How Many Lottery Combinations Do You Need to Guarantee a Jackpot?
There’s a Surefire Way to Win a Jackpot. But Is It Worth It?
You know that the odds of winning a lottery jackpot are sky-high, right? Well, that’s only kind of true. There are a limited number of possible winning numbers, so the odds of hitting a jackpot can be 100% if you buy enough lottery combinations. But how many ticket combinations would you have to buy? How much would you have to invest to do it? And would your investment be worthwhile?
The (Only) Guaranteed Way to Win a Powerball or Mega Millions Jackpot
Lotteries like Powerball or Mega Millions differ from sweepstakes because the winner isn’t randomly drawn from all of the qualified entries. Instead, entrants play by buying a ticket with a combination of numbers, and one of those combinations is drawn as the jackpot winner.
That means that the chances of winning are fixed and that they aren’t influenced by how many people buy tickets. Because there are a fixed number of lottery combinations, a very determined entrant with enough money at their disposal could buy every single possible combination and guarantee a jackpot win.
Take the Powerball lottery, for example. To win the jackpot, you need to have a lottery ticket with the correct combination of five white balls and the red Powerball. There are 69 possible numbers for the white balls and 26 possible results for the Powerball. Thus, the odds of picking that perfect combination with a single ticket are one in 292,201,338.
Each Powerball ticket costs $2. That means you could buy all the possible combinations of tickets for $584,402,676.
You can also guarantee a jackpot win for Mega Millions. For Mega Millions, you need to have a lottery ticket with the correct combination of five white balls and the Mega Ball. The five white balls have possible numbers ranging between 1 and 70, while the Mega Ball can be between 1 and 25. That means you need to cover 302,575,350 combinations to guarantee a jackpot.
Mega Millions tickets cost $2 each so covering all combinations would cost $605,150,700. In some regions, you can also buy a “jackpot only” ticket that covers two combinations for $3. That means that if you want to guarantee a jackpot for the lowest possible investment, you could do it for “only” $453,863,025.
Given that some of the largest lottery jackpots can reach a billion dollars or more, that doesn’t seem like such a bad deal, right? But of course, it’s not that easy.
Does It Make Sense to Buy All Possible Lottery Combinations?
While covering all of the possible combinations takes an astounding of money, some of the biggest lottery jackpots have advertised jackpots that outstrip what you’d need to pay to win them. Powerball’s biggest jackpot to date was advertised at $1.5 billion. Tripling your investment on a guaranteed jackpot sounds pretty good, doesn’t it?
The problem is that, while you can guarantee a jackpot win, you can’t guarantee that you will end up with a profit. Even with an advertised jackpot bigger than the amount you’d have to invest, there are costs that will eat into your earnings.
First of all, you might have to split the jackpot with other winners. In the case of Powerball’s $1.5 billion jackpot, there were three winning tickets. That means even the simple math of $1.5 billion divided by three winning tickets would have brought the value of the prize below the $584,402,676 in ticket combinations you would’ve had to pay to guarantee the win.
But you have to do more than simple math to find out what you will net when you win the lottery. For one thing, you have to pay taxes on those winnings. You can expect to pay at least 25% in federal taxes on your prize, and you might be responsible for state taxes on your jackpot as well, Depending on the state you live in, that could add up to another 8.82% that you need to pay to the government.
Next, you’d have to consider whether you’ll take the lump-sum or annuity payout. You’ll only get the full advertised amount of the jackpot if you take the annuity option, but that means that you will have to wait 30 years until you see your return on investment. There are many other ways to invest half a million dollars that could be more profitable and offer more liquidity.
If you take the lump-sum payout, you’ll receive significantly less money. In the case of the $1.5 billion Powerball jackpot, each of the three winners took the lump sum and received $327.8 million instead of $500 million.
So far, the largest jackpot won by a single person was a $758.7 million dollar Powerball jackpot. Even then, the winner only walked away with $336 million after taxes and the lump-sum reduction, far less than it would have cost to buy all possible lottery combinations.
Finally, there are a number of things that you should do before you cash in a major lottery win, including hiring lawyers and accountants to protect your interests. Hiring good people is important, but it costs money, further eating into your jackpot profits.
Can the Jackpot Get Big Enough to Be Worth Buying All Combinations?
So maybe a $1.5 billion jackpot isn’t enough to be worth buying all of the possible ticket combinations. But jackpots can grow ever larger than that, can’t they?
Well, kind of, but not really. As jackpot values rise, lottery fever kicks in and more and more people buy tickets. The more tickets get sold, the higher the chances that all possible combinations will be covered. So before the jackpots get close to big enough to be worth buying all the tickets, someone will almost certainly buy a winning ticket.
While you can guarantee a lottery jackpot given enough money, it rarely works in your favor. And the chance of a lottery jackpot getting big enough to ensure a good return on your investment is slim. When the $1.5 billion Powerball jackpot was won, lottery fever was so high that 89 percent of all possible combinations had been purchased. It’s highly unlikely that a Powerball jackpot will ever get much higher than that.
There are better strategies to win the lottery than tying up a half a million bucks in lottery tickets. Treat the lottery as it’s intended: a game, not an investment strategy. Buy a single lottery ticket any time the jackpot soars over $350 million, which is the point at which the risk becomes worth the $2. Then cross your fingers, hope for good luck, and have fun with the results.You can guarantee a jackpot win by buying enough lottery ticket combinations. But how much would it cost to do it, and is the result really worth it?
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. ]]>