The Best Time to Play the Lottery

Abstract

The best time to play the lottery is when the jackpot has rolled over several times and grown large, but not so large that you must share the prize if you win. We examine maximizing the expected value of a winning ticket as well as that in a random ticket. The derived optimality criteria depend on the prize elasticity of ticket demand. A regression analysis on data obtained from the Mega Millions^® and Powerball^® multi-state lotteries suggests ticket sales grow quadratically in the size of the advertised lump-sum cash jackpot prize. With quadratic growth, the best time to play is when ticket sales are 1.25 to 2.5 times the jackpot odds, currently about 300 M to one for these two lotteries. Since ticket sales are not known to ticket buyers, we invert the regression function to prescribe the best time to play in terms of the cash prize. It turns out that these lotteries offer a (pre-tax) fair wager with positive expected value in a surprisingly wide interval of jackpot prizes. That is a good time to play; the best time is in the neighborhood of the nearly 1 $B record cash jackpot awarded in these lotteries in recent years.

KEYWORDS:

• lotto
• jackpot
• probability
• regression
• wagering
• optimization

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