Balls to be drawn
Number of matches
Number of balls in the pool
Winning odds are 1 to...
Bonus ball (from remaining balls)
Number of matches
Winning odds are 1 to...
Bonus balls (from bonus pool)
Balls to be drawn
Matches with bonus pool
Balls in the bonus pool
Winning odds are 1 to...

# Lottery Calculator

By Bogna Haponiuk

If you get frustrated because you never get these number right, this lottery calculator will tell you the sad truth - what are your actual chances of winning in a lottery. All you have to do is write down how many numbers you chose from the pool, and it will automatically calculate the lottery odds.

## How does the lottery odds calculator work?

Begin with typing in the following values:

• Balls to be drawn: how many balls are drawn from the pool. For example, if in a Lotto game, the machine chooses 6 winning numbers.
• Number of matches: how many matches satisfy you? In this example, you can match up to 6 numbers. The lower this number will be, the higher the chances of winning.
• Number of balls in the pool: the total number of balls that can be chosen. For example, if your lottery coupon includes numbers from 1 to 60, then there are 60 balls in the pool.

The lottery calculator will determine the probability of winning such a lottery (in other words, the odds) as 1 to x. This means that if you play x times, you will most probably win only once.

## The lottery formula

What kind of formula does our calculator use? It finds the lottery odds according to the following equation:

`x = C(n,r) / [C(r,m) * C(n-r, r-m)]`

where:

• n is the number of balls in the pool;
• r is the number of balls to be drawn;
• m is the expected number of matches;
• C(n,r) is the number of combinations (in how many ways you can choose r out of n numbers?)
• C(r,m) and C(n-r, r-m) stand for the number of combinations to choose m out of r and r-m out of n-r respectively.

For example, in a typical Lotto game, where you choose 6 numbers out of 59, the chances of winning (matching all six numbers) are as 1 to 45,057,474. That means that statistically, you would have to play over 45 million times to win just once. Chances for matching five numbers are bigger, but also not too optimistic - 1 to 141,690. On the other hand, the odds for matching three numbers are as 1 to 96 - a bit over 1%. It means that matching three numbers is fairly common. Too bad it doesn't really pay off...

## Bonus balls

Some lotteries include a bonus ball that is drawn after the initial balls. Our calculator allows you to take into consideration two types of bonus balls:

1. Bonus balls taken from the remaining pool. In this case, an additional ball is chosen from the pool to give players who hit all but one number a chance for a better prize. For example, in a game where you choose 6 numbers of 59, a seventh ball is randomly selected. Let's assume that you matched 5 out of 6 numbers. Our calculator tells you what are the odds of the sixth number you chose being on the bonus ball.
• Number of matches is set by default to m-1. That means that if you initially wanted to match 6 balls, the lottery calculator will find the odds of matching 5 balls and a bonus ball.
1. Bonus balls taken from a bonus pool. In this case, bonus balls are randomly picked from a separate pool. That means that one number can come up twice. Our lottery odds calculator finds what are the chances of you getting m matches and picking a bonus ball number. For example, if you want to hit a jackpot (6 matches out of 6 numbers), this calculator will find the odds of matching six numbers and a bonus ball.
• Balls to be drawn: number of balls drawn from the bonus pool.
• Matches with bonus pool: how many numbers from your lottery ticket should come up in the bonus pool?
• Balls in the bonus pool: total number of balls in the bonus pool. It can be, but does not have to, be equal to the number of balls in the initial pool.
Bogna Haponiuk