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The simple resolution above assumed that the person who invented the argument for switching was trying to calculate the expectation value of the amount in Envelope A, thinking of the two amounts in the envelopes as fixed (''x'' and 2''x''). The only uncertainty is which envelope has the smaller amount ''x''. However, many mathematicians and statisticians interpret the argument as an attempt to calculate the expected amount in Envelope B, given a real or hypothetical amount "A" in Envelope A. One does not need to look in the envelope to see how much is in there, in order to do the calculation. If the result of the calculation is an advice to switch envelopes, whatever amount might be in there, then it would appear that one should switch anyway, without looking. In this case, at Steps 6, 7 and 8 of the reasoning, "A" is any fixed possible value of the amount of money in the first envelope.
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 (1988).<ref>{{Cite journal|last1=Nalebuff|first1=Barry|date=Spring 1988|title=Puzzles: Cider in Your Ear, Continuing Dilemma, The Last Shall Be First, and More|journal = Journal of Economic Perspectives|volume = 2|issue=2|pages=149–156|doi = 10.1257/jep.2.2.149 }} and Gardner, Martin (1989) <i> Penrose Tiles to Trapdoor Ciphers: And the Return of Dr Matrix. </i> </ref>)
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.
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