What to do? What to do??

Remember the Monty Hall problem?  If not, you might like to look back at my post of 23/2/08.  So here's a somewhat similar conundrum.  You are presented with two envelopes and told that both contain money, but one contains twice as much as the other.  You are invited to choose an envelope and then told that you can take whatever is in that envelope, or you can swap to the other envelope and take whatever is in there. What should you do?  You could argue this way - (1) the envelope I have chosen contains a sum of money.  I don't know what it is, so call it X. (2) The other envelope then either contains 2X or X/2.  (3) It's just as likely to be the one as the other.  (4) The "value" of the other envelope is therefore 1/2 x 2X + 1/2 x X/2 and this works out as X + X/4.  (5) But this is more than the X in my envelope, and I should therefore swap.  So what do you think?  Are you persuaded by that argument? Think about it and we'll come back to it in a few days' time.