When I saw tillys question for the first time, i was really confused.
My problem, as always, turned out to be that i didn't really understand the question in the first place.
The English combined with my lack of attention to detail, really warped my perception of what the question was.
Here's my version of the question (modified so normal people can understand):

Suppose I have two envelopes. All you know is that they contain a different number of
flashcards, with different numbers on each of them.
I randomly hand you one of them. You open it, look at it, then hand it back.
You now have sufficient information to, with guaranteed better than even odds, correctly
tell me whether I gave you the envelope with the larger sum. How?

This is how i understood tilly's problem at first, so i thought, "what the $@@$!?! THATS IMPOSSIBLE!!!"
Then i thought "OK,ok, don't give up so fast, he says there's a solution."
I continued thinking about this problem and the answer tilly gave occured to me,
but i thought you don't know how many flashcards you have, so the sum can be anything.
But think about it.
You make up a number, and pretend it is in between the sums of the two envelopes,
and that the number on the flashcard I handed you is between the number of flashcards in each envelope,
and so you can guarantee to have better than 1/2 odds of guessing which envelope has the largest sum.
It is more miniscule percentage than the one from tilly's original problem but it is the same principal.

1/2 + (crazy math) = better than 1/2

update: May 2, 2001 11:50AM PST
I've been reviewing some of my posts lately, and I've noteiced that this one doesn't quite reflect my ignorance and misunderstanding of the question. With that said, I point out that what is written here is not what was in my head at the time of writing, but rather a broken argument of misunderstanding. So please just accredit this one to irresponsibility, sleep depravation, and whatever else you want. Like all(most) of my posts, I leave this one as a reminder and example of what to avoid, in hopes i will not repeat my stupdeneous error, or merely dislexic miscommunication.

"cRaZy is co01, but sometimes cRaZy is cRaZy".
- crazyinsomniac