A Chance of Winning the Lottery

Math will help you calculate the probability of winning and determine which is more profitable: buy 10 lottery tickets for one game or a ticket for 10 different ones. In the American TV series “Numb3rs”, the main character is a mathematician who helps the FBI solve crimes. In one of the episodes, he utters the phrase that the probability of being killed on the way to getting a lottery ticket is higher than the probability of winning the lottery. At the end of the article, you’ll find a calculation related to this statement, and before that, you’ll learn a little about the mathematics behind mass gambling and how it can help increase your winning chances.

Rule 1. Assess the Risks

For a modern enlightened person, it is no secret that casinos and various gambling establishments configure all their games to have a profit. The principle is simple: a person is motivated to repeatedly use their winning to play. There are no exceptions unless a casino wants to give you money. Keep in mind this simple rule to always look at the situation soberly.

Game theory evaluates any strategy depending on the amount of money. Roughly speaking, if winning $20 is guaranteed, the chance of winning $40 is 50%. This principle allows you to compare different games. Which is better: a million dollars with a chance of 1/100,000 or 50 dollars with a chance of 1/4? Intuitively, the first option is riskier but more profitable. 

If you stay within the framework of mathematics alone, you can conclude that it is impossible to win at the casino. Any chosen strategy can’t eliminate one fatal obstacle — the probability of winning the payout amount is always lower than the bet the player has already made.


However, people play because they win money and experience intensive emotions when they play, especially when they win. And also because money is non-linear for us. While getting $1 right now is like getting a million dollars with a chance of 1/1,000,000, losing a dollar will not affect our condition — nothing will change in our life. Getting a million is an extremely life-changing event for most of us.

Rule 2. Play in the Open

Unfortunately, we cannot get into the inner workings of the lottery. But it is useful to understand at least the formal procedure of how exactly the draw is going. Therefore, we have given some examples below.

For example, the famous slot machines “One-Armed Bandit” and other slot machines are hoaxes to a degree. Symbols of different values are drawn on the wheel that the player sees, but everything is arranged so that the player thinks that the chances of each symbol falling out are the same. In fact (in old machines — mechanically, and in modern ones — with the help of a program), behind each visible wheel hides the one where valuable symbols are rare and cheap ones are frequent. 

The chances of 777 falling out on a slot machine are lower than the probability of getting any three cherries, and the difference can be dozens of times. “Open” lotteries are much more honest in this sense. In the USA, a common format is when a ticket contains a sequence of numbers or is chosen by the buyer independently. In lotteries, the lotto format is preferred: there are several lines of numbers on the ticket, and you need to close either one of them (a regular win) or all of them (a jackpot). (Take France latest results, for example.)

 In theory, the company conducting the lottery can “specially” print and sell non-winning tickets and then manipulate the order of the balls. However, in practice, large companies do not do this: lottery organizers always win, and the scandal in the event of open dishonesty will be huge.


Rule 3. Know Your Chances

The jackpot probability in any lottery is based on only one formula. However, using this formula in calculations is not easy — explaining how to do that would take an entire article, or maybe more than one. That’s why we will focus specifically on the jackpot.

Let’s say we bought a lottery ticket. It has random numbers on it. During the lottery draw, balls are pulled out, and if the numbers on them match the numbers on the ticket, we have won. That’s how we calculate how likely it is that we can get this lucky: the probability of winning = 1 ÷ number of ball combinations.

So, if 5 balls are drawn, and the total amount of balls is 50, , then the probability of winning it will be equal to one to the number of combinations at k = 5 and n = 50, that is:

1 ÷ 2 118 760 = 0,00005%.

Rule 5. Stop in Time

And finally, I want to say that even a 1/100 probability from the point of view of virtually anyone is very small. If you checked the results once a month, you would do 100 such checks in 8 years. Imagine how many times lower the probability of 1/1,000,000 or 1/100,000,000 is. So always bet only the amount you are not afraid of losing completely, and not a cent more.

Finally, as promised, we will evaluate the statement from the beginning of this article. This data is for the United States. Statistically, there were about 17,000 murders in the U.S. in 2016. Let’s consider that an average figure. And let’s also assume that a person is a potential target for murder when they are an adult but not old — that is, about 50 years during their lifetime. So there would be about 850,000 murders during those 50 years. The U.S. population is 325.7 million, which means the chances of getting into a random sample size of 850,000 are such:

850 000 ÷ 325 700 000 = 1 ÷ 383 = 0.003%.

But wait, that’s just the chance of being killed. Specifically, on your way to pick up a lottery ticket? Suppose you leave home to work every weekday, go out one weekend and stay home the next. That’s an average of 6 days a week, or about 26 days a month. And once a month, you buy a lottery ticket. So you have to divide those numbers by 26:

(1 ÷ 383) ÷ 26 = 1 ÷ 9 958 = 0,001%.

And even with this rough estimate, it is significantly more likely than winning. More precisely, it is 30,000 times more likely. In reality, the numbers will be different: a person is not only exposed to danger on the street. Some people take more risks than others. Women are killed almost four times less often than men. But the principle is this. However, even if you know your math, living without faith in good events and constantly expecting bad events is not a good choice.


An experienced tipster and big football lover.