Powerball or Mega Millions: Which is better for you?

Both the Powerball and the Mega Millions lottery jackpots recently reached the $1 billion zones. When lottery jackpots soar to such lofty levels, ticket sales surge.   

For example, when the Mega Millions jackpot hit $1.35 billion Jan. 13, sales for that drawing exceeded 170 million tickets. More recently, on Aug. 4, when the jackpot hit $1.35 billion, the Powerball sales were more than 132 million tickets. The typical drawing attracts sales between 6 million and 12 million tickets. 

Lotteries are a tax on the poor. Most of the people who regularly buy lottery tickets are low income, who can ill afford the money spent. They may justify their purchase as entertainment, the chance to buy a dream for the impossible. Yet when thousands of dollars are being spent every year for lottery tickets, with around 40 percent of what they spend retained by the lottery agency and its partners, such entertainment can be quite expensive. 

Lotteries are designed to benefit the lottery agencies, not the lottery ticket purchasers. The Michigan couple who found loopholes in the Michigan and Massachusetts lotteries that enabled them to consistently win was due to an oversight by these lottery commissions in how they designed the lottery payouts, not due to luck.   

Unlike the Powerball and Mega Million lotteries, which increase the jackpot only when there is no jackpot winner, the Michigan and Massachusetts lotteries increased the lesser prize payouts, making the games’ expected return in favor of the lottery players, provided that someone bought enough tickets for the law of large numbers to kick in. The movie “Jerry & Marge Go Large” tells their story in an entertaining and informative way. 

When jackpots reach stratospheric levels, the biggest winners are the lottery agencies. With more tickets sold, they earn more revenue. The publicity that they get is priceless to them, all at no cost. 

Yet the likelihood of winning the jackpot is exceedingly small. Even Jerry and Marge Selbee, who purchased millions of tickets during their lottery escapade, never won the jackpot. 

So, what are the odds of winning the jackpot for the Powerball and Mega Millions lotteries? 

For the Powerball, there are 292,201,338 possible combinations, with just one matching the jackpot number. For the Mega Millions, there are 302,575,350 possible combinations. For both lotteries, almost two-thirds of the tickets bought will typically not match any of the numbers drawn.   

As more tickets are sold, and the jackpot increases, the payouts for the lesser prizes, or partial matches, remain the same. This was the loophole that Jerry Selbee uncovered, when their lotteries increased the payout for these lesser prizes, which flipped the expected payout for each ticket from negative to positive. 

What this means is that since winning the jackpot is unrealistic, most winners will come from the partially matched prizes. Since those payouts remain the same, independent of the size of the jackpot, the lottery agencies are the big winners when the jackpot soars, and the people buying lottery tickets are, I am sorry to say, the dupes. 

When comparing the two lotteries, excluding the jackpot prizes, the expected payout for a $2 ticket for Mega Millions is around 25 cents, an expected loss of $1.75.  For the Powerball, it is around 32 cents, an expected loss of $1.68. This makes the Powerball lottery a marginally better game to play, no matter what the jackpots are. Yet neither would be classified as a good investment.  

So, if a person buys five Mega Millions tickets for each drawing, they will spend $1,040 over the entire year and can expect a return of around $128. If they did this over a five-year period, they would have an expected net loss of more than $4,500.   

But if they took this money and put it into a money market account earning 4 percent, then over five years, they would have more than $5,600 in their account. The difference between the two is more than $10,000. 

If a person did the same with the Powerball lottery, they can expect a return of around $166 over an entire year, slightly better than the Mega Millions lottery.    

These are the numbers that the lottery agencies prefer you not to be aware of and thinking about when you buy extra tickets because of a billion-dollar jackpot. 

If the lottery agencies were kind, they would marginally raise the lesser prizes when the jackpot reaches higher levels, without you paying for this step up. Lotteries are legalized gambling; the “house” must always come out on top, which means that the expected winnings from each ticket must remain negative. Raising the lesser prizes would give a bit more back to those buying lottery tickets.  

Unfortunately, the lottery agencies make too much revenue during these times that killing their “golden goose” would be foolish and not in their best interests. 

For those of you who will buy even more tickets when the jackpots soar beyond $1 billion, know that you are being exploited by the lottery agencies. You are likely a willing participant in their charade, and they are a willing charlatan that entices you to do so.  

Good luck.     

Sheldon H. Jacobson, Ph.D., is a founder professor in computer science at the University of Illinois Urbana-Champaign. A data scientist, he applies his expertise in data-driven risk-based decision-making to evaluate and inform public policy.