[dukemagic]

The one thing I wasn't sure about was whether or not you want to switch before you open up the envelope. You could use the same logic that you apply to the open envelope:

Let's say the envelope I offer you first is Envelope 1, containing A amount. Envelope 2 would then contain either A/2 or 2A. So the expected value of switching would be (A/2 + 2A) / 2, or 5/4 A (B = 5/4 A). So it seems you do want to accept the offer to switch.

But if you do accept this offer to switch and open envelope 2, you're still going to change back to Envelope 1 EVERY single time since now you expect Envelope 1 to have more than Envelope 2, on average. In fact (if my math is correct) you expected Envelope 1 to have (5/4) B, or 25/16 A which is greater than the 5/4 A you expected Envelope 2 to have. Is this a paradox? What am I missing?