If you are thinking of playing the lottery, you surely know that the odds of becoming a millionaire are not very good.
But that doesn’t stop anyone from playing. According to the North American State and Territory Lottery Association, during fiscal year 2019, the year for which the latest numbers are available, lottery sales in the United States totaled more than $91 billion.
There are lotteries in 45 states, the District of Columbia, Puerto Rico, and the US Virgin Islands. Each Canadian province also has its own lottery. Canada’s sales in 2019 reached more than $10 billion. Worldwide, there are at least 100 countries that have their own lotteries.
But how does the lottery work, and is it worth playing? We’ll bet you’re interested to know.
How does the lottery work?
In short, it’s very simple. People spend some money – usually a dollar or two but sometimes more – on a lottery ticket, which contains a set of numbers. Usually once a day, a lottery—usually run by the state or city government—selects a set of numbers at random. If your combination of numbers matches the numbers on your lottery ticket, you win some of the money spent on lottery tickets, and the state or city government gets the rest.
Mega Millions and Powerball are two of the biggest multi-state national lottery games that get the most news attention, but there are quite a few multi-state lotteries, such as Cash Five, Lucky for Life, and Cash4Life.
What are the odds of winning the lottery?
Harvey Langoltz, professor of psychology at William & Mary, studies the psychology of decision-making and the psychology of decision theory, a study that uses mathematics, philosophy, statistics, and psychology when determining how decisions are made.
He says the odds of winning vary a bit depending on the lottery, but he points to Powerball as a good example of how hard it can be for someone to win.
“As stated on the Powerball website, the chances of winning are 1 in 292 million,” says Langoltz.
In order to beat these odds, you have six numbers to guess, five numbers from 1 to 69 and one red Powerball number from 1 to 26.
Langolts explains the mathematics behind it:
- “The probability of someone guessing the five white balls correctly is five (because there are five numbers that will turn out to be correct) out of 69, or 5/69,” says Langoltz.
- “The probability of guessing the second, given that the player guessed the first correctly, is four (only four remaining will turn out to be correct at the time of drawing) out of 68 (because you’ve already canceled one out of the original 69). So that comes to 4/68.”
- “And the probability of correctly guessing the three, four and five white balls is 3/67, 2/66 and 1/65.”
- And the probability of a player guessing the correct number on the red Powerball is 1/26. So what is the probability of guessing all five numbers of the white ball and the number of the red Powerball? It is 5/69 x 4/68 x 3/67 x 2/66 x 1/65 x 1/26 or 1/292201338.”
That’s all that has to happen for math to work in your favor. So the chances are really slim, though Langholtz says that lotteries usually give lower payouts for correct partial guesses.
How are lottery odds calculated?
Again, math is included, and it helps to understand what a factor is. In short, the factor is the total you get after multiplying a number against all the numbers below it. For example, a factor of 3, which can be written as “3!” , equals 6. You multiply 3 by 2 by 1, and you get 6.
If you think of Mega Millions, you have five numbers taken from a set of numbers from 1 to 70, says Dave Gulley, who studies economics at Bentley University in Waltham, Massachusetts, and who has done research on the lottery.
“How many different combinations of five numbers can be drawn from a set of 70?” Julie asks.
Well, he says that to find out, you can use the formula: 70! Divided by (5 times 65!)
“The” is read as “my factor,” so 5! is my five factorial,” Julie says. “5! It is calculated as 5 times 4 times 3 times 2 times 1, equals 120.”
He says that 70! is 70 times 69 times 68, and so on, until you get to multiply the numbers by 1.
and 65! It is 65 multiplied by 64 multiplied by 63 and so on.
“Variable factors are very useful for knowing how many sets of events can occur,” says Gulley.
Once you make Mega Millions accounts? “This means that the person who plays one ticket has a 1 in 302,103,014 chance of winning the jackpot,” says Gulley.
What are the odds of winning the lottery – compared to other events?
Of course, the odds of winning the lottery become more difficult when you put it against other events, most of which you definitely don’t want to happen. It doesn’t rain on anyone’s parade, but all of the following scenarios are more likely to happen to you than to win the Powerball or Mega Millions.
- You have 1 in 18,043 being struck by lightning in your lifetime, according to the Lightning Safety Council.
- You have a 1 in 4332817 chance of being attacked by a shark, according to the International Shark Attack Profile.
- You have a 1 in 2.1 million chance of being exposed to a bear, according to the National Park Service.
- You have a 4 in 1,000 chance of getting your taxes audited, according to TRAC-IRS, a comprehensive, independent, 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 getting a hole in one are as high as 1 in 3000 if you’re a professional golfer, according to the National Hole-in-One Record.
What are some of the best lotteries to play, given the chances?
There are a lot of lotteries, and without guarantees of winning any of them, it is impossible to direct anyone to any one lottery with great confidence. However, there are some things to consider when playing the lottery if you want to improve your odds of winning.
Your best bet is to play the lottery where the return is minimal. Less people playing overall means that your odds of winning are higher. Of course, if you focus on lottery games that are not very popular, it could mean that you are knocking yourself out of the race to win $300 million or any of the bigger prizes.
You can also do yourself a favor to read the possibilities; Sweepstakes generally should have this information somewhere on their website or in fine print. For example, some scratch-off ticket lotteries have very good odds. Derek Smith, a mathematics professor at Lafayette College in Easton, Pennsylvania, who teaches community gambling lessons, points out that the Pennsylvania scratch games are Ghost and Goblin, which list the total chances of winning any prize (not just the first prize) 1 in 4.61.
However, even with these scratch games, your odds may not be as good as they seem.
“One of the prizes could be a free ticket,” Smith says. “But what does that actually make you? Just a chance to be in the same situation 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 prizes and choose groups of numbers that have at least one or two numbers greater than 31,” says Gulley. “This is because some people choose numbers based on birthdays or other relatively low numbers. Choosing larger numbers will not increase their chances of winning but it will reduce the chance of sharing the jackpot with other winners.”
Finding out what we know about the lottery, why do so many people play it?
Odds are, if you play the lottery, you will lose. Why do people play it? There are a lot of reasons, according to experts.
- The lottery gives players hope. “Hope against odds” is the main driver for people who play the lottery, says Langoltz. People may not be interested in calculating the probability of winning, but if they can feel hopeful by paying $2, they are willing to pay that little price. Some do it every week or even with every trip to the store.
- The media is driving a lot of this. Yes, the article you are reading right now makes you think about playing the lottery. Nor does it help that the media only cover the winners. “We just think and talk about winners, or we see in the media, winners,” says Jennifer Johnston, associate professor of psychology at Western New Mexico University. “We never hear or think about thousands – millions actually – of losers and their stories. Seeing winners makes people think about winning and how common it must be as losing.”
- Maybe your social circle is playing the lottery? If your friends and family play the lottery, your odds of playing go up, Johnston says, citing research by social scientists on lottery players. “It’s fun to talk about how you spend the winnings or dream and fantasize about it with others.”
Another reason why people play the lottery is because they are struggling financially, and a lottery ticket may seem like their best chance to solve all their financial problems.
A lot of people on low incomes don’t play the lottery, but many do, Johnston says, adding that some people below the poverty line have spent 6% of their limited income on lottery tickets.
“Yes, poverty is associated with high impulsivity, but more likely, these individuals view their prospects for well-paying jobs as equally impossible as winning the lottery — and therefore, that is also possible,” Johnston says.
“Unfortunately, this becomes an unfair tax on those who cannot afford it,” says Langoltz. “It would be better for them to put $2 in the bank every week and see it build up 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 the fun. Or if you can, state and city lotteries have set that price to a dollar or two.
Some math professors even admit to playing the lottery – once in a while.
“The only time I play the lottery is when I teach my seminar on community gambling,” Smith says. “Everyone brings a ticket to class before a big lottery is drawn, and we have a lively discussion about what we would do if we win the jackpot.”
He says his students often dream of buying cars and islands, investing and donating to charity. He says that taking care of the family also comes a lot.
“These dreams are worth a lot,” Smith says. “But then, we start the next semester with a realistic account of how much money we’ve lost as a group.”