# Lottery Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Feb 08, 2022

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

Also, check out any of the following tools for comparing payout options from a lottery.

## 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 — Number of balls in the pool;
• r — Number of balls to be drawn;
• m — Expected number of matches;
• C(n,r) — Number of combinations (in how many ways you can choose r out of n numbers?); and
• C(r,m) and C(n-r, r-m) — 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 chance of winning the jackpot (matching all six numbers) is 1 in 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 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 pick 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.
2. 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 the 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, but does not have to, be equal to the number of balls in the initial pool.
Bogna Szyk
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...
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