The envelope problem, and a possible solution

[SamIAm]

I got frustrated with Aaron in this dialogue before. Sure am glad you started it up again. [img]/images/graemlins/smile.gif[/img]

Here's how my dialogue would go when I hear the problem.

Paradoxer: "I put a random amount X in one envelope and 2X in the other."
Me: "Wait, how was X chosen?"
P: "I'm not telling you. Now, you open and find $100. Should you switch?"
M: "Man, I dunno. I can tell you the correct move if you describe the opponent."
P: "I'm not going to tell you. So, what's the best move?!"

It's retarded. Of course you and I can arrive at different answers if we try to fill-in the gaping hole differently. That doesn't show that the problem's clever; all that shows is that the problem has gaping holes.
-Sam

P.S. Assuming that X is chosen equally likely from the set of all positive integers is flat wrong. You're not allowed to assume that, because it doesn't make sense. [img]/images/graemlins/smile.gif[/img]