Two envelopes problem: Difference between revisions

Revision as of 06:31, 3 July 2024

Revision as of 09:32, 3 July 2024

Line 210:

In 1988 and 1989, [[Barry Nalebuff]] presented two different two-envelope problems, each with one envelope containing twice what is in the other, and each with computation of the expectation value 5''A''/4. The first paper just presents the two problems. The second discusses many solutions to both of them. The second of his two problems is nowadays the more common, and is presented in this article. According to this version, the two envelopes are filled first, then one is chosen at random and called Envelope A. [[Martin Gardner]] independently mentioned this same version in his 1989 book ''Penrose Tiles to Trapdoor Ciphers and the Return of Dr Matrix''. Barry Nalebuff's asymmetric variant, often known as the Ali Baba problem, has one envelope filled first, called Envelope A, and given to Ali. Then a fair coin is tossed to decide whether Envelope B should contain half or twice that amount, and only then given to Baba.

Broome in 1995 called thea probability distribution 'paradoxical' if for any given first-envelope amount ''x'', the expectation of the other envelope conditional on ''x'' is greater than ''x''. The literature contains dozens of commentaries on the problem, much of which observes that a distribution of finite values can have an infinite expected value.<ref>{{cite journal |last1=Syverson |first1=Paul |title=Opening Two Envelopes |journal=Acta Analytica |date=1 April 2010 |volume=25 |issue=4 |pages=479–498 |doi=10.1007/s12136-010-0096-7|s2cid=12344371 }}</ref>

== See also ==