FINDING GOOD BETS IN THE LOTTERY, AND WHY YOU SHOULDN’T TAKE THEM

Abstract. Should you invest in the lottery? The recent Mega Millions and Powerball lottery jackpots of more than $300 million have made us wonder: When, if ever, is it a good idea to buy lottery tickets? Some lottery drawings do indeed have a positive rate of return. We use a little elementary calculus to give general criteria for lotteries to have positive or negative rates of return. We then use a little economic theory to show that buying lottery tickets is generally not a good investment, even when the rate of return is spectacularly good. Everybody knows that the lottery is a bad investment. But do you know why? How do you know? For most lotteries, the obvious answer is obviously correct: lottery operators are running a business, and we can assume they have set up the game so that they make money. If they make money, they must be paying out less than they are taking in; so on average, the ticket buyer loses money. This reasoning applies, for example, to the policy games formerly run by organized crime described in [13] an