A ticket showing previous Powerball lottery winning numbers sits on the counter at a 7-Eleven store on August 7, 2013 in Chicago, Illinois. Photograph by Scott Olson/Getty Images
A ticket showing previous Powerball lottery winning numbers sits on the counter at a 7-Eleven store on August 7, 2013 in Chicago, Illinois. Photograph by Scott Olson/Getty Images

My mother could have been one of the winners of this week's $448 million Powerball jackpot.

True, she died 35 years ago. But she was a player. She liked to buy her lottery tickets at the Maine State Liquor Store -- something of a test of wills for a recovering alcoholic, but hey, you can't give up everything. And for a lately divorced Boston Brahminette of slowly declining fortunes, I guess that once-a-week shot at free money was worth staring down all those bottles.

She was also the kind of more affluent buyer that lotteries need to attract more of. You know the rap: Lotteries are a horrible regressive tax on the poor and uneducated. There's plenty of research to back that up, as well as plenty of spectacular post-win crack-up stories. One of my favorite fallacies is the tendency to buy more tickets at a store that has sold a winning ticket: According to one 2005 study, stores that sell a winning jackpot ticket "experience relative increases in ticket sales of the winning game between 12 and 38 percent the following week."

The research also shows, however, that the bigger the jackpot, the more affluent the ticket buyers. One 2004 study by Emily Oster, now an economist at the University of Chicago, actually projected (with the usual academic caveats) a jackpot size at which Powerball becomes progressive: around $806 million.

Oster looked at buyers of Connecticut state lottery tickets by zip code and found that as the size of the jackpot grew, sales increased in richer areas: in fact, "at the highest jackpot levels the poorest 20% contribute only about 19% [of state sales] and the richest contribute close to 32%." She suggested that "fewer games, with longer odds and higher jackpots, could allay some fears about regressivity."

So come on all you state governments struggling to pay your pensions, bring on that billion-dollar jackpot.

(James Gibney is a member of the Bloomberg View editorial board. Follow him on Twitter.)