The wallet paradox was introduced by Martin Gardner in his Scientific American column. I will review the wallet game when players' fixed-mean distributions of money in their wallets are over nonnegative integer dollar amounts. Then, I will prove that there is no best strategy if the amount of money a player can carry in his or her wallet is unbounded. Curiously, the proof involves carrying no money (zero dollars) in one's wallet with high probability. However, if monetary amounts are bounded, then carrying no money is never part of a best strategy, as long as the mean is above one dollar.

This talk is based on a paper of the same name, coauthored with Stanley R. Huddy and Michael Ivanitskiy.