e1 = x (money you might get by picking the first envelope)
e2a = 2x
e2b = x/2
Okay? So, what are the odds of each event?
There is 100% of chance that the envelope 1 contains x dollars.
There is 50% of chance that envelope 2 contains x/2 or 2x.
The universe you have is: e1-e2a and e1-e2b, 50% of chance for each.
On e1-e2a if you pick the first envelope, you lose x. If you pick the second envelope, you gain x.
On e1-e2b if you pick the first envelope, you gain x/2. If you pick the second envelope, you lose x/2.
There is 25% of each choice be made.
Pick E1, lose x
Pick E1, gain x/2
Pick E2, gain x
Pick E2, lose x/2
Hmn... Seems to me it's more logical to switch, as you can lose the less and gain more dollars if you pick correctly.
BUT since NO ONE is going to give 100 dollar bills into envelopes to someone like that, WHO CARES?!