Powerball: Somebody’s Gotta Win!

The case evolves around the Powerball lottery and the rule changes implemented in 2015, which, among other things, changed the chances of winning the jackpot from 1 in 175 million to 1 in 292 million. What is the impact of such rules on lottery revenues? The expected value rule is unable to explain why people play in the first place and fails to give the appropriate weight to the factors that explain the attractiveness of a lottery. This case is ideal to introduce the notion of decision weights as put forward by Kahneman and Tversky’s prospect theory. By calculating decision weights, we obtain a reasonable prediction for the willingness to pay for the lottery as a function of different jackpot amounts. Using past data, we can correlate lottery revenues with predicted willingness to pay for a ticket. Quantitative-inclined audiences can then develop a simulation model of how likely it is that the jackpot grows, which, coupled with the prediction of revenues as a function of the jackpot, would give the evolution of the revenues under the new rule. The accompanying spreadsheet provides data for students to work out various scenarios to narrow objectives and maximize revenue from Powerball tickets.