How the Lottery Works, and Is It Worth Playing? | Personal Finance

If you’re thinking of playing the lottery, it’s a sure bet that you know your odds of becoming a millionaire are not good.

But that never stops anybody from playing. According to the North American Association of State and Provincial Lotteries, during fiscal year 2019, the year for which the most recent numbers are available, U.S. lottery sales totaled over $91 billion.

There is a lottery in 45 states and the District of Columbia and Puerto Rico and the U.S. Virgin Islands. Every Canadian province also has its own lottery. Canada sales in 2019 reached over $10 billion. Around the world, at least 100 countries have their own lottery.

But how does the lottery work, and is it worth playing? We’ll gamble that you’re interested in finding out.

How Does the Lottery Work?

In a nutshell, it’s pretty simple. People spend some money – usually $1 or $2 but sometimes more – on a lottery ticket, which has a set of numbers on it. Usually once a day, the lottery – typically run by a state or city government – randomly picks a set of numbers. If your set of numbers matches the numbers on the lottery ticket, you win some of the money that was spent on the lottery tickets, and the state or city government gets the rest.

Mega Millions and Powerball are the big multistate national lotteries that get the most news attention, but there are a slew of multistate lotteries out there, like Cash Five, Lucky for Life and Cash4Life.

What Are the Odds of Winning the Lottery?

Harvey Langholtz, professor of psychology at William & Mary, teaches both psychology of decision making and psychology of decision theory, which is a study that uses mathematics, philosophy, statistics and psychology when determining how decisions are made.

He says the odds of winning are a bit different depending on the lottery, but points to the Powerball as a good example of how daunting it can be for someone to win.

“As stated on the Powerball website, chances of winning are 1 in 292 million,” Langholtz says.

In order to beat those odds, you have six numbers to guess, five numbers from 1 to 69 and one red Powerball number from 1 to 26.

Langholtz explains the math behind that:

  • “The likelihood of someone correctly guessing the first of the five white balls is five (because there are five numbers that will turn out to be right) out of 69, or 5/69,” Langholtz says.
  • “The likelihood of guessing the second, given that the player has correctly guessed the first, is four (only four remaining that will turn out to be correct come the time of the drawing) out of 68 (because you already eliminated one of the original 69). So that works out to 4/68.”
  • “And the likelihood of then correctly guessing white balls three, four and five, are 3/67, 2/66, and 1/65.”
  • “And the likelihood of a player guessing the correct number on the one red Powerball is 1/26. So what is the probability of guessing all five white ball numbers and the red Powerball number? It is 5/69 x 4/68 x 3/67 x 2/66 x 1/65 x 1/26 or 1/292,201,338.”

That’s all that needs to happen for the math to work out in your favor. So the chances are truly slim, although Langholtz says the lottery typically does grant smaller payouts for partial correct guesses.

How Are the Odds of a Lottery Calculated?

Again, math is involved, and it helps to understand what a factorial is. In a nutshell, a factorial is the total you get after multiplying a number against all the numbers below it. For instance, a factorial 3, which would be written as “3!,” is equal to 6. You multiply 3 times 2 times 1, and you get 6.

Dave Gulley, who teaches economics at Bentley University in Waltham, Massachusetts, and who has done research on the lottery says that if you think of the game Mega Millions, you have five numbers that are drawn from a pool of numbers from 1 to 70.

“How many different combinations of five numbers can be drawn from a pool of 70?” Gulley asks.

Well, he says that to figure that out, you can use the formula: 70! divided by (5! times 65!)

“The “!” is read as ‘factorial,’ so 5! Is five factorial,” Gulley says. “5! is calculated as 5 times 4 times 3 times 2 times 1, equals 120.”

He says that 70! is 70 times 69 times 68 times, and so on, until you get to multiplying the numbers by 1.

And 65! Is 65 multiplied by 64 multiplied by 63, and so on.

“Factorials are super useful for figuring out how many combinations of particular events can occur,” Gulley says.

And once you do the calculations for Mega Millions? “This means that someone who plays one ticket has a 1 in 302,103,014 chance of winning the jackpot,” Gulley says.

What Are My Odds of Winning the Lottery – Compared to Other Events?

Of course, the odds of winning a lottery become even more daunting when you stack them up against other events, most of these that you definitely would not like to have happen. Not to rain on anybody’s parade, but all of the following scenarios are more likely to happen to you than winning Powerball or Mega Millions.

  • You have a 1 in 18,043 of being struck by lightning in your lifetime, according to the Lightning Safety Council.
  • You have a 1 in 4,332,817 chance of being attacked by a shark, according to the International Shark Attack File.
  • You have a 1 in 2.1 million chance of being attacked by a bear, according to the National Park Service.
  • You have a 4 in 1,000 chance of having your taxes audited, according to TRAC-IRS, a comprehensive, independent and nonpartisan website about the Internal Revenue Service.
  • You have a 1 in 12,000 chance of making a hole-in-one, although the odds of making a hole-in-one drop to 1 in 3,000 if you’re a professional golfer, according to the National Hole-in-One Registry.

What Are Some of the Best Lotteries to Play, Given the Chances?

There are so many lotteries, and with no guarantees of winning any of them, it’s impossible to steer anyone to any one lottery with much confidence. Still, there are a couple things to consider when you play the lottery if you want to improve your odds of winning.

Your best bet is to play a lottery where the payout is small. Fewer people playing generally means your odds of winning are higher. Of course, if you focus on lotteries that aren’t as popular, that may mean you take yourself out of the running of winning $300 million or any of the larger prizes.

You also would do yourself a favor to read about the odds; the lotteries generally should have that information somewhere on their website or fine print. For instance, some scratch-off ticket lottery games have pretty decent odds. Derek Smith, a professor of mathematics at Lafayette College in Easton, Pennsylvania, who teaches classes about gambling in society, points out that the scratch-off games in Pennsylvania is Ghost$ and Goblin$, which lists the overall chances of winning any prize (not just the top prize) as 1 in 4.61.

Still, even with these particular scratch-off games, your odds still may not be quite as good as it would seem.

“One of the prizes can be a free ticket,” Smith says. “But what does that actually get you? Just a chance to be in the same position you were before you scratched the first ticket.”

Gulley has another suggestion for those who want to improve their odds of winning the lottery.

“The best advice for people who want to play these games is to wait for the biggest jackpots and to pick combinations of numbers that have at least one or two numbers bigger than 31,” Gulley says. “This is because some people choose numbers based on birthdays or other relatively low numbers. Picking larger numbers won’t increase their chances of winning but will reduce the chance of having to share the jackpot with other winners.”

Knowing What We Know About the Lottery, Why Do So Many People Play It?

Odds are, if you play the lottery, you’re going to lose. So why do people play it? There are a lot of reasons, according to experts.

  • The lottery provides players with hope. Langholtz says that “hope against the odds” is a big driver of people playing the lottery. “People may not be interested in calculating the probability of winning, but if they can have a sense of hope by paying $2, they are willing to pay that small price. Some do so each week or even with each trip to the store,” he says.
  • The media drives a lot of this. Yes, the article you’re reading now is getting you to think about playing the lottery. It also doesn’t help that the media only covers the winners. “We only think and talk about, or see in the media, the winners,” says Jennifer Johnston, associate professor of psychology at Western New Mexico University. “We never hear or think about the thousands – millions, actually – of losers and their stories. Seeing winners just makes people think about winning and how it must be almost as common as losing.”
  • Maybe your social circle is playing the lottery? If your friends and family are playing the lottery, your odds of playing go up, Johnston says, citing research that sociologists have done on lottery players. “It’s fun to wax on about how you will spend the winnings or dream and imagine it with others.”

Another reason people play the lottery is that they’re struggling financially, and a lottery ticket may seem like their best chance to solve all of their money problems.
Plenty of people with low incomes don’t play the lottery, but many do, Johnston says, adding that some people below the poverty line have been estimated to spend 6% of their limited income on lottery tickets.

“Yes, poverty is associated with higher impulsivity, but more likely, these individuals see their odds of landing good-paying jobs as equally impossible as winning the lottery – therefore, equally possible as well,” Johnston says.

“Unfortunately, this becomes an unfair tax on those who can afford it least,” Langholtz says. “They would be better off putting their $2 in the bank each week and seeing it accumulate over time.”

But, of course, as a society, that’s not what we do. We play the lottery and we dream big. Maybe we play the lottery because it’s fun, and you can’t put a price tag on fun. Or if you can, state and city lotteries have determined that that price is a buck or two.

Even some math professors confess to playing the lottery – once in awhile.

“The only time I play the lottery is when I’m teaching my seminar on gambling in society, Smith says. “Everyone brings a ticket to class before some big lottery drawing, and we have a lively discussion about what we would do if we won the jackpot.”

He says that often his students are dreaming about buying cars and islands, investing and giving to charities. Taking care of family also comes up a lot, he says.

“Those dreams are worth a lot,” Smith says. “But then we invariably start the next class with a sobering account of how much money we lost as a group.”

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Matt Lucas

Writer by day and an aspiring Artist by night. Creative thinking is what I'm all about. Lottos are one of my passions and I'm happy to be contributing to Lottery Papa News

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