The paradox comes from the fact that $1000 is arbitrary.Spoiler for my take
Can you gain as much by switching back? Using the same reasoning?
There is a paradox: A gain for switching can be anticipated.
Yet, there is a preferred envelope, and if we initially chose it we should not switch.
Not sure what you mean by "switching back". The 50/50 comes from randomly picking one of 2 envelopes from which we know one has double the money of the other. I don't see a paradox.
Suppose I were to point to an envelope before any were opened, and I said "That envelope contains some amount of money; call it $X. The other envelope therefore must contain $2X or $X/2." You could now argue that the expected earnings from picking the other envelope are $5X/4, so you should choose the other envelope. But in reality, have I actually given you any more information than you already had when you only knew that one envelope contains twice as much money as the other?