Talk:Monty Hall problem

External link

Richard, CZ does not allow self-promotion. Therefore I removed the link to your paper. I hope you understand this and agree with it. After some progress has been made with the main article, we may put it (together with other references) on the Bibliography subpage. --Peter Schmitt 23:18, 15 January 2011 (UTC)

I agree that we ought to see how the article progresses, but I wouldn't see a problem with adding that particular paper to the Bibliography if the math editors think it is appropriate since it is specifically about the subject and he is not selling anything. It also helps to let someone else place the link for you. D. Matt Innis 00:28, 16 January 2011 (UTC)

Agree, at a quick glance the paper does not appear to be specific self-promotion, but it should not be on the main page.

Go ahead and add it to the Bibliography page and let's encourage a maths editor to review it for appropriateness.

I'd like to see this article expanded fairly quickly; at present it doesn't tell us exactly what the Monty Hall problem is. Putting the definition as the introduction would probably be enough of a start.

Aleta Curry 00:43, 16 January 2011 (UTC)

That's about what I thought. I was, however, uncertain if current policy classifies such a link as self-promotion. Was I saying it too unfriendly? But, in any case, the link cannot replace an unwritten article. --Peter Schmitt 00:52, 16 January 2011 (UTC)

Oh, I don't know about unfriendly, but Richard is new here so I didn't want him to think his efforts were unappreciated. Aleta Curry 01:09, 16 January 2011 (UTC)

While we may indeed need to clarify the policy with an EC motion, I've never thought that a link to a clearly noncommercial page is self-promotion. This is even more the case when pointing to one's own peer-reviewed publications and presentations, which I have done -- I might not have written them if I thought there were better references. Howard C. Berkowitz 01:05, 16 January 2011 (UTC)

I had some discussion about this with Larry years ago, with respect to using one's own articles if one were a) an authority in the field or b) the only person writing in the field! His answer, basically, was 'use common sense and ask an(other) Editor to review/confirm'.

Aleta Curry 01:09, 16 January 2011 (UTC)

Thanks everyone. The point of the reference was just to be a resource for anyone interested in joining in. Over on Wikipedia a fight has been going on for two years, basically between laypersons who find a short intuitive solution of MHP completely satsfying, and mathematicians who dogmatically insist on a tricky solution using Bayes theorem. My own modest contribution (he said modestly) was merely to present the mathematical facts of the matter and go some way to resolving the Wikipedia conflict. Partly, by creating a "reliable source" (wikipeda terminology) for both sides of that battle. Partly by showing that the "full conditional solution" can be obtained by making one small step from the "popular simple solution" by the use of symmetry - a neat trick which I learnt from our friend Boris in this context! However the paper is too mathematical for most laypersons.

I think it's challenging to get across to laypersons what the difference is between the simple solutions and the conditional solutions, as they are often referred to. More below.

Problem variant as a cartoon

I must share a memorable cartoon idea based on this problem, from Playboy (I read it for the cartoons). The problem is reduced to two doors, and the contestant is faced with legends of "damned if you do" and "damned if you don't". Monty Hall, the game show host, is in devil garb, prodding the contestant with a pitchfork. Howard C. Berkowitz 00:12, 16 January 2011 (UTC)

As an aside, is Monty Hall his real name, or was it a joke referring to 3 card Monte? Aleta Curry 01:09, 16 January 2011 (UTC)

I looked it up, Monte Hall was apparently the stage name for Monte Halperin of the TV game show, "Let's make a Deal", so it looks like his mother was the one pulling the 3 card Monte :)D. Matt Innis 01:28, 16 January 2011 (UTC)

There is question related to it: Should this be "Monty Hall Problem" or "Monty Hall problem". I tend to the latter, but this is a question for language experts. --Peter Schmitt 01:33, 16 January 2011 (UTC)

I remember that! I was...ahem...two years old, of course, but....Aleta Curry 01:34, 16 January 2011 (UTC)

It would be nice, @Howard, to find that cartoon on internet! @Peter, Regarding the P for problem: as a rusty native English speaker who was never all that good at spelling or grammar, I'd say that in plain text, whether you write Monty Hall Problem or Monty Hall problem depends on context. If you are writing about many different problems, then the Monty Hall problem is just one of those many problems. However when you are writing about The Monty Hall Problem capitalization of the P is appropriate. The word is part of the common name of one individual problem. Richard D. Gill 13:07, 26 January 2011 (UTC)

Hmmm...I think Playboy rather than New Yorker. When I read Playboy, it is for the cartoons. Howard C. Berkowitz 21:25, 26 January 2011 (UTC)

Proposal for main content

Apart from history, sources, variants, and so on, the main content of the article should obviously be the presentation of a solution to MHP. The challenge is to simultaneously satisfy mathematical pedants and be intelligible to ordinary lay-persons. This requires an almost purely verbal solution, using only plain words of everyday English, which does however, sentence by sentence, cover every single logical step, including explicit use of all necessary assumptions. That's what I plan to write first. Now. Richard D. Gill 11:22, 26 January 2011 (UTC)

First try done. Please edit or comment. Richard D. Gill 13:08, 26 January 2011 (UTC)

Better than WP, which is however not a compliment: on WP it is too bad. Well, this is just good, I think so.

A remark: you mention Bayesian probability (and I understand why), but just above that you use frequentist probability (you count the winning ratio in the long run!). Some readers may be confused. --Boris Tsirelson 21:03, 26 January 2011 (UTC)

You're right. I should remark explicitly on the "paradigm shift". It was kind of deliberate. I think that the "standard" uniformity assumptions of MHP are only well-justified within a subjectivist notion of probability. For a frequentist, it is harder to come up with any probability model or at all, and even if it does make some sense, the probabilities cannot be considered as known in advace. But the frequentist picture is also valuable. Personally, I understand the arithmetic of relative frequencies much better than the "logic" of subjective probability. Fortunately, whatever your personal choice, subjectivist and frequentist probability satisfy the same rules, so I can always give a frequentist story about a subjectivist probability inspired model.

One of the wikipedia MHP editors wrote "no one who thinks seriously about MHP cannot avoid pondering on the meaning of probability". My own opinion is that the infinitely many repetitions of the frequentist are equally imaginary to the "parallel worlds" of the subjectivist. Both are equally meta-physical, thus the choice is a matter of opinion, of religion, of choice of meta-phor. The important thing is that we use probability in scientific discourse hence we need some kind of inter-subjectivity. You have to make the repetitions, of whichever kind, appealing and understandable to the people you want to communicate with. Richard D. Gill 23:56, 26 January 2011 (UTC)

I would find a truth table of some sort particularly illustrative in the explaination in the first paragraph or two, showing the 3 possible car locations, the host's choice(s) of doors to open, and the contestants win/loss result of switch/no switch. David E. Volk 19:36, 27 January 2011 (UTC)

I don't think that a "truth table" or, rather, a tree showing the possibilities is useful. It looks impressive but makes it also look more complicated than it is. There are, essentially, only two distinct cases - the door first chosen is the winning one, or it is not ... (For those looking for such a diagram, it could, perhaps, be put on a subpage.) --Peter Schmitt 20:41, 27 January 2011 (UTC)

Peter, if we were writing for PhD mathematicians who can obviously grasp that point, I would agree, but others get the aha moment by looking at the possible outcomes. David E. Volk 21:13, 27 January 2011 (UTC)

I very much doubt that a table (as in your sandbox) makes it easier for a "non-mathematician". I rather expect that the non-initiated looks at it and thinks "well, if the mathematicians say that thse are the formulas to use, then I tend to believe it.) The table does not help to understand the crucial point.

I think it is easier to argue as informally as possible: Your chances are 1 in 3 (or 1 to 2) to choose the winning door first, thus chances are 2 in 3 (or 2 to 1) that you have not chosen the winning door and switching opens the winning door.

Everyone understands that you have a 1/3 chance at the onset, and 2/3 chance of being wrong at the onset, but almost everyone fails to understand why the opening of one door, thus leaving the car behind only one of two closed doors, does not equal a 50:50 chance. In other words, they fail to see why opening one of the doors does not change your odds. A layman thinks, 1 car in 1 of 2 locations = even odds.

In this particular problem, the general masses heard the answer of the mathematicians and said no ****** way!. They did not believe that the solution was correct, and still don't after much explaination. David E. Volk 21:54, 27 January 2011 (UTC)

Another problem

I recall when the original vos Savant column came out and the thousands of letters it generated. To me, the biggest problem was believing that the woman with supposedly the highest IQ in the world was actually named "von Savant" (I mistakenly thought it was "von", not "vos".) It seemed to me like a supreme put-on. It wasn't until many years later, when the Internet, and, I suppose, Wikipedia, had come along, that I Googled this improbable name and discovered, to my astonishment, that it was an actual name. As if the *stupidest* person in the world was actually named George vos Dumb.... Hayford Peirce 21:01, 27 January 2011 (UTC)