suppose for the sake of argument, we start by imagining an amount 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: falk and konold, 1992). 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.