I believe that it is correct, and it concisely represents a concept I have never understood. It seems obvious to me that the chance of getting the higher bill would be 50/50, and if you ran enough simulations then you would do no better by consistently choice to switch than by choosing to keep the tenner. Yet I have heard this concept of expected payoff repeatedly and it contradicts the above. Can you explain it? Suppose you know there are two bills in a hat and that one bill is twice the size of the other bill. You draw one bill from the hat and it is a $10 bill. You are then given the option to exchange you $10 bill for the other bill in the hat…do you make the exchange? Based on expected values, you should make the exchange. The expected value of the trade is 0.5*5 + 0.5*20 = 12.25 given the other bill is half the time a $5 bill and half the time a $20 bill.