Bob and Charlie have heard of a game, and must decide whether they will play.
They each have a wallet in their pockets, with a random amount of money in it (for our purposes: literally any amount, but more than zero). The game is that they each count the money in their wallets, and whomever has the least in their wallet wins the contents of the other’s wallet.
Bob has X pounds in his wallet, so he knows that the worst that can happen is that he will lose X pounds. If he wins, he knows that he will win more than X pounds (that’s why he wins). The probability of winning is 0.5, and he would win more than X; the probability of losing is 0.5 and he would lose only X. The game therefore favours him, and he reasons that he should play.
Charlie has Y pounds in his wallet, so he knows that the worst that can happen is that he will lose Y pounds. If he wins, he knows that he will win more than Y pounds (that’s why he wins). The probability of winning is 0.5, and he would win more than Y; the probability of losing is 0.5 and he would lose only Y. The game therefore favours him, and he reasons that he should play.
They can’t both be right. Where are they wrong in their reasoning?