From: "Steven Taschuk" Subject: Re: puzzlement Date: Sat, 29 Dec 2001 22:33:43 GMT Newsgroups: alt.math,alt.math.recreational,alt.math.undergrad,aus.mathematics,sci.math Summary: The two-envelope paradox "Elaine Jackson" wrote: > On a table before you are 2 envelopes, each containing a sum of money. You > know one contains twice as much as the other, but you don't know which is > which. The game is to open an envelope at random, examine the contents, and > then decide whether you want to keep that amount or take the amount in the > unopened envelope. ... > expected payoff if you take the other envelope is (1/2)(2x)+(1/2)(x/2) = > 5x/4 > x. Hence you get the greatest expected payoff by choosing an envelope > at random and taking the contents of the other envelope. > > Would someone please criticize this argument? I would like to understand > where it goes wrong. This is a well-known problem; it is discussed in, among other places, the rec.puzzles archive. See .