[Longwelwind]

>The puzzle is to find the flaw in the very compelling line of reasoning above. This includes determining exactly why and under what conditions that step is not correct, in order to be sure not to make this mistake in a more complicated situation where the misstep may not be so obvious. In short, the problem is to solve the paradox. Thus, in particular, the puzzle is not solved by the very simple task of finding another way to calculate the probabilities that does not lead to a contradiction.

[kazinator]

I did solve the paradox: it emanates from falsely looking at the switch as doubling or halving the money.

If the envelopes contain, say, $50 and $100, it looks like a doubling/halving. But nothing materially changes if we add $1000 to each one to make $1050 and $1100. The probabilities don't depend on what is in the envelopes, and the win/loss is just a spread of the difference between their values.

Why would anyone, while solving some problem, worry about some unspecified more complicated situation which supposedly resembles that problem?

Give me the specific of that more complicated problem and I will knock it out of the ballpark using whatever reasoning fits that problem.