional 2/3 result on my talk page in a notation which I think you might like better. Comments welcome. Richard Gill (talk) 10:28, 5 April 2011 (UTC)

I have replied on the MHP talk page. glopk (talk) 03:09, 6 April 2011 (UTC)

Thanks! Yes this is also fine. But MacKay is using different symbols and notation from the rest of our article, so you would have to rewrite MacKay's formulas substantially to bring them into line with the rest of the article, or rewrite the rest of the mathematics in the article in line with MacKay. I have no problem with his approach. He is careless with his notation but he says so in advance. He's very careful that nothing he writes is ambiguous. He's from physics and engineering and computer science, not from mathematics. He assumes the reader already knows elementary probability.

I wanted for a long time to get hold of Henze's writing on MHP, do you have a pdf or a scan of the relevant pages for me?

MacKay does (but not very carefully) distinguish probabilies from probability mass functions, and random variables from possible values which they take. I'm sure my old friend Norbertus Henzius does make these distinctions, very carefully - he is a very precise German mathematician. Richard Gill (talk) 10:06, 6 April 2011 (UTC)

MHP FAR

I have nominated Monty Hall problem for a featured article review here. Please join the discussion on whether this article meets featured article criteria. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" the article's featured status. The instructions for the review process are here. Tijfo098 (talk) 22:57, 7 April 2011 (UTC)