You can swap your envelope of money for a sealed one that might hold double. Swap?
You're told one envelope has twice as much money as the other, but not which. Holding envelope A, you reason: the other envelope has either half or double what's in mine, each equally likely, so swapping has a positive expected gain. But that same argument works for whichever envelope you're holding, which can't be right for both. What's wrong with the reasoning?
Reveal the answer
The flaw is treating 'the amount in my envelope' as a fixed number while also treating the other envelope's content as a 50/50 gamble built from it; both envelopes can't simultaneously be the reference point. Once you fix an actual pair of amounts in advance, swapping gains you nothing on average, exposing the trick in the probability argument.