Proper noun
the two envelopes problem
A puzzle of this kind: "You are given two indistinguishable envelopes, each containing money; one contains twice as much as the other. You may pick one envelope and keep the money it contains. Having chosen an envelope at will, but before inspecting it, you are given the chance to switch envelopes. Should you switch?" Because you stand to gain twice as much money if you switch while risking only a loss of half of what you currently have, it is possible to argue (fallaciously) that it is beneficial to switch.
Synonym: exchange paradox