Record $1.5B Powerball: Know the Math

The Powerball drawing is at 10:59 p.m. EST on Wednesday.

The record-breaking $1.5 billion Powerball jackpot is the stuff of dreams, but it all boils down to math. From the huge prize to the enormous odds against winning it, Wednesday night's drawing is a numbers game that gives players good reason to brush up on their algebra, maybe as they stand in line to buy a ticket. A look at some of the statistics:


For those who match all five white balls and the red Powerball, the key numbers are the $1.5 billion jackpot, paid out over 29 years or as an immediate $930 million in cash payment. But 39.6 percent of the lump sum would go to federal income taxes.

"Almost everyone chooses the lump sum, but you do take a pretty significant hit," said Mark Luscombe, principal federal tax analyst for Wolters Kluwer Tax & Accounting. "I guess people just feel they can do better than waiting 30 years to get all their money."

To breakdown that 39.6 percent tax on the lump sum: the U.S. government automatically withholds 25 percent of such large prizes and the remaining 14.6 percent would be paid in federal taxes during the April 2017 tax season. That leaves about $561.7 million, according to CNBC.

Plus, most states would take a chunk, potentially cutting off another 15 percent.

That's unless you're a resident of Florida, South Dakota, Texas, Washington or Wyoming where there is no personal income tax. California, New Hampshire, Pennsylvania, and Tennessee generally exempt lottery winnings from income taxes.


To put it gently, not good. The odds of winning Wednesday's jackpot are one in 292.2 million. There are 292.2 million possible combinations of the five white balls and red Powerball. That's where the one in 292.2 million odds comes from, and they stay the same regardless of how big the jackpot grows or how many people buy tickets. Realistically, you were really, really, really unlikely to win. One hopeful thought: Scott A. Norris, an assistant professor of mathematics at Southern Methodist University, says your tiny odds improve a bit if you let the computer pick your numbers rather than choosing yourself.


No one has won the Powerball jackpot since early November, which is why the prize has grown so large. The bigger prize entices more people to buy tickets, and that drives up the jackpot. The increased ticket sales also make it more likely there will be a winner, simply because all those extra tickets mean more number combinations are covered.


Your odds increase with additional tickets, but it's important to keep in mind how small they are to begin with. If you have a 1 in 292.2 million chance of winning with one ticket, you have 10 times the odds if you buy 10 tickets. Yet the probability is still incredibly small.

"The odds are so astronomically small that even 100 times that number is exceedingly unlikely to win," Norris said. "It's probably still not going to happen if you buy a hundred tickets or a thousand tickets or even a million tickets."

If you have extra cash and are thinking of buying all possible number combinations, that is allowed, but it wouldn't be very smart. At $2 a ticket, the strategy would cost about $584 million, and when taxes are subtracted, you'd end up losing money.

And if someone else had the winning numbers, you'd need to split the prize. You'd make back some of that money by smaller prizes paid for matching three, four or five of the balls plus the Powerball, but chances are it still wouldn't be a good bet.

Some people feel that pooling their money with co-workers will improve their chance of winning — but with such tiny odds, adding 50 or 100 chances doesn't give you a leg up. And if your group is lucky, lottery officials recommend preventing hard feelings by putting in writing how you plan to split the prize, since it's easy for misunderstandings to crop up when hundreds of millions of dollars are at stake.


Despite the odds, someone will eventually win the prize. What then? Is it better to take the money as an annuity or in cash?

Olivia S. Mitchell, a professor of insurance and risk management at the Wharton School at the University of Pennsylvania, said to avoid the risk of overspending or an investment mishap, a safe option would be to take the annuity, guaranteeing a huge annual payout for three decades.

"We know the average American is quite financially illiterate," Mitchell said.

For those who want to invest the money themselves, Mitchell suggested setting aside part of the cash option to buy their own annuity that would give them a guaranteed income in case the return on the money they do invest comes up short.

"That way, you still might not beat what the state pays," she said. "But on the other hand, you've protected your basic consumption needs."

Copyright AP - Associated Press
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