We can think of 3 major problems with buying 292,201,338 lottery tickets with every combination of Powerball numbers

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 partially match 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 we’ve bought every ticket exactly once, we can see how much we will win based on the jackpot and the smaller prizes:

Indeed, this is something of a low-ball 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 extra complications to this project.

### Actually buying 292 million tickets

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 possible Powerball tickets 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.

### Splitting the jackpot

The second and larger problem with our comprehensive Powerball scheme is the risk of splitting the jackpot. While the fixed prizes do provide about $93 million of our winnings, the overwhelming bulk of the money comes from the big prize.

That would mean splitting the jackpot two or more ways with other players would be absolutely devastating to our plan. A two-way split cash-prize jackpot 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 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 6 drawing in which there were no winners, paving the way to the current insanely 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% chance that we would be the only winner.

We could also expect that, with the over a billion-dollar headline prize, 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:

### Other people trying the same thing we are

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 US 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. This situation is similar to the game Chicken, in which two drivers start out driving directly at each other. If one driver swerves while the other keeps going straight, the first driver “loses” and the second driver “wins.” If both drivers swerve, the game is a draw. Naturally, if both drivers keep going straight, their cars crash and they die in a fiery wreck.

In Chicken, the strategy you adopt depends on what you think the other driver is going to do — assuming you’re actually playing something as reckless and stupid as Chicken in the first place. If you think he’s crazy enough to keep barreling forward, you should be more likely to swerve. If you believe, on the other hand, that he’s going to veer out of the way first, then you might be more likely to keep driving straight.

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.

On the one hand, you would definitely win the jackpot. On the other, you'd probably have to share it. ]]>