Sheldon H. Jacobson: How to win the lottery without buying a ticket

Lotteries have become ubiquitous, available in nearly every state. The most recognized national lotteries, Mega Millions and Powerball, have jackpots that reach $1 billion a few times every year.

Of course, that payout is spread over 29 years, with the first year around $15 million and the final year around $62 million. Most winners opt for the lump sum payout, which is around $450 million. After taxes, depending on what state they live in, their take home winning will be around $300 million, certainly a large sum, but far off from the billion-dollar payout that the lotteries advertise to entice people to buy more tickets.

Many people dream to win the jackpot. Unfortunately for nearly every person who buys a ticket, such dreams are never realized. Some may say that it is just a few dollars, a cheap prize for entertainment and dreaming. The issue is whether just one ticket is purchased, or many are purchased for each drawing throughout the year.

The Powerball drawings are held every Monday, Wednesday and Saturday, while the Mega Millions drawings are held every Tuesday and Friday. This provides five opportunities every week to pick numbers and indulge in a dream.

So what is the payback for these indulgences?

Setting aside the jackpot, every $2 Powerball ticket returns around $0.32 on average amongst the non-jackpot prizes, while every $2 Mega Millions ticket returns around $0.25 on average amongst the non-jackpot prizes. Note that on April 8, the new Mega Millions will be launched, though the non-jackpot payback will be similarly skewed. Both these lotteries provide the raw data to make such computations, but do not advertise the resulting low returns for the non-jackpot prizes.

Such rational thought is not anything that regular lottery players think about. That is why as the jackpot grows, the number of tickets sold also grows. When the Powerball jackpot topped $1.32 billion on April 6, 2024, sales exceeded $217 million for that drawing, which was more than the total sales for the following nine drawings.

However, the jackpots are typically won just a few times per year. Banking on such rare events is not rational.

Some will say that if you do not buy a ticket, you can never win the jackpot. That is of course true. Yet the likelihood of winning the jackpot is so unlikely that focusing on it distorts what the actual payout for you will be, which are the non-jackpot prizes.

The case study to confirm this is Jerry and Marge Selbee. Jerry uncovered a loophole in Michigan and Massachusetts lotteries such that when the jackpot reached a certain level because it has not been won for several drawings, the non-jackpot payouts would be adjusted upward, making the expected payout per ticket positive for lottery players a few times every year. However, to exploit this advantage required them to literally purchase millions of tickets. Despite all such tickets bought, they never won the jackpots (as Marge noted in the movie “Jerry and Marge Go Large”), methodically winning the non-jackpot prizes for profit.

Given the negative expected non-jackpot payout per ticket, buying a ticket is equivalent to voluntarily paying a tax. Given that the majority of people who regularly purchase lottery tickets are on the lower end of the socioeconomic spectrum, this make such a tax highly regressive.

This means that every person who does not purchase a ticket is benefiting from each ticket purchased. It is providing additional revenue to state coffers, allowing some states to not raise income tax rates and to fund programs that would require revenue from other sources that may not be voluntary to residents.

So the best way to win the lottery is by never buying a ticket, even though that may not be as exciting as dreaming about the jackpot that you may win.

For those who remain unconvinced, remember the experiences of Jerry and Marge Selbee. No person, past or present, will ever buy as many lottery tickets in their lifetime as they did, yet they never won the jackpot. They were big winners not because of the jackpot that most people focus on, but on the non-jackpot prizes that were adjusted to give them an edge that no lottery provides today.

Sheldon Jacobson is a computer science professor at the University of Illinois Urbana-Champaign. He uses his expertise in risk-based analytics to address problems in public policy.