Talk:Two envelopes problem/Archive 10

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What does the letter 'A' stand for?

In the article, sometimes 'A' is the amount in the selected envelope:"I denote by A the amount in my selected envelope.",
another time 'A' is the name of the selected envelope:"...given that envelope A contains less than envelope B."
If 'A' is a name, the expressions 2A or A/2 don't make sense. There is a considerable confusion concerning the usage of the letter 'A'. So both the sections "Problem" and "Simple resolutions" have to be revised. --TotalClearance (talk) 09:03, 9 April 2016 (UTC)

Yes, and the problem of A (envelope or envelope's amount) is that there is B also. Mathematicians use to disregard the obvious and easily perceived interdependency of the task presented, that is forced by the unchangeable total amount T of x + 2x (3x). No "average A" nor "any A" will ever be doubled – but only that very specific A that actually amounts to "x" (T/3), and in that specific case B consequently amounts to "2x", giving a difference of x.

On the other hand, no "average A" nor "any A" can ever be halved, but only that very specific A that actually amounts to 2x (2/3 T), difference between A and B again x.

So the confusing "expected value formula" (brazenly implying A=2A=A/2, hence ="zero" resp. =infinite, see Ruma Falk) evidently was just a smart joke to muck around with mathematicians and philosophers. Gerhardvalentin (talk) 09:42, 23 June 2016 (UTC)

This strikes be as the best resolution provided so far. The carrier of the money is confused with the contents of the carrier. All I can add is a starker example representation of the fallacy. Suppose the two choices are between a one dollar bill or a two dollar bill. With sighted people watching, a blind person is asked to give the argument presened in the actual article. For the process to work, sometimes there would have to be a conversion to a $0.50 bill or a $4.00 bill for the process to work. — Preceding unsigned comment added by PEBill (talk • contribs) 17:54, 10 July 2016 (UTC)

Yes, false switching argument. You are fully right in saying "if the two envelopes contain 1 and 2 (total=3), then the false argument says 0,5 and 2, resp. says 1 and 4".

The problem is that the "given switching argument" is tremendously defective and misleading for the described underlying symmetric task/variant of two indistinguishable, unknown envelopes with a fixed, unchangeable total amount T of 3x, where "envelope A" is no valid variable, but means x respectively 2x at the same time (of a total T of 3x).

The switching argument (expected value B=1,25A) only reflects the purposive asymmetric (!) one-way task/variant (Nalebuff: Ali vs. Baba), with some not yet decided total amount, where first of all only envelope A (that is "known" to be some predeterminated amount !) had already been fixed with any amount (only in that asymmetric task "A" is a valid variable) and is given to "Ali", and only thereafter the decision was made to equip the "known" to be the derived amount ! of envelope B equally likely with either double (2A, giving a total T of 3A) or half (A/2, giving a total T of 1.5*A). So solely in this latter task/variant with a not yet fixed total amount, on average envelope "B" will contain 1.25*A, and B is given to "Baba". Only in this purposive asymmetric one-way variant, where A is a variable, with B=1.25*A, you will gain A/4 (of "any A" !) and consequently get on average "5A/4" by switching from A to B, and you will lose B/5 and consequently get on average only "A" by switching from B to A. The diametrical difference of those two completely different tasks is thoroughly ignored by the present so-called "paradox". Most ignore that obvious and significant distinction.

So the trappy illusory switching argument does never apply to the presented symmetric basic setup of two indistinguishable, unknown envelopes with a fixed total amount. For the underlying symmetric variant of a fixed total (T=3x), the defective appraisal of the switching argument is fragmentary, incomplete, deficient and misleading.

As per Ruma Falk, the appraisal for the presented symmetric variant with a fixed total amount T=3x has to read instead:

3  The other envelope may contain either 2A (hence 2x) in case envelope A contains x, or A/2 (hence x) in case envelope A contains 2x. Total T in any case =3x.

4  If A is the smaller amount of x, then the other envelope contains 2A, hence 2x (difference =x)

5  If A is the larger amount of 2x, then the other envelope contains A/2, hence x (difference =x).

6  Thus both envelopes contain 2x with probability 1/2 and x with probability 1/2, hence both envelopes contain on average 3x/2 (T/2), so evidently no argument for switching.

For the presented basic setup of two unknown envelopes, the fragmented appraisal of the switching argument is incomplete and deficient, thus misleading.

In its fragmentary form, the switching argument addresses solely the asymmetric one-way variant of a not yet decided total amount (Nalebuff) of any envelope "A" (Ali) that is "known" to contain any already predeterminated amount, and any envelope "B" (Baba) that is "known" to contain the derived amount of 5A/4. Who will help to improve the awkward article. Sources en masse. Gerhardvalentin (talk) 14:06, 17 July 2016 (UTC)

How is this correct?

This problem is very similar to The Monty Hall problem. Only, there is only two envelopes. So you pick one. You have a 1/2 of getting the smaller amount of money. Then if you switch you would get the greater sum of money. However, there is also a 1/2 chance you got the greater sum of money. Then you would switch and get the smaller amount of money. The chance is equal!!!!!!!!!!!!!!!!!!!!!!!!! The article isn't bad, someone should just include this. Ghostana (talk) 21:06, 28 March 2022 (UTC)

Nvm. Ghostana (talk) 21:08, 28 March 2022 (UTC)

Nvm. I'm stupid. Ghostana (talk) 21:09, 28 March 2022 (UTC)

Nvm. I'm stupid. LOL Ghostana (talk) 21:09, 28 March 2022 (UTC)

Don't put article content in Talk page

Ref 4 in the current version points to Talk:Two_envelopes_problem/Literature. This makes that Talk sub-page in effect part of the article. This needs resolving: article content should be in the main namespace, not the Talk namespace and citations on Wikipedia shouldn't be pointing to other pages on Wikipedia. The papers in that literature list (the ones that support the statement) need to be moved into the article as citations. MartinPoulter (talk) 18:06, 2 July 2020 (UTC)

I changed the citation to a single WP:RS. Rolf H Nelson (talk) 22:57, 5 July 2020 (UTC)

Haha so one randomly chosen single paper is now supporting the claim that there is a "voluminous literature"? This is silly beyond belief. iNic (talk) 09:35, 6 July 2020 (UTC)

If it's helpful, I added a relevant quote from the paper. Rolf H Nelson (talk) 02:55, 7 July 2020 (UTC)

Since material on Wikipedia is never permanently deleted the list of literature is here to stay for ever, and people outside of Wikipedia can refer to its existence. Too bad. The rules of Wikipedia are mutually inconsistent. Wikipedia must disappear and be replaced by an even more complete encyclopedia with rules which are even more difficult to figure out. Naturally, being a compendium of all existing knowledge, it will be able to guide anyone to anywhere on any version of Wikipedia which ever existed in the past. I think we should cherish anomalies like this, not get upset about them. Richard Gill (talk) 14:08, 14 July 2020 (UTC)

Anyway, the Wikipedia circular references rule says "An exception is allowed when Wikipedia itself is being discussed in the article, which may cite an article, guideline, discussion, statistic, or other content from Wikipedia (or a sister project) to support a statement about Wikipedia. Wikipedia or the sister project is a primary source in this case, and may be used following the policy for primary sources. Any such use should avoid original research, undue emphasis on Wikipedia's role or views, and inappropriate self-reference. The article text should make it clear the material is sourced from Wikipedia so the reader is aware of the potential bias." It is not clear that this is the only exception which is allowed. New exceptional cases can arise. The rules of Wikipedia need to be adapted to reality, not the other way round. Possibly we should add references to the relevant story by Borges, and possibly add a subsection to the article mentioning the notable fact that the wikipedia article itself *did* become a reliable source in reliable scientific literature. Self-reference is a wonderful source of puzzles! Richard Gill (talk) 14:44, 14 July 2020 (UTC)