# User talk:Nijdam

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User talk:Nijdam/Discussion

Welcome!

Hello, Nijdam, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

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 have any questions, check out Wikipedia:Where to ask a question or ask me on my talk page. Again, welcome!

And don't forget, the edit summary is your friend. :) Oleg Alexandrov (talk) 01:34, 24 January 2006 (UTC)

## Monty Hall

Hello Rick. The 'discussion' about this subject gets completely out of hand. It's almost everywhere the same. Schools in different countries use the problem to illustrate something about probability, or use it as a task for their pupils, always in the wrong way. Most of the discussiants have no idea what they are talking about. I make an exception for Martin Hogbin, but I'm surprised he doesn't understand the conditional nature?

In my opinion the article needs to be changed. And no comprimising, that does'n lead to a better understanding. Let's look for an easy understandable formulation of the right solution. I also think it will be necessary to mention the wrong explanation, and show why. I'll try to think about the wording, but hope you'll be willing to improve my text if (and it will be) necessary. Nijdam (talk) 21:33, 14 February 2009 (UTC)

Hi. Thanks for the encouragement. I've asked folks who presumably do understand this to weigh in at Wikipedia talk:WikiProject Mathematics#Proposed addition to Monty Hall problem. I suspect where this is headed is that the article will take on a slightly different structure, effectively with a "popular solution" section (referenced to some particular popular explanation, perhaps vos Savant's) and then a "rigorous mathematical solution" section (which I think should be referenced to Morgan et al. and Gillman - as the first two to publish rigorous treatments). The focus needs to be on what the sources have to say about the problem. Non-academic sources nearly uniformly present unconditional "solutions". The article should as well (sourced to a non-academic source). Wikipedia doesn't (shouldn't) "take sides" here, but instead should use wording like "vos Savant's solution is <this>" and then "Morgan and Gillman say "<that>". It usually isn't this hard in a math related article - but for whatever reason this particular problem generates a tremendous amount of deeply entrenched (usually wrong) opinions. I suspect any inherently conditional problem does as well, see for example Boy or Girl paradox. Bedankt (is that idiomatically correct?). -- Rick Block (talk) 22:16, 14 February 2009 (UTC)

Okay, I'll have a look at the mentioned page. BTW: your Dutch, allthough short, was absolutely correct. Where did you pick up your Dutch?Nijdam (talk) 22:40, 14 February 2009 (UTC)

I don't speak Dutch at all, just noticed you were (and looked up how to say thank you). -- Rick Block (talk) 02:44, 15 February 2009 (UTC)
Martin reverted your change, which is what I thought would happen. I'm not sure, but I think some progress is being made on the talk page. Fighting over the lead at this point is probably not that productive. It may be best to just leave it alone until things settle down a bit. -- Rick Block (talk) 01:45, 16 February 2009 (UTC)

Regarding the German Wikipedia, I think the approach you're suggesting is roughly how you originally found the article in the English Wikipedia - i.e. carefully worded (not incorrect) unconditional solution first, followed with an explanation and a conditional solution. As I recollect you didn't like this very much. Another approach is to present, say, vos Savant's solution clearly identified as such (with a citation) followed by a conditional solution (perhaps some choice words from Morgan et al.). At this point I'm actually leaning to a fully rigorous solution (like Morgan's), followed with various other "solutions" (with critical commentary, meticulously sourced). -- Rick Block (talk) 03:03, 3 March 2009 (UTC)

BTW - Regarding this edit aren't we generally assigning the odds to the doors, not the players? The reason the little green men have a 50/50 chance is because they must randomly select between the doors, so 50% stay and 50% switch. If the probabilities of the doors are p and 1-p this results in 50% win regardless of p. -- Rick Block (talk) 03:53, 3 March 2009 (UTC)
Of course, but I made the remark, because I read somewhere in the discussion, that even the "green men" would win in 2/3 of the cases when switching. The meaning of my remark is that a different type of player may have different odds. So the odds regarding the doors are assigned to the type of player.Nijdam (talk) 09:41, 3 March 2009 (UTC)
Ah. The comment was that of the green men who switch (as opposed to all green men), 2/3 would win - i.e. the 2/3 applies to the door, not the player. This is exactly where I'm going with user 216. -- Rick Block (talk) 13:10, 3 March 2009 (UTC)
Sorry, may be my English fails here. Anyway I meant to say that green men cannot switch, because they did not choose. They just may open one of the still closed doors, and on the average win the car in 1/2 of the cases. So for them 1/2 is applicable for each door. Note that a green man, finding door 3 open, doesn't know which of the other has been originally picked, and hence the average is taken over all situations with door 3 open, the ones with door 1 picked and the ones with door 2 picked. Nijdam (talk) 15:13, 3 March 2009 (UTC)
But of the green men choosing door 1, 1/3 will win the car (and similarly, 2/3 who choose door 2). BTW - I'm "watching" this page so you don't need to ping me when you reply. -- Rick Block (talk) 15:24, 3 March 2009 (UTC)
No no, be carefull, because in repeating, not only green men are involved where door 1 has originally be picked by the earthly player, but also the ones where door 2 has been picked. That's precisely the meaning of introducing the green men! They form a conditioning on the event "door 3 is open" in the complete sample space. And that's why I said chances (regarding the doors) are assigned to the play(er).
Yes, it is important to be precise. I mean in cases where the player has initially picked door 1 and the host has opened door 3. -- Rick Block (talk) 16:00, 3 March 2009 (UTC)
But no green man ever knows which door is picked. Nijdam (talk) 18:19, 3 March 2009 (UTC)
Yes, but whether they know or not, in cases where the player has picked door 1 and the host has opened door 3, if they pick door 1 they have a 1/3 chance of picking the car. I'm conditioning on the event "player picked door 1 and door 3 is open", not just "door 3 is open". -- Rick Block (talk) 00:07, 4 March 2009 (UTC)
Your remark puzzls me. The trick of the green man is his ignorance of the choice of the player. I come back to it later. Nijdam (talk) 22:50, 4 March 2009 (UTC)
Yes, but any given green man is trading places with a player who has initially picked a door. Whether the green man knows the player's choice or not, any green man's choice wins with probability 1/3 if that green man chooses the door that was the player's choice and wins with probability 2/3 if that green man chooses the door the player did not pick. The green man's choice wins with probability 1/2 but it's 50%(1/3) + 50%(2/3). This is the exact issue I'm discussing with 216. -- Rick Block (talk) 01:20, 5 March 2009 (UTC)

## Back

I'm back, and have been considering green men. In all of the problem the wording with payers and host and green men are not relevant, but the probabalistic formulation is. Then the "normal situation" is covered by the event: chosen door 1, opened door 3. The green man is an imaginative representation of the event: door 3 opened, that's all. So it is no use to ask about the probability of the green man to find the car behind door 1 in the "normal situation"; simply because he is not in that situation. A problem with the green man is the distribution of the initial choice of the player. Because it is not necessarily random, the green man has not necessarily a 50/50 chance.Nijdam (talk) 00:32, 16 March 2009 (UTC)

The green man (who has swapped places with a player at the point the player is asked whether to switch) has a 50/50 chance, but it is because his choice is random, not because the distribution of the car behind the doors is 50/50. At the point the green man is choosing we might as well have rolled a 3-sided die and put the car behind one door if the die was 1 and behind the other door if the die was 2 or 3. p(D1) = 1/3, p(D2) = 2/3 - but a random choice between these ends up with a 50/50 chance of winning the car. We can also ask what is the probability the green man wins if he happens to choose the player's initial door (D1), which is the same question as what is the probability that the car is behind this door. And the answer is 1/3. We can make the distribution of the car behind the doors as uneven as we'd like, and a random choice always has a 50/50 chance of finding it, since (1/2)p + (1/2)(1-p) = 1/2. According to 216 (in a discussion on the arguments page), Massimo Piattelli-Palmarini (a cognitive psychologist) presents a version of the MHP where the player "guesses" at the end. This strikes me as extremely bizarre - why go to all the trouble of establishing a non-equal probability distribution between two unknowns and then turn it into a 50/50 chance because the player guesses? -- Rick Block (talk) 04:10, 16 March 2009 (UTC)

## Fair coins

BTW: in your discussion with 216 a fair coin itself as a coin doesn't have the 50/50 property. As a fair coin it is physical symmetric, so in a right flipping experiment the total experiment has the 50/50 property. A deck of 52 cards only has the property of cardinality 52. The experiment of drawing one at random shows the property of 1/52 chance for each individual card. Nijdam (talk) 15:37, 3 March 2009 (UTC)

Agreed, although I'm not sure this distinction is particularly relevant. -- Rick Block (talk) 16:00, 3 March 2009 (UTC)
Well, I think in the MHP the doors have no intrinsic probability properties, but the rules of the game determine the probs. Nijdam (talk) 18:19, 3 March 2009 (UTC)
Or, put another way, the probabilities of the doors are due to the rules of the game. Like the probability of heads/tails is due to the physical properties of the coin. -- Rick Block (talk) 00:07, 4 March 2009 (UTC)
Well, we like to believe this, but the way the coin is flipped is part of the fairness. I even may argue that the flipping to some extent is more important than the physical symmetry. Nijdam (talk) 22:35, 4 March 2009 (UTC)
Yes - there are two issue, the fairness of the coin and the fairness of the experiment. But again I think not relevant at 216's level of understanding. -- Rick Block (talk) 01:20, 5 March 2009 (UTC)

If you think that this notice was placed here in error, you may contest the deletion by adding {{hangon}} to the

## Proposed new math formulation for the MHP.

Hello, I have responded to your comments on the proposed Math. Form. for the MHP. Thanks for taking your time to reply, if you care to. glopk (talk) 17:19, 1 July 2010 (UTC)

## My Monty Hall analysis page

Thanks for your input to my page. I have started again near the end with the player's initial choice being shown explicitly under the main heading 'Full calculations including the players initial car choice'. I think the player's choice is important in some cases. I have then worked the most general case through to provide a solution for every possible formulation of the MHP with the standard rules I think this is a better way of looking at the problem. We now have a general solution to which can be applied the various distributions and conditions to get a specific answer. My aim is to separate the maths, about which there can be no disagreement, from the philosophy which we have all been arguing about.

Although there are no new concepts in the complete solution it has not been published anywhere. Maybe it could be. If you are interested I suggest we discuss it further on the analysis talk page. Martin Hogbin (talk) 16:36, 24 July 2010 (UTC)

I am grateful for your help in getting my analysis page right. I want to try to separate plain mathematical fact from philosophical argument. I would like to discuss the best way to present the information clearly with you, either here or on the analysis talk page. Martin Hogbin (talk) 11:05, 29 July 2010 (UTC)

## MHP reference

• Martin Hogbin, W. Nijdam. [1] The American Statistician. May 1, 2010, 64(2): 193-194. doi:10.1198/tast.2010.09227.

## Mediation resumes

The mediation of the MHP case has re-started. If you wish to participate, would you be willing to check in on the case talk page here? Note that the mediators have asked that participants agree to certain groundrules. Sunray (talk) 06:57, 11 August 2010 (UTC)

## Game theoretic issue

You put up:

Nijdam: MHP has to be treated with game theory
Most people consider the MHP a psychological game, and hence it may best be treated with simple game theory.

I respond as follows.

@Nijdam, isn't this quite a straw man you're putting up here? I'm not aware of anyone in the world that thinks this, and I cannot imagine how you could possibly think they exist. Suggestion for rephrasing (but of course, it's your perceived issue of a perceived opponent):

Nijdam: Game Theory gives insight to MHP
Some people (perhaps many, at first exposure to MHP) start instinctively, it seems, to think in terms of psychology. Is Monty Hall trying to trick me? If I do that he might... Does he know that I know that he knows...? Correspondingly, one might say, it has also been treated mathematically with elementary game theory in the economics / decision theory / game theory world. Correspondingly, vos Savant did not ask 'What is the conditional probability?' but 'Should you switch?'

Vos Savant asked for a decision, please note, not a probability!

Now go on to try to mention the useful insights. Let me give you a little help

From game theory we learn that the wise player would randomize his initial choice secretly at home in advance, in order to get the best of all possible worlds; to be totally free of any mathematical "assumptions", how academically natural or conventional they might seem to be.

You're supposed to present a perceived view of a perceived opponent with as much empathy as you can muster.

It's about being on a game show. But we're not nuts. You're not allowed to ask advice when you stand there on the stage! You'ld better ask advice in advance.

Maybe vos Savant should have written "You're going to be on a game show. If you answer the silly questions correctly, you'll be faced with a choice of three closed doors..."

I'm not trying to put words into your mouth here, just trying to help things along. Gill110951 (talk) 12:43, 15 August 2010 (UTC)

## Reading this message could be to your advantage

Here's something else it would be good to discuss over a beer one of these days, when I get out of this hell-hole (Athens in August).

Please take a look at [[2]]

There you will find out why the answer is "2/3" or "switch", as you like, and the method is unconditional, but the assumptions are NOT what some people like to call the standard assumptions, but the result is much much better, since much more useful in practice, much more often applicable, and just as easy to argue, whether formally or informally. And if you like you can refine or complete it, if you like, by proving that 2/3 is the best answer i.e. this is the best strategy. But I don't think anyone will ask you to prove that, since if one could do better than 2/3, we should have heard about it by now, agreed?

Hellpimp showed us the way but no-one noticed. Now the economists and game theorists know all this too and have frequently published on it so there would be no problem backing it up with super reliable sources. (Nalebuff is a bigger guy in the big scheme of things than Selvin or Morgan et al, sorry). But anyway it is such a clean and different simple argument that is "out there" that I think it deserves some consideration. But really I am not talking about pushing it onto the MHP page in order to push my POV; I am talking about something which I think is worth thinking about, if one likes to think of oneself as an authority on MHP. Which seems to be something we both have in common, right? Gill110951 (talk) 18:46, 15 August 2010 (UTC)

## test

$Y_0 = \frac{1}{Z_0}\,$
$Y_0 = \frac{1}{Z_0}\,$
$zzz\,$

## In case you missed this (I missed your comment)

You wrote:

If you mean to say that when the car is placed randomly (what used to mean uniformly), the conditional probs are at least 1/2, okay. But what do you mean by equivalent? If we do not make assumptions about the distributions, the conditionals being at least 1/2 is not equivalent to the overall being 2/3.Nijdam (talk) 15:19, 19 August 2010 (UTC)

Sorry, let me spell it out. Sometimes I'm too fast, often I'm too slow. You naturally agree that

Prob(switching wins) = sum (over 6 pairs of possible door chosen, door opened)
Prob( switching wins | door chosen, door opened ) times Prob( door chosen, door opened) .

Meaning:

$P(C\ne X) =$
$P(C=1|X=2, H=3)P(X=2, H=3) +$
$P(C=1|X=3, H=2)P(X=3, H=2) +$
$P(C=2|X=1, H=3)P(X=1, H=3) +$
$P(C=2|X=3, H=1)P(X=3, H=1) +$
$P(C=3|X=1, H=2)P(X=1, H=2) +$
$P(C=3|X=2, H=1)P(X=2, H=1) = ??$

=2/3 if you make an assumption about the distribution. So what do you want to proof? Nijdam (talk) 23:40, 20 September 2010 (UTC)

We know the left hand side equals 2/3 if and only if the initial choice had 1/3 chance to hit the car. The only way we could have a strategy with a larger hit-chance than than 2/3 would be by not switching for some configuration which we know satisfies Prob( switching wins | door chosen, door opened) < 1/2. Because then we would replace a term on the right hand side by a larger term, Prob( staying wins | door chosen, door opened), resulting in a better probability on the left hand side for Prob ( this modified and mixed strategy wins). Assuming Prob( door chosen, door opened) > 0, which is the case in non degenerate situations - every door can be chosen, every door can hide the car.

We know that if all cars are initially equally likely, then all conditional probabilities are at least 1/2. Proving 2/3 (unconditional) can't be beaten is equivalent to proving that all the conditional probabilities are known to be at least 1/2. So yes, the conditionals being provably at least 1/2, under assumptions known by the player to be true, is mathematically equivalent to it being impossible to beat unconditional 2/3. QED.

BTW, I like your math! Must learn this myself. Gill110951 (talk) 17:27, 20 September 2010 (UTC)

Another try at explaining. One can make more or less assumptions and get more or less conclusions. I am telling you about the equivalence of two of the conclusions. They are mathematically equivalent.

There are six configurations (door chosen, door opened). Hence there are 2^6=64 non-randomized strategies for the player and a 64 dimensional continuum of randomized strategies: for each of the 64 configurations one can stay or switch or randomize between them.

Under no assumptions at all, the law of total probability tells us that the strategy "always switch" is the best strategy of all (with respect to unconditional hit-chance), if and only if no conditional probability disfavours switching.

If we only know the players' initial choice is right with probability 1/3, then we know that "always switch" beats "always stay" (unconditional 2/3 versus 1/3), but we don't know anything about the hit chance of mixed strategies.

If however we also know that the host is constrained to hide the cars uniformly at random, then one can show with Bayes that no conditional probability disfavours switching, hence "always switch" is optimal - beats all possible strategies. But one can also prove via a different route, in that situation, that "always switch" is optimal (2/3 can't be beaten). By the mathematical equivalence which I've explained to you, you've then also proven that no conditional probability disfavours switching.

The conditional solution completes the unconditional solution by showing that "always switch" is globally optimal, unconditional 2/3 can't be beaten. At the cost of a further condition on the host's behaviour. While the weaker assumption can be engineered to be true by the player.

In summary:

"always switch" is the optimal player strategy in terms of optimal unconditional hit-chance

if and only if

all conditional probabilities are known by the player to favour switching (or are neutral about it)

if and only if

the host is constrained to hide the cars uniformly at random.

But if you only know that your initial choice hits the car with probability 1/3, you do at least know that "always switch" beats "always stay" (2/3 versus 1/3). My conclusion is that all the approaches give you complementary and important information. The good solution to MHP is to give the results of all the approaches.

Gill110951 (talk) 05:49, 21 September 2010 (UTC)

## confidence interval

Hi, please use the talk page of confidence interval if you want to include the word, likely. Your last edit incorrectly implied that a realized confidence interval has some probability of containing the true value. This is exactly the implication you want to avoid.

Generally, since you didn't respond to my last comment and another editor RVed you on this edit, I think you should start with the talk page. 018 (talk) 15:42, 11 October 2010 (UTC)

## friendly reminder

Hi, I just wanted to remind you that RVing an good faith edit (such as this edit) that is not vandalism or a policy violation, is a little jarring for the other editor. If you do want to take this extreme action for a good faith edit, please, at a minimum start a talk page discussion on the topic. Everyone forgets these things from time to time, so it is not a huge deal, but I just wanted to remind you that it is not taken as a kindness by other editors. Thanks, 018 (talk) 17:13, 19 November 2010 (UTC)

I do not doubt the good faith of the edit. On the other hand, discussion doesn't just hold for the revert, but likewise for the edit.Nijdam (talk) 10:22, 20 November 2010 (UTC)
I don't understand what you are saying. I edited a page, you RVed it. I'm saying, please don't RV good faith edits, and when you do, please go to the talk to start a discussion. What are you saying? 018 (talk) 03:14, 21 November 2010 (UTC)
Well if you want to make a major edit, first discuss it. Nijdam (talk) 16:21, 21 November 2010 (UTC)
Nah, better to just be bold. 018 (talk) 00:53, 22 November 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—

Thanks, Rick Block (talk) 06:38, 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)

## Your comment on the arbitration conclusion talk page

You say I admit that the simple solutions are wrong: this is not true. Of course I agree that it is "wrong" (incomplete) as a full answer to what you see as the "right question". But I do not agree with you that what you call the right question, is the right question.

Please correct your summary of my point of view. Richard Gill (talk) 09:11, 17 March 2011 (UTC)

Done, not a correction, but an clarification. Nijdam (talk) 10:11, 17 March 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:

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

Discuss this

## About the simple solution

From Richards talk page

Richard, Why are you that keen in stating that the simple solution is correct be it together with symmetry arguments, where it's just the simple solution without any further arguments we, the other editors are fighting, and that is not correct, as you yourself have said, as a solution to the full MHP. You seem to spread some smoke curtain as if you want people to accept the simple solution (in its simple form), because your authority guarantees it may be extended to be correct. It never will be, because as you also have agreed, the simple solution does not set out to consider the needed conditional probability. I should not have to ask you this. And I hope you remember, calculating (or determining) the conditional probability by symmetry arguments is one of the solving methods I showed, and I also like to promote in the article. But why do you want to refer to this as "simple solution", while you definitely know, it is something completely different than THE simple solution. WHY? Have you yourself in the past accepted and defended the simple solution (the simple one) as solution to the full MHP? And do you try to justify this error??? Nijdam (talk) 10:13, 22 February 2011 (UTC)

Of course the simple solution alone does not solve the "full problem". But I do not agree that you *have* to solve MHP with the "full problem". Simple solution plus symmetry, and symmetry plus simple solution, do solve the full problem. Actually, symmetry first tells you that you do not have to solve the full problem: you need not condition on stuff which is independent. From the mathematical point of view the full conditional solution is just one way of showing that the simple solution is optimal (in the sense of achieving the highest possible overall success-rate), as well as good. Mathematics does not have moral or legal authority. Mathematics can't ever tell you that you *must* act in a certain way. It can only tell you that it is wise to act in a certain way. The applied mathematician must explain to his client why it is wise. In the real world there are many other issues, and maybe it is wise not to be wise in some respects. Richard Gill (talk) 11:27, 22 February 2011 (UTC)

#### Conclusion

1. Full MHP = the player is asked to decide after the host has opened the goat door
2. Simple MHP = the audience is asked to decide even before the player made her first choice
3. Simple solution = decision based on the unconditional probability
4. Bayes solution = decision based on the conditional probability, calculated with the use of Bayes' law
5. Symmetry solution = decision based on the conditional probability, calculated with the use of symmetry
6. Simple solution solves the simple MHP
7. Simple solution does not solve the full MHP
8. Bayes solution solves the full MHP
9. Bayes solution is equivalent to the symmetry solution
10. Simple solution <> Bayes solution
11. There are a number of logically incorrect reasonings, presented as solutions

### Situation

Involved editors (before Arbcom decision): On one side:

• Rick Block
• Nijdam
• Kmhkmh
• glopk

all more or less experts on the matter and aware of the above mentioned points; hence strongly advocates of the clear mentioning of the problem with the simple solution. As they are completely right (confirmed by several reliable sources) the criticism that they are not flexible is unjust. Rick Block, more or less the spokesman, is completely right in sticking to his idea of presenting the article. BTW sources that consider the simple solution satisfying, cannot be reliable.

On the other side:

• Martin Hogbin (originally)
• Glkanter
• Gerhardvalentin (as far as I know, still does not understand the shortcoming of the simple solution)

all laymen at the start with only a basic knowledge of probability; strongly opposed to point 7

More or less in between:

• Martin Hogbin (recently),

has changed his position concerning the simple solution; now admitting (in an email to me) it is deficient as a solution to the full MHP, but considers the defect of minor importance, and just like Gill opposes the clear mentioning of the criticism

• Richard Gill

an expert on the topic, and also aware of the mentioned points, but for some strange reasons taking side of the second group as it comes to the presentation of the MHP in the article

### Question

Why are the editors in the second group that strongly opposed to the clear mentioning of the criticism on the simple solution????

### My concern

I did take part in this discussion because the MHP is widely used for educational purposes, And by just accepting the simple solution, which is no solution at all, students and teachers get the wrong idea about probability.

## From Gill's talk page

Let me spell it out for you: the simple solution S0 reads: the car is with probability 1/3 behind door 1. As the opened door 3 does not show the car, it will be with probability 2/3 behind the remaining door 2. Another simple solution S1 reads: the initial choice of door 1 hits the car with probability 1/3, Hence switching gives the car with probability 2/3. My simple (!) question is: do you mention any of these solutions as a solution to the MHP in your courses? Just answer with no or yes, and the number of the solution. Nijdam (talk) 05:25, 18 July 2011 (UTC)

Nijdam, I do understand what you're getting at. I am careful to say things which are correct. So of course I don't give S0 as a solution. I do give S1 as a solution. But on wikipedia the rules are that you can only write what has been published in reliable sources, and the definition of reliable sources had got nothing to do with the truth or falsity of what is written in them. Wikipedia summarizes what people write. Also things which are incorrect. If you would like to correct wikipedia the only option you have is to write reliable sources yourself, and hope that others will write about what you have written. Then maybe in ten years or so wikipedia will cite you, too. Richard Gill (talk) 15:00, 18 July 2011 (UTC)

## The Guy Macon Solution

No doubt you have been watching as I try to resolve the longstanding conflict. I will also be watching your talk page and will take any comments or suggestions you have under consideration. I also encouraged Glkanter to email me if he had any comments or suggestions, but he started insulting me so I blocked his emails. Guy Macon (talk) 21:16, 28 May 2011 (UTC)

Thank you for your trust. Nijdam (talk) 09:44, 29 May 2011 (UTC)

## Suggestions

[keep] Vos Savant explained that the contestant should always switch to the other door. Initially, the contestant's chance of winning was 1/3. The chance the car was behind one of the other two doors was 2/3. When the host uncovered door No. 3, the chance that the car is behind door No. 2 became 2/3. Consequently, if the contestant switches, he has double the chance of winning the car.

Many people refuse to believe that switching is beneficial. After the Monty Hall problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine claiming that switching was wrong. (Tierney 1991) Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy.

[change; Savant's solution is not the simple solution] Some sources criticise the simple solutions because they because they fail for a variant of the problem in which the car is still placed randomly but the host is taken not to randomly choose between which of the two doors he may open under the game rules. In this variant the player still cannot lose by switching and will probably gain, having a 2/3 chance of winning on average if he switches.

[into; (I need help with my English)] Some sources point to the fact that Vos Savant seems to automatically assume the chance of the first door to hide the car to be fixed. However, after the host opened door 3 a new situation arises with new chances. It turns out the new chance for door 1 has the same value 1/3 as before, and hence one may conclude that door 2 has now a chance of 2/3. When Vos Savant was confronted with this criticism she tried to find a way out and finally said she considered the overall chance of winning the car when switching. This is often called a simple solution, as it does not count for the specific situation the contestant is in. This simple solution does not solve the full Monty Hall problem, in which the specific situation of the contestant is known.

#### On 2nd thoughts

As Savant's "solution" is not correct, it may be better to replace the explanation in the lead with the following:

[into (English??)] Most readers automatically assume the doors to equally likely hide the car, the contestant to be unaware of its position. and furthermore symmetry as to the role of the doors. Then the choice of the player and the opening of a door by the host does not influence the original 1/3 chance for the chosen door No. 1 on the car. When the contestant is offered to swap doors, the chance for door No. 1 is also 1/3, and hence the remaining door No. 2 has then chance 2/3 on the car. Consequently, if the contestant switches, he has double the chance of winning the car.

## Incredibly: now write this out in proper math

Read the recent eprints by A.V. Gnedin on arXiv.org (maths section) if you want to see things written out completely and rather formally. But I would expect that for a smart person it is enough to notice that a player who is going not to switch in some situation, has at least a 1/3 chance of ending up with a goat. For instance, consider a player who chooses Door 1 and intends not to switch if the host opens Door 3. There is a 1/3 chance that the car is actually behind Door 2. Player chooses Door 1. Host is forced to open Door 3. Player doesn't switch. Player gets a goat.

We know that a player who always switches gets the car 2/3 of the time. So such a player has only a 1/3 chance of ending up with a goat. Conclusion: however you play, you'll end up with a goat with probability at least 1/3. "Always switching" is therefore optimal. Therefore all conditional probabilities of getting a car by switching must be at least 1/2 (none of them can favour staying).

Note that we only assumed here that the car is initially equally likely behind any of the three doors. We didn't assume anything about how the host chooses a door, when he has a choice.

Thus this short and elementary analysis covers the biased host case and makes computation of conditional probabilities superfluous. Remember: Vos Savant asks for a decision, not for a probability! Insights from decision theory (or game theory) can be useful when solving decision problems. Probability is not the only game in town. Richard Gill (talk) 10:21, 5 July 2011 (UTC)

## Reliable source

Copied from Wikipedia:Requests for comment/Request board:

Can a source that is clearly mistaken, still be considered a reliable source for reference? Nijdam (talk) 19:07, 18 July 2011 (UTC)

Thank you for your question. If a source makes an obvious error of fact, it is clearly unreliable. Were you thinking of a specific source that makes such an error? hare j 22:25, 18 July 2011 (UTC)

## The dispute

Then main difference in the dispute is about the "simple solutiion". This solution reads: the probability to hit the car in the initial choice of door is 1/3, hence switching gives the car with probability 2/3. This simple solution is NOT a solution for the full MHP, i.e. the version in which the contestant is offered to switch after the chosen door and the opened door are known (MartinHogbin and Gill have mentioned to agree on this). Yet this is the version most people consider to be the MHP. One side, MartinHogbin, Gerardvalentin, Gill as the main participants, are unwilling either to accept this, or to make this clear to the readers. The other side, Rick Block, Kmhkmh, glopk, myself and others, want to structure the article in such a way that from the start this difference is clear to every reader. 09:45, 23 July 2011 (UTC)

Nijdam, I guess you are talking here about a famous paradox, not about teaching and learning conditional probability theory in the mathematics class room, being quite another thing. What you call here a "difference" makes no difference whatsoever to the decision asked for, because this is completely irrelevant to the decision asked for. Even the greatest difference is completely irrelevant, because to switch will never ever be of disadvantage, and by switching now and here you produce the maximum benefit, just read the sources. Gerhardvalentin (talk) 10:08, 23 July 2011 (UTC)
Sorry Gerhard, it turned out to be pointless to try to make you understand the problem and its solution. You just demonstrated this again. Nijdam (talk) 16:33, 23 July 2011 (UTC)
@Gerhard: instead of wildly kicking around and commenting, just write down your own vision on the content dispute. That may help others to understand where you stand. Nijdam (talk) 11:32, 24 July 2011 (UTC)

#### Comment on Martin's proposal for a content resolution question

Martin Hogbin is circumventing the actual content dispute. He formulates in one long sentence several statements, some of which are not true. (1) The MHP is indeed a simple probability puzzle, but just because of this, used as an undergraduate exercise in conditional probability. (2) It is part of the dispute whether VosSavant and others solve (correctly) this simple puzzle. Nijdam (talk) 14:03, 25 July 2011 (UTC)

#### Richard's truth

Interesting to notice Richard's plea for the truth, seemingly as long as it is his truth. As he himself has admitted (see above) the simple solution does not solve the full MHP. Yet the full version is what most people consider the MHP. And for good reasons! So, let's present the truth, i.e. the correct (conditional) solution (maybe without being too technical and not explicily mentioning the term conditional) to the full MHP. Nijdam (talk) 21:26, 26 July 2011 (UTC)

Maybe Richard can be more specific about: The simplists should be aware of the concepts of conditional probability and take care not to write statements which are mathematically speaking false. The conditionalists could think about presenting conditional solutions which build on the simple solutions. Or is this also a red herring? Nijdam (talk) 15:38, 28 July 2011 (UTC)

## Covariance

Hi there. I am new to Wikipedia. May I know what's your objection with my edit on "Geometrical Interpretation" of the covariance?

Tfkhang (talk) 07:55, 4 December 2011 (UTC)

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## From Martin's talk page

Nijdam, you continue to try to teach me what I already know. Let me start by giving you a brief moment of victory. Using modern probability theory and with the sample space that you prefer and seem to assert is the only possible one to use, what you ask cannot be done. You are quite right, on the basis that you prefer, the "combined doors solution" makes no sense. However, there are other ways of tackling this problem, even within modern probability theory. Please explain to me why you select the sample space that you do. Martin Hogbin (talk) 09:20, 22 February 2011 (UTC)

## Dispute resolution survey

 Dispute Resolution – Survey Invite Hello Nijdam. I am currently conducting a study on the dispute resolution processes on the English Wikipedia, in the hope that the results will help improve these processes in the future. Whether you have used dispute resolution a little or a lot, now we need to know about your experience. The survey takes around five minutes, and the information you provide will not be shared with third parties other than to assist in analyzing the results of the survey. No personally identifiable information will be released. Please click HERE to participate. Many thanks in advance for your comments and thoughts. You are receiving this invitation because you have had some activity in dispute resolution over the past year. For more information, please see the associated research page. Steven Zhang DR goes to Wikimania! 22:53, 5 April 2012 (UTC)

## Invitation to comment at Monty Hall problem RfC

Because of your previous participation at Monty Hall problem, I am inviting you to comment on the following RfC:

Talk:Monty Hall problem#Conditional or Simple solutions for the Monty Hall problem?

--Guy Macon (talk) 22:23, 6 September 2012 (UTC)

## Apology

It seems I misunderstood your intention. I have struck my comment. I do believe you have some uber-solution in your head that you are going to reveal eventually (or coax Martin into demonstrating), I apologise for believing that you would try to put it unsourced into the article. --Elen of the Roads (talk) 12:58, 17 September 2012 (UTC)

Accepted, no hard feelings.Nijdam (talk) 18:34, 17 September 2012 (UTC)

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## Regarding your recent reversion in Statistical Hypothesis Testing.

Nijdam, You recently reverted an edit of mine in Statistical hypothesis testing with the comment "Why the remove?". I don't know whether it is better to reply here or in a talk section. The short answer is that opinions by Fisher properly belong in the prior Origins and early controversy section which is already lengthy. I was hoping that the Null hypothesis statistical significant testing vs hypothesis testing section would focus on more recent facts and (perhaps) opinions rather than repeating the classical disagreement. The reverted edit also deleted the "opinion" that the two formulations are complimentary while retaining the supporting facts. What is your view?159.83.196.1 (talk) 23:35, 1 May 2013 (UTC)

I do not care much where the remark of the clash properly belongs. Of course it fits into the opinion section, but the section from which you removed it, also even needs the mentioning of it. Nijdam (talk) 16:07, 2 May 2013 (UTC)
I disagree and may remove it again, but not before I have well-sourced material to replace it. I just got a recent book by Lehmann that discusses the contributions of Fisher & Neyman including the dispute. Lehmann seems balanced to me, but reflects Neyman's opinion on the mathematical unity of the two formulations. Do you have any more recent references that support Fisher's position that they are different?172.249.254.111 (talk) 18:12, 2 May 2013 (UTC)

## Confidence intervals

Why did you undo my '(or less)' edit? Thanks. Mmitchell10 (talk) 14:30, 26 December 2013 (UTC)

Sorry, I didn't well look at the given definition. It all depends on the definition. As the article mentions, some authors, quite a lot actually, and for good reasons, use as a definition
${\Pr}(U<\theta
Then the "(or less)", is necessary. Maybe this has to be explained better. Also in some discrete cases, the given definition may not lead to a CI with exact the desired level. Nijdam (talk) 12:34, 30 December 2013 (UTC)
OK, but the whole of the article up to that point assumes that a 90% CI (for example) means exactly 90%, not at least 90%, in which case it is exactly 10%. As we can't have the probability of the CI covering the parameter value + the probability of the CI not covering the parameter value not equalling 100%, surely the sentence should either be a '90% (or more)' CI, to go with a '10% (or less)' chance, or else it's a 90% CI with a 10% chance.
The fact that a calculated CI may not end up giving exactly the expected or required level of confidence sounds to me like an important issue which merits a section of its own, rather than appending this fact onto the end of a section with a different aim. What do you think? Mmitchell10 (talk) 11:54, 31 December 2013 (UTC)
I agree; maybe we even mention this already in the definition. Nijdam (talk) 12:14, 1 January 2014 (UTC)