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. (a mathematician would moreover prefer to use the symbol "a" to stand for a possible value, reserving the symbol "a" for a random variable). 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.