In Search of a Fair Bet in the Lottery

Although state-operated lotto games have the worst average expected payoffs among common games of chance, because the jackpot can accumulate, the maximum expected payoff is potentially unlimited. It is possible, therefore, that lotto can exhibit a positive expected return. This paper examines 18,000 drawings in 34 American lotteries and finds approximately 1% of these drawings provided players with a fair bet. If it were possible for a bettor to purchase every possible combination, however, most lotteries commonly experience circumstances where such a purchase would provide a positive return with 11% of the drawings providing a fair bet to the player.