"So you pick an envelope, and are about to see how long you�ll get in heaven when�
The angel makes you an offer. If you�ll do a day in Hell to cover for a friend of his that got caught up in a little scandal, he�ll give you the other envelope. He argues that this must be a good deal, as follows. Let y be the number written on your slip. The other envelope has either 2y or y/2 written on it. Each is equally likely, so your expected number of days in heaven if you switch envelopes is 0.5 * 2y + 0.5 * y/2 = 1.25y. So the expected gain from swapping is 1.25y - y = y/4. Since we know y > 10, y/4 > 2.5, so this is more valuable to you than a day in Hell."
At the risk of sounding incredibly simplistic, a bird in the hand is worth two in the bush.