Talk:Monty Hall problem

Archived earlier talk

In order to regain focus I created a first talk archive of talk up to this point: Talk:Monty_Hall_problem/Archive_1. Richard D. Gill 15:21, 2 February 2011 (UTC)

General remarks

This talk page has quickly become very long with a difficult to follow structure. I'd like to make a few general remarks:

• Let us avoid to repeat and continue the endless (and mostly useless) discussion of this problem.
• The MHP is not a "paradox". Its solution may be surprising, but it is not paradoxical.
• There are not two (or more) "solutions".

• Once the question has been unambiguously posed there is only one solution -- the correct solution.
• There may be (essentially) different arguments leading to this correct solution.
• There may be several (didactically) different ways to present the same argument.

What should an article on the MHP contain (with the reader searching information in mind)? My answer:

• It should state the problem and present its solution as brief and as clear (and in an as informal language) as possible.
• It should summarize the history of the problem and the disputes it has caused.
• It should not contain a large amount of historical details, different approaches, discussion of subtleties, etc. that the ordinary reader will not want, and that would probably be confusing for him.

Supplementary material can be presented on subpages or separate pages:

• A page on the detailed history of the problem.
• A page on the discussion caused by the problem.
• A (Catalog) subpage containing various ways to present the solution(s). It may help a reader to find an explanation he likes.

--Peter Schmitt 13:42, 1 February 2011 (UTC)

I agree with everything you say here Peter, except for one thing. MHP is defined (IMHO) by the definitely ambiguous words of Marilyn Vos Savant quoted in the article. Both before her popularization of the problem, and later, different authorities have translated or transformed her problem into definitely different mathematically unambiguous problems. And I'm only referring to problems to which the solution is "switch"! That is part of the reason why there is, I think, not a unique "correct solution" - there are as many correct solutions as there are decent unambiguous formulations.

I think there are two particularly common solutions: one focusing on the overall probability of winning by switching, and the other focussing on the conditional probability of winning by switching given the specific doors chosen and opened. The present draft intro contains elements of both and even at attempt at synthesis. Richard D. Gill 23:26, 1 February 2011 (UTC)

By the way, the meaning I am used to of the word "paradox" is an apparent contradiction. And there certainly is an apparent contradiction between ordinary people's immediate and instinctive solution "50-50, so don't switch", and the "right" solution: "switching gives the car with probability 2/3". Richard D. Gill 15:39, 2 February 2011 (UTC)

Which MHP?

In Talk:Monty_Hall_problem/Archive_1, Wietze Nijdam started discussion of which of the following two problems is "the MHP". That discussion has been raging on wikipedia unabated for over two years, producing only polarization. Wikipedia editors interested in sensible compromise have left in bemusement, disgust or frustration. Richard D. Gill 10:12, 3 February 2011 (UTC)

Returning to Wietze's text:

• F0: (Conditional formulation) If the contestant is offered to switch after the host has opened the goat door, the decision has to be based on the conditional probability given the initial choice and the opened door.

• F1: (Unconditional formulation) If we are asked whether the contestant should switch, even before he has made his initial choice, and we are not allowed to give a solution for every possible combination of initial chosen door and opened goat door, the decision will have to be based on the (unconditional) probability of getting the car by switching.

The discussion point is: which formulation is more natural to be the MHP and should be presented as such.

My opinion: F0. Wietze Nijdam 22:45, 2 February 2011 (UTC)

Both are of interest; but

• F1 is of interest to nearly everyone;
• F0 is of interest for those already understanding F1 and wishing to widen and deepen their understanding.

In this sense, F1 is the basic MHP while F0 is the advanced MHP.

--Boris Tsirelson 07:06, 3 February 2011 (UTC)

@Wietze, you cannot say "the decision has to be based on the conditional probability". You could say that it would be wise to base your decision on the conditional probability. Moreover, if you want to reach the general public, you had better explain why this would be the wise thing to do. Please draft some material on this in the article on conditional probability.

If indeed you want to reach the general public, it would also be wise to note that given that the player has chosen Door 1, whether the host opens Door 2 or Door 3 has no relevance at all to whether or not the car is behind Door 1 (under the probabilistic assumptions which many people find natural). So the general reader can be informed of the truth and the whole truth of the standard MHP - F0 and F1 combined - using plain non-technical English and without needing to follow a course in probability theory first.

PLEASE let us not repeat this endless discussion here. Draft appropriate subpages to MHP as Peter Schmitt indicated is the next step which ought to be made. Get to work on the article on conditional probability. Richard D. Gill 09:55, 3 February 2011 (UTC)