You're given two sealed envelopes. You're told one contains twice as much money as the other, but you don't know which is which. You pick envelope A and find $100. You reason: "Envelope B either has $50 or $200. If I switch, I have a 50% chance of getting $50 and 50% chance of getting $200. Expected value of switching = 0.5($50) + 0.5($200) = $125. That's more than $100, so I should switch." But wait - this logic would apply no matter what amount you found. That can't be right. What's the flaw in this reasoning? Provide a rigorous explanation.