How Many Lottery Combinations Must You Buy to Guarantee a Jackpot?

You know that the odds of winning a lottery jackpot are sky-high, right? Well, that's only kind of true. The number of possible winning numbers you can choose is limited, so you can actually get your odds of winning the lottery to 100%, guaranteeing you'll win a jackpot. All you have to do is buy one ticket for every possible lottery combination.

So how many ticket combinations would you have to buy? How much would you have to invest to do it? And would the 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 buy a ticket with a combination of numbers. At a specific time, a winning combination is drawn from among all the potential winning numbers. Any tickets with all those numbers win the jackpot.

That means that the chances of winning are fixed. They aren't influenced by how many people buy tickets, or any other factor.

Because the number of lottery combinations is limited, a wealthy and determined entrant with enough money at their disposal could buy every 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 — just under $585 million. 

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 also cost $2 each, so covering all possible combinations would cost $605,150,700.

Now of course, if you have a $40 million lottery jackpot, spending half a million dollars or more buying tickets would be foolish. But some of the largest lottery jackpots can reach a billion dollars or more, which doesn't seem like such a bad deal.

So should you try to buy all of the lottery combinations when the jackpots are at their highest values? 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. Nearly tripling your investment on a guaranteed jackpot sounds pretty good, doesn't it?

Here's the problem. While you can guarantee a jackpot win, you can't guarantee that you'll end up with a profit. Even with an advertised jackpot bigger than the amount you'd have to invest, there are costs that eat into your earnings. Here are some of the reasons why guaranteeing a lottery win doesn't make sense.

There Might Be Other Winners

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 purchases you would've needed to buy every combination and guarantee the win.

Paying the Taxes

But you have to do more than simple math to find out the profit you'll make 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.

So if you win a billion-dollar jackpot, the taxes could easily bring your winnings down to $600,000 or less, meaning you're not making a lot of profit even without splitting the win. However, winning a billion-dollar jackpot still doesn't mean you take home a billion bucks, even before taxes, as you'll see next.

Lump-Sum or Annuity Payment

Next, you 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 — which means that you 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. As you can see, this means that you'd take a loss on that big win.

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 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 the "normal" way.

Conclusion

While you can guarantee a lottery jackpot given enough money, doing so is unlikely to work in your favor. 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% 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 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.