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Suppose for the sake of argument, we start by imagining an amount of 32 in Envelope A. In order that the reasoning in steps 6 and 7 is correct ''whatever'' amount happened to be in Envelope A, we apparently believe in advance that all the following ten amounts are all equally likely to be the smaller of the two amounts in the two envelopes: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 (equally likely powers of 2<ref name=":1" />). But going to even larger or even smaller amounts, the "equally likely" assumption starts to appear a bit unreasonable. Suppose we stop, just with these ten equally likely possibilities for the smaller amount in the two envelopes. In that case, the reasoning in steps 6 and 7 was entirely correct if envelope A happened to contain any of the amounts 2, 4, ... 512: switching envelopes would give an expected (average) gain of 25%. If envelope A happened to contain the amount 1, then the expected gain is actually 100%. But if it happened to contain the amount 1024, a massive loss of 50% (of a rather large amount) would have been incurred. That only happens once in twenty times, but it is exactly enough to balance the expected gains in the other 19 out of 20 times.
Alternatively, we do go on ad infinitum but now we are working with a quite ludicrous assumption, implying for instance, that it is infinitely more likely for the amount in envelope A to be smaller than 1, ''and'' infinitely more likely to be larger than 1024, than between those two values. This is a so-called [[
Many authors have also pointed out that if a maximum sum that can be put in the envelope with the smaller amount exists, then it is very easy to see that Step 6 breaks down, since if the player holds more than the maximum sum that can be put into the "smaller" envelope they must hold the envelope containing the larger sum, and are thus certain to lose by switching. This may not occur often, but when it does, the heavy loss the player incurs means that, on average, there is no advantage in switching. Some writers consider that this resolves all practical cases of the problem.<ref name=":2">{{Citation | first = Barry | last = Nalebuff |title = Puzzles: The Other Person's Envelope is Always Greener| journal = Journal of Economic Perspectives | volume = 3 | issue = 1 | pages = 171–181 | doi=10.1257/jep.3.1.171| year = 1989 | doi-access = free }}.</ref>
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