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
.