Consider a simple shell game. A dealer has three red shells and puts a small yellow ball under one of the shells. The dealer proceeds to move the shells around quickly and randomly to the point that you can't follow along. After this shuffling, you choose one of the shells. If the shell you choose has the yellow ball under it, the dealer pays you $20 (you don't pay him anything at all). However, if you choose a shell with nothing under it, you owe the dealer $20 instead. What is your expected profit from a single play of this game? Round to the nearestā
