this interpretation of the two envelopes problem appears in the first publications in which the paradox was introduced in its present-day form, gardner (1989) and nalebuff (1989). it is common in the more mathematical literature on the problem. it also applies to the modification of the problem (which seems to have started with nalebuff) in which the owner of envelope a does actually look in his envelope before deciding whether or not to switch; though nalebuff does also emphasize that there is no need to have the owner of envelope a look in his envelope. if he imagines looking in it, and if for any amount which he can imagine being in there, he has an argument to switch, then he will decide to switch anyway. finally, this interpretation was also the core of earlier versions of the two envelopes problem (littlewood's, schrödinger's, and kraitchik's switching paradoxes); see the concluding section, on history of tep.