How Lotteries Work

In the United States, 38 states and the District of Columbia (Washington, D.C.) have lotteries. A lottery is a form of gambling that is run by the state. Most states have several different games, including instant-win scratch-off games, daily games and games where you have to pick three or four numbers. 

The game with the biggest jackpot is almost always Lotto. This game usually involves picking the correct six numbers from a set of balls, with each ball numbered from 1 to 50 (some games use more or less than 50). 

Ever wonder why the lump sum payout amount is about half of the actual jackpot amount, or how to calculate the odds of winning the Lotto? In this article, we'll learn the answers to these questions, as well as how the ball-drawing machines work and how much money you could expect to take home if you win.

Lottery Odds

Let's take a look at how to calculate the odds of picking the right number for a typical Lotto game. In order to win our example game, you have to pick the correct six numbers from 50 possible balls. The order in which the numbers are picked is not important; you just have to pick the correct six numbers. 

The odds of picking a single correct number depend on how many balls have been chosen already. For instance, let's say none of the six numbers had been picked yet and you had to guess just one number correctly. Since there are 50 numbers to chose from, and since six balls are going to be picked, you have six tries at picking the number correctly. The odds of picking one number correctly are 50/6 = 8.33:1.

Using a similar calculation, we can determine the odds of picking another number correctly after one number has already been drawn. We know there are 49 balls left, and that five more balls will be drawn. So the odds of picking a number correctly after one has been drawn are 49/5 = 9.8:1. 

Now let's say five numbers have been picked and you have to guess what the last number is going to be. There are only 45 balls left to choose from, but you only get one shot at it, so your odds are only 45:1. 

In a similar manner, we can calculate the odds of picking the right number when two, three, four and five balls have been drawn. You know the odds of a coin toss resulting in heads are 1/2 = 2:1. The odds of two consecutive tosses both resulting in heads are 1/2 x 1/2 = 4:1. The odds of three consecutive tosses all resulting in heads are 1/2 x 1/2 x 1/2 = 8:1. The odds of picking all six lottery numbers are calculated the same way -- by multiplying together the odds of each individual event. In this case:

50/6 x 49/5 x 48/4 x 47/3 x 46/2 x 45/1 = 15,890,700:1

Some states have been increasing or decreasing the number of balls in order to change the odds. If the odds are too easy, then someone will win the jackpot almost every week and the prize will never grow. 

Large jackpots tend to drive more ticket sales. If the prize is not large enough, ticket sales can decrease. On the other hand, if the odds against winning are too great, ticket sales can also decline. It is important for each lottery to find the right balance between the odds and the number of people playing. 

If you add just one number to our hypothetical lottery, so people now have to pick from 51 balls, the odds increase to 18,009,460:1. 

Some states have joined together to run multi-state Powerball lotteries. Since so many people can play, they need a game with really large odds against winning. In this multi-state lottery game, the winner has to pick the correct five numbers from a set of 50 balls, and they have to pick the single correct number from a separate set of 36 balls. So the odds of picking the correct number in this game are: 

36 x (50/5 x 49/4 x 48/3 x 47/2 x 46/1) = 76,275,360:1 

Some people try to increase their odds using a variety of strategies. Although these strategies probably won't improve your odds by very much, they can be fun to experiment with. Check out How to Play the Lottery to learn more. 

So let's say you pick the right six numbers and win a $10 million jackpot -- you're going to get $10 million, right? Well, sort of; somehow, you end up with about $2.5 million. In the next section, we'll look at where all the money goes.