What If You Bought All 292 Million of the Possible Powerball Combinations?

A very weird thought experiment

Alan Diaz / AP

At the time of this writing, the Powerball jackpot is up to $1.5 billion. The cash grand prize is estimated at $930 million.

In a Powerball draw, five white balls are drawn from a drum with 69 balls and one red ball is drawn from a drum with 26 balls. If you match all six numbers, you win the jackpot. If you match only some of the numbers, you win a smaller fixed prize.

There are 11,238,513 ways to draw five white balls from a drum of 69 balls. Multiply that by the 26 red balls, and there are a total of 292,201,338 possible Powerball tickets.

At $2 for each ticket, then, it would be possible to buy every possible ticket for $584,402,676. As a journalist, I don’t have that much money sitting around, but either a consortium of a few million Americans or a large and wealthy institution like a bank could conceivably assemble that level of cash.

With the sky-high jackpot in play, this actually at first glance guarantees a profit—at least before taxes. Since in this scenario we’ve bought every ticket exactly once, we can see how much we will win based on the jackpot and the smaller prizes:

The Powerball Drawing’s Possible Outcomes, and Prizes If You’ve Bought Every Ticket Combination
Andy Kiersz, Business Insider | Data: Powerball.com, Business Insider

Indeed, this is something of a conservative estimate. As we are buying another half-billion dollars’ worth of tickets, part of that money will be added into the jackpot pool.

Of course, there are a few complications to this project.

The first problem is the actual physical act of buying 292 million Powerball tickets and filling them out by hand. Since we need to very carefully and systematically make sure we get every possible ticket, using the computer-generated random quick draw will not work for us.

According to Statista, JPMorgan Chase Bank has about 189,000 employees. That means that there are about 1,546 Powerball combinations for each employee. If each employee spent 10 hours a day buying and filling out Powerball tickets for three days, this would mean each employee would need to fill out about 50 tickets per hour. So while this would be extremely difficult to do and perhaps not the best use of a large organization’s resources, it seems that it might be physically possible, if somewhat grueling, to actually buy every Powerball ticket.

Similarly, a large, decentralized consortium of several thousand or a few million Americans connected over the Internet—something like an office Powerball pool on a mass scale—would be physically capable of buying 292 million lottery tickets. Of course, the logistical coordination of such a consortium would be a daunting task, and one could imagine various legal and practical difficulties with distributing the money after the drawing.

The second (and larger) problem with this Powerball scheme is the risk of there being multiple winning tickets. While the fixed prizes do provide about $93 million of our winnings, the bulk of the money comes from the big prize.

That would mean splitting the jackpot two or more ways with other players, which would be absolutely devastating to our plan. A  cash-prize jackpot split two ways would give us $465 million before taxes. Adding in the fixed prizes, we get a total of about $558 million in winnings, which is now less than the ticket costs of about $584 million, leaving us with a loss of nearly $26 million.

The likelihood of splitting the pot is determined by how many other tickets are sold. Business Insider looked at this after the January 6th drawing, in which there were no winners, paving the way to the current high jackpot. Following the logic from that post, we can estimate our odds of getting the jackpot alone based on a few guesses about ticket sales.

According to LottoReport.com, a site that tracks lottery sales and jackpots, 440,321,172 tickets were sold before Saturday’s drawing. With that many tickets sold, and under the assumption that everyone else playing Powerball is picking numbers more or less at random, and independently from each other, there's just a 22 percent chance that we would be the only winner.

We could also expect that, with the headline prize over a billion dollars, even more tickets will be sold before Wednesday's drawing, greatly hurting our chances of walking away with the full jackpot without having to share:

The Likelihood of Avoiding a Split Pot vs. Number of Tickets Sold
Andy Kiersz, Business Insider | Data: Powerball.com, Business Insider

The above analysis of our odds of splitting the pot assumed that all the other tickets sold were to normal people who would choose their numbers more or less at random. But seeing as we are going all in and buying every ticket, it's possible that someone else could be attempting this as well. There are, after all, several organizations in the U.S. that have the financial and personnel resources to theoretically go out and buy 292 million Powerball tickets.

Of course, if two or more banks or consortia tried this plan, they would be certain to have to split the pot and thus lose a bunch of money. Banks or billionaires with thousands of employees that are considering buying every Powerball ticket need to make a similar consideration. If there's a low likelihood that a competitor is going to also mobilize a small army of people in a bid to win a historically high lottery jackpot, then perhaps that risk is worth taking. If, on the other hand, we think that there might be not just one but several other wealthy organizations or people that are making similar plans to our own, we should stay out of the fray.

This article appears courtesy of Business Insider.