The scenario: Lotteries have the worst odds among virtually all legal gaming options. Nevertheless, for many players, the idea of spending $2 for something that gives them a chance to win big money is entertaining — and not very expensive. And, players reason, the lottery supports public programs such as education and mass transportation.
Plus, most states have marketing campaigns that offer hope for winning. Anti-gambling advocates have never gained much traction in statehouses arguing that state-advertised lotteries prey on problem gamblers or act as a “tax on the poor” by providing a glimmer of hope that problem gamblers could become millionaires.
Despite widespread acceptance of state-backed lotteries, when Powerball ticket sales declined in all but four states and sales nationwide dropped by 19 percent, the Multi-State Lottery Association decided it was time to do something.
Industry insiders attributed the decline to “jackpot fatigue,” which meant that casual players bought tickets only when a huge jackpot was up for grabs. With fewer people playing, it took more time to generate jackpots large enough to get these players to buy tickets. Some believed that increasing the chances of winning something — not just the jackpot — would encourage ticket sales.
The resolution: The association looked at rule changes to address the falling revenue problem and implemented them in 2015. Historically higher jackpots drove higher ticket sales. Under the new rules, there would be new sets of numbers from which to choose. The range for the five white balls increased from 1–59 to 1–69. The range for the red “Powerball” numbers were reduced from 1–35 to 1–26. This change meant the overall odds of winning any prize improved, going from 1 in 32 to 1 in 25, but the odds of winning a jackpot would drop from 1 in 175 million to 1 in 292 million. The Powerball ticket price would remain the same ($2), and initial jackpots would still begin at $40 million.
The lesson: Both the odds of winning and the size of the prize contribute to sales of lottery tickets. But how much does each really contribute? Orthodox economic theory dictates that the expected value — the product of the probability of winning, times the prize — determines the value of a lottery ticket. Psychologists and behavioral economists, however, have long known that the perceived value of a lottery ticket may be quite different from expected value.
Most individuals grow insensitive to probabilities once the odds of winning diminish. Behavioral economists use the notion of decision weights to model how small probabilities are transformed into disproportionately large decision weights, making lottery tickets — as well as insurance for rare accidents — quite attractive.
Small probabilities carry large decision weights, as well as insensitivity to changes in probabilities. If this model is correct, the change made by the association will not significantly reduce sales of Powerball tickets for small jackpots but will greatly increase situations when the jackpot accumulates to high values, which will then attract sales.
Baucells is an associate business professor and Yemen a senior researcher at the University of Virginia Darden School of Business.