So, you want to win the lottery.

The odds are, of course, against you. That’s how a lottery works, after all. Your chances of winning a Powerball lottery vary, currently, you’re looking at about a 292-million-to-1 shot for the grand prize. If you want to walk away with a relatively paltry $1 million, your chances are much better: about 1 in 11.68 million.

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But there’s good news: you can, technically, improve your chances of winning the lottery, and not just by buying extra tickets. How? Well, simple math…along with a bit of not-so-simple math.

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We’ll guide you through the process, but first, keep in mind that while the lottery is a fine diversion, it’s not exactly a retirement plan. As long as you can remember that important principle, you can stand a slightly better chance than the next Powerball player (even if you’re still basically guaranteed a loss).

1. Buy a single ticket per drawing.

Okay, we’ll admit that if you buy more tickets, you have a higher chance of winning, but if you’re trying to determine how to get the most value from your purchase, buying a single ticket actually makes sense.

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Picking up a single lottery ticket will only increase your chance of winning slightly; you’ll stand a 0.000000003 percent chance, rather than a 0 percent chance. On paper, this might not seem like much of a gain, and…well, it isn’t.

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However, let’s leave practicality out of it. From a purely mathematical standpoint, you’ve just taken the one step that realistically improves your chances of winning. Buy two tickets, and you’ve got a chance of 0.000000006—statistically speaking, that’s not a gain, depending on where you round, and certainly not as much of a gain as that first ticket. In a purely technical sense, buying a single ticket makes sense.

If that’s not doing it for you, don’t worry; we’re just getting started.

2. Don’t worry about picking the same numbers every time.

It’s every lottery player’s nightmare: The one week you decide to switch up your lucky numbers, your old numbers come up. If only you’d listened to conventional wisdom and played the same ticket! Except that makes no sense.

It’s a well-known perception error called the gambler’s fallacy. Basically, it’s incorrect to assume that you have a higher chance of winning simply because your numbers haven’t come up yet.

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To understand the fallacy, consider a coin flip. The coin has an equal chance of coming up heads or tails, regardless of how many coin flips you’ve executed. Over time, the coin flips will probably average out to 50 percent heads, 50 percent tails, but those percentages mean nothing in the single flip of a coin.


The lottery works the same way, since the numbers are supposedly random. But wait…are they random?

3. Yes, Powerball is truly random…sort of.

Those plastic balls in the Powerball machine aren’t just for show. They actually play an important role in keeping the Powerball truly random.

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This is because computers have a really tough time generating random numbers. To do so, they need to choose numbers, and by making these determinations according to a pattern, they eliminate randomness. The programming of the computer will prevent any truly random number from being chosen. Even when computers use unpredictable processes to determine numbers—for instance, atmospheric noise—there’s a slight preference towards larger numbers.

The good news is that modern programmers have gotten really, really good at simulating randomness, and for most applications, “pseudo-randomness” is perfectly fine. But that’s not good enough when you’re talking about distributing billions of dollars, since if someone gamed the system, they’d be making off with an incredible jackpot. That’s part of the reason that the Powerball still uses those balls; they’re technically more truly random than, say, the Quick Pick numbers, which are generated by computers.


Now, this isn’t to say that lotteries are always random. The weight of the balls, for instance, can influence the results, but high-jackpot lotteries like Powerball always weigh their balls carefully to ensure as close to a random result as is possible.

4. When a lottery adds new numbers, you actually should change your numbers.

Yes, we’re walking back what we said two sections ago, but for a very good reason.

Any set of valid numbers should have the same chance of winning the lottery, but in an ideal scenario, you’d want to be the only person who wins. After all, you don’t want to split your money with anybody else.

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When a lottery adds new numbers—usually as a way of drumming up press while decreasing the odds of a jackpot—people are slow to adapt. That’s because they’re victims of the gambler’s fallacy, which we referenced earlier; they believe that their old numbers will eventually win. They ignore the new numbers, and as a result, those new numbers have a higher chance of a solo jackpot.


That’s why you should avoid playing common lottery numbers, like the numbers from Lost or any numbers in a sequence. You want to maximize your winnings, since your chances of winning are so incredibly low in the first place.

5. Historically, certain numbers have come up more or less often than others.

But that means absolutely nothing, for the same reason that the hypothetical coin flip from earlier meant nothing. The lottery is random, but that doesn’t mean that a specific set of numbers can’t come up multiple times.

In fact, if the next seven Powerball drawings were the exact same numbers, it still wouldn’t mean anything (other than the breakdown of the lottery system and mass chaos, since people would reasonably believe that the system was rigged).


So, keeping that in mind, what numbers come up more often?

Dr. Min Su Kim, professor of statistics at Southern University, studied Powerball numbers over 10 years and determined that the most frequently picked numbers are 20 and 6. The most frequently picked white balls are 26, 41, 16, 22, 42, 35, and 39. With that said, Dr. Kim admits that he doesn’t play the Powerball. Why?

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I learned statistics and probability, he told WAFB News.

6. You could not even guarantee a profit by purchasing every single available ticket.

This is where the math gets mind-blowing. Get ready for some big numbers.

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There are 292,201,338 Powerball combinations, regardless of the jackpot. At the time this article was written, the jackpot was $478 million; to guarantee a win, you’d have to buy every number combination. At $2 per ticket, you’d spend over $584 million.

But what about the really huge jackpots? The cost of a ticket doesn’t go up with the jackpot, and neither do your odds, since you’ll always use the same pool of numbers.

Here’s where you might use the math to your advantage. The biggest jackpot in Powerball history was $1.586 billion, which is certainly enough money to buy every ticket combination and guarantee a profit.


Well, almost. Here’s the thing: large jackpots attract more players, greatly reducing your chances of walking off as the sole jackpot winner. The $1.586 billion jackpot was split by three winners, so each won $528.8 million.

Realistically, that wouldn’t be enough money to buy every ticket, since you’d also need to fill out each by hand—that would either mean hiring a ton of people or tricking a college into sending you millions of interns, so we can cross this plan out.

This starts to show the size of the lottery pool, which is difficult to conceptualize, and it brings us to our final and most important point.

7. Recognize the forces working against you.

You will not win the lottery. Statistically, it’s just about as close to impossible as it gets.

“But wait,” you say, “somebody has to win.”

No, that’s not actually true; nobody has to win, and in many lotteries, nobody does. That’s how the jackpot keeps growing. Eventually, someone will win, but that’s just because of the sheer number of people playing.

The biggest issue is that we have trouble visualizing big numbers, so we’ll try to help. Picture the crowd at Super Bowl 50. That was about 71,000 people. Here’s a visual.

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Fill up that stadium 4,115 times, and you’ll get close to the number of possible entries in a single Powerball contest. However, to be the sole winner, you’d have to beat out the 300 million people who buy tickets in heavy jackpot drawings. Fill up the stadium 4,225 times to visualize that number.

Not working? Don’t feel bad. The human brain isn’t built to handle numbers of this size, which is why we all think that we’re different. We know that we’ll win the lottery if we buy a ticket, because when we’re filling out the lottery card, we can envision it happening.

Sadly, the math doesn’t care about your feelings. If you want a true mathematical advantage, buy a single ticket. Past that point, there’s absolutely nothing you can do.

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Oh, but try playing your dog’s birthday. That seems to work.