One Powerball ticket is the difference between having a 1-in-292,201,338 chance of winning the now-$1.5 billion jackpot, or no chance at all.
Buy any more tickets than that and you're likely wasting money.
However, the one-ticket strategy makes less sense if you have untold riches to spend and power to put it to use.
That's because there is a 100% guaranteed way to hit the jackpot: Buy all possible number combinations before Wednesday evening's drawing.
How this works
Powerball changed its ball-drawing setup in October 2015.
Its machine used to suck up five white balls from a bin of 59 balls, each with a different number, plus one red Powerball from a bin of 35 different balls.
Today it's 69 white balls and 26 red balls. To take home the jackpot, your ticket must have the same five white numbers — order doesn't matter — and the one red number.
If you do the math, there are 11,238,513 possible combinations of five white balls without order mattering. Multiply that by the 26 possible red balls, and you get 292,201,338 possible Powerball number combinations. (Powerball's recent changes make it about two times harder to win the jackpot, yet easier to win a small amount of money.)
At $2 per pick, you'd need $584,402,676 to buy every single combination and guarantee a win.
But assuming you're filthy rich, think this out for a moment.
The Powerball draws only twice a week: Every Wednesday and Saturday. So how are you going to print that many tickets in less than four days? And just how do you plan to ensure each combination is different? And that no one walks off with your money?
Raise an army
First, you'd need an army of trustworthy people at thousands of locations across the country, sucking the Powerball ticket-printing machines dry.
You'd also need state, regional, and local coordinators to keep everything streamlined, and good technology to verify every number requested is different. Plus scary-sounding contracts to make sure none of your workers walk off with your winnings.
You could save some time by maxing out the number of picks per ticket — 10 per slip of paper, by our estimate — but you'd still have to make those picks and print 29,220,134 tickets.
If you could somehow hire a more than 10,000 trustworthy people to drop into 10,000 bodegas, grocery stores, and gas stations across the US, each worker at eaxch location would have to print 2,922 tickets. Better hope the stores don't run out of Powerball ticket paper and their machines don't break.
Now you have nearly 30 million slips of paper. You can't trust your workers to correctly enter all of those numbers manually into a spreadsheet, so you'd ask them to photograph them all and upload the images to a central database. You'd need about 60 terabytes of data storage, minimum, for 2MB per image.
Next you'd have to pay for some supercomputer time, then use it to run an artificial intelligence program that can recognize and catalog all of those numbers. This way, you know which bag of tickets from the 10,000 locations has the winning ticket inside.
You can't leave the physical tickets with anyone after the drawing, though, so right after your workers finish photographing them all, they'd have to express-mail them all to a secure warehouse. Each bag or box of tickets would have the location's name on the box or bag, so you can efficiently claim your prize after the winning numbers come out.
And so on.
Yes, there are catches
Even if you're able to orchestrate such an operation, you're still not guaranteed to win the current estimated $1.5 billion jackpot — before paying your army and before taxes, that is.
You also have to weigh the risk that one or more other people got the winning combination for that draw, splitting the jackpot. Although you'd dramatically raise the jackpot by buying so many tickets, and you'd pick up all of the lower-tier cash prizes, just one other jackpot winner could leave you $26 million in the red. (Business Insider quant reporter Andy Kiersz dutifully crunched the numbers on this.)
At the end of the day, buying out the lottery isn't practical. Yet buying just one ticket, especially now, does seem to make some economic sense.
Two dollars won't break the bank, for one, and we re-crunched the numbers on the estimated value of buying one Powerball ticket. With $1.5 billion at stake, conditions are more favorable: It's now about $0.87 after taxes if you take an annuity payment. (This was -$0.14 when the jackpot was $1.3 billion.)
