Since this is our final case, we can admit that we do not have the answer—and even if we did, we probably wouldn’t share it. Nonetheless, strategic thinking can help make a more educated guess. The trick is to put yourself into the casino owners’ shoes. They make money only when people play the disadvantageous machines at least as much as the favorable machines.

Is it really possible that the casinos could “hide” the machines which are offering the favorable odds? If people play the machines that pay out the most, won’t they find the best ones? Not necessarily, and especially not necessarily in time! The payoff of the machine is in large part determined by the chance of a jackpot prize. Look at a slot machine that takes a quarter a pull. A jackpot prize of $10,000 with a 1 in 40,000 chance would give a payoff ratio of