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This is thetalk page for discussing editorial changes to thetwo envelopes problem article.Please place discussions concerning solutions to the two envelopes problem itself on theArguments page. Questions or statements of this kind here will be moved to that page without notice. A list of publications on the two envelopes problem can be found at thesources page

Two envelopes problem/sources was nominated fordeletion.The discussion was closed on24 August 2011 with a consensus tomerge. Its contents weremerged intoTwo envelopes problem. The original page is now a redirect to this page. For the contribution history and old versions of the redirected article, please seeits history; for its talk page, seehere.

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An extensive literature list is available atTalk:Two envelopes problem/LiteratureParadoctor (talk)04:10, 8 October 2020 (UTC)[reply]

If the amount of money is odd, it's better to switch. Since it can't be the X2 enveloppe. If it's even, switching is slightly riskier since maybe one of the envelopes is odd amount of money and you want to avoid it...— Precedingunsigned comment added by70.48.133.1 (talk)11:00, 6 November 2017 (UTC)[reply]

Nice comment. However, as far as we know, there are just slips of paper in the envelopes with the amounts of money written on them. The envelopes need not contain US bank notes.Richard Gill (talk)07:48, 21 July 2020 (UTC)[reply]

My manuscript on TEP is now posted on arXiv (will appear on Tuesday) and submitted to a journal. Here is a sneak preview.https://www.math.leidenuniv.nl/~gill/tep.pdfRichard Gill (talk)10:08, 7 March 2020 (UTC)[reply]

Nice paper, but you might consider removing your reference toTalk:Two_envelopes_problem/Literature as this turned out to be an illegal talk page and will consequently soon be deleted.iNic (talk)12:18, 7 July 2020 (UTC)[reply]

That doesn't worry me.Richard Gill (talk)14:36, 14 July 2020 (UTC)[reply]

Ok that's good but I'm quite sure it will be deleted from Wikipedia.iNic (talk)11:43, 15 July 2020 (UTC)[reply]

A correspondent tells me that the following paper is not referenced and seems to them to be the definitive solution:The Two-Envelope Paradox Resolved.Author(s): Timothy J. McGrew, David Shier and Harry S. Silverstein.Source: Analysis , Jan., 1997, Vol. 57, No. 1 (Jan., 1997), pp. 28-33Published by: Oxford University Press on behalf of The Analysis Committee.Stable URL:http://www.jstor.com/stable/3328431Richard Gill (talk)07:50, 21 July 2020 (UTC)[reply]

There are indeed many solutions and ideas not mentioned in the article. Why? Well there are simply too many of them and many are quite technical and thus not easily explained in an encyclopaedic article. Wikipedia can never be a replacement for the literature itself. An obvious fact that many people need to be reminded of over and over. This paper was, however, referenced indirectly until just recently inTalk:Two_envelopes_problem/Literature. It is the first entry for 1997. But this list is now so kindly removed as a reference byRolf H Nelson so yes, now this paper is not mentioned at all at Wikipedia.iNic (talk)11:10, 21 July 2020 (UTC)[reply]

I found an interesting list of inconsistencies of the articlehereiNic (talk)02:00, 25 November 2020 (UTC)[reply]

Latest version of that article is dated 2018-01-02. A quick glance lets me doubt its value even when it was current.Paradoctor (talk)02:28, 25 November 2020 (UTC)[reply]

Although "the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have", what this omits to mention is that they stand to double only the SMALL amount, but risk losing half the LARGE amount, so in fact the gains and losses even out, and the "paradox" evaporates. I think it would be useful to mention this up front, for the benefit of readers who maybe can't cope with the more mathematical explanations.2A00:23C8:7B0C:9A01:87F:AA06:BD33:A284 (talk)13:30, 15 April 2024 (UTC)[reply]

The simple explanation is not useful because it doesn't state which step in the incorrect resolution is the fallacy. To "resolve the paradox", you have to state which step in the switching argument is wrong, and why it's wrong. The simple resolution doesn't tell you where the mistake in the switching argument is. The mistake in the switching argument is in combining the terms in step 7, because they aren't the same A. it's not an expression with 1 variable, it's an expression with 2 of them. Solving for both variables gives the correct expected value, which is not in terms of A.73.151.32.230 (talk)00:12, 30 August 2025 (UTC)[reply]

maybe put something about the monty hall problem in there? it's very similar.174.176.97.132 (talk)20:52, 22 August 2025 (UTC)[reply]

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