[accountLost]

My take :

let M be the maximum amount of money that a envelope can contain (at worst it can be the total amount of money in the world). You don't know the value of this upper bound M.

Most of the time, you get 2*x or x/2 with 50% chance if you choose the other envelope (which on average is a win)

But when x=M you get M/2 instead of M and therefore you loose M/2 with 100% chance. And when it happens you have lost much more than in the other cases (because exponentiel...)

If you do the math, you can see that what you win for 1 2 4 8 16 ... M/2 is equal to what you loose for M.

And so on average what win from switching is 0.