This is the talk page for discussing improvements to the Two envelopes problem article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
Archives: Index, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10Auto-archiving period: 360 days |
This is the talk page for discussing editorial changes to the two envelopes problem article. Please place discussions concerning solutions to the two envelopes problem itself on the Arguments 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 the sources page |
Two envelopes problem/sources was nominated for deletion. The discussion was closed on 24 August 2011 with a consensus to merge. Its contents were merged into Two envelopes problem. The original page is now a redirect to this page. For the contribution history and old versions of the redirected article, please see its history; for its talk page, see here. |
Games Unassessed (inactive) | |||||||
|
An extensive literature list is available at Talk:Two envelopes problem/Literature Paradoctor (talk) 04:10, 8 October 2020 (UTC)
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... — Preceding unsigned comment added by 70.48.133.1 (talk) 11:00, 6 November 2017 (UTC)
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.pdf Richard Gill (talk) 10:08, 7 March 2020 (UTC)
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)
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. 28-33 Published by: Oxford University Press on behalf of The Analysis Committee. Stable URL: http://www.jstor.com/stable/3328431 Richard Gill (talk) 07:50, 21 July 2020 (UTC)
I found an interesting list of inconsistencies of the article here iNic (talk) 02:00, 25 November 2020 (UTC)
At last we can put an end to this long discussion. The correct answer is really easy.
Question: What is the correct solution to the two envelope problem?
ChatGPT: The two envelope problem is a classic problem in probability theory. The basic premise is that you are given two envelopes, each containing a certain amount of money. One envelope contains twice as much money as the other. The question is, if you are allowed to open one envelope and see its contents, should you switch to the other envelope to maximize your chances of getting the larger amount of money?
The correct solution to this problem is to always switch envelopes. This may seem counterintuitive, but the reason it works is because of the way the problem is set up. Since one envelope contains twice as much money as the other, if you choose an envelope at random, you have a 50% chance of choosing the envelope with the smaller amount of money and a 50% chance of choosing the envelope with the larger amount of money.
If you choose the envelope with the smaller amount of money, and you then switch to the other envelope, you are guaranteed to get the larger amount of money. This is because the other envelope must contain the larger amount of money, since the one you chose contains the smaller amount. Therefore, by switching envelopes, you will always get the larger amount of money.
On the other hand, if you choose the envelope with the larger amount of money, and you then switch to the other envelope, you will only get the smaller amount of money. This is because the other envelope must contain the smaller amount of money, since the one you chose contains the larger amount. Therefore, by switching envelopes, you will only get the smaller amount of money in this case.
Therefore, the correct strategy is to always switch envelopes. This will maximize your chances of getting the larger amount of money.iNic (talk) 11:59, 9 December 2022 (UTC)