In non-technical language, what goes wrong (see [[Necktie paradox]]) is that, in the scenario provided, the mathematics use relative values of A and B (that is, it assumes that one would gain more money if A is less than B than one would lose if the opposite were true). However, the two values of money are fixed (one envelope contains, say, $20 and the other $40). If the values of the envelopes are restated as ''x'' and 2''x'', it's much easier to see that, if A were greater, one would lose ''x'' by switching and, if B were greater, one would gain ''x'' by switching. One does not gain a greater amount of money by switching because the total ''T'' of A and B (3''x'') remains the same, and the difference ''x'' is fixed to ''T/3''.
Line 7 should have been worked out more carefully as follows:
