Lottery odds calculator
Enter how many numbers are drawn from how many, and the bonus drum if your game has one. The calculator gives the exact jackpot odds and, for every combination of main and bonus matches, the odds of matching exactly that many.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the size of the main pool and how many numbers are picked.
- If there is a bonus drum, enter its size and how many bonus numbers are picked; otherwise leave 0.
- Read the jackpot odds and the table of match levels.
How it works
The number of equally likely tickets is C(n, k) · C(m, b) for k of n main numbers and b of m bonus numbers. The ways to match exactly i main and j bonus numbers are C(k, i) · C(n − k, k − i) · C(b, j) · C(m − b, b − j). Each level’s odds are the total divided by its ways, computed with exact whole numbers.
Worked example
6/49 without a bonus: the jackpot is 1 in 13,983,816. Matching exactly 5 is 6 · 43 = 258 ways (1 in 54,200.84), exactly 4 is 15 · 903 = 13,545 ways (1 in 1,032.4) and exactly 3 is 246,820 ways (1 in 56.66). At least 3 adds up to 260,624 ways: 1 in 53.66.
Tips
- The odds do not say what you win: prize amounts depend on ticket sales and how many winners share a tier.
- To pick numbers at random, use the lottery number generator.
Frequently asked questions
How are lottery odds calculated?
Every set of k numbers from n is equally likely, and there are C(n, k) = n! / (k!(n − k)!) of them. A 6/49 game has C(49, 6) = 13,983,816 combinations, so one ticket has a 1 in 13,983,816 chance of the jackpot.
How is the chance of matching some of the numbers found?
To match exactly m of your k numbers, m must come from your numbers and k − m from the others: C(k, m) · C(n − k, k − m) ways. For 3 of 6 in a 6/49 game that is 20 · 12,341 = 246,820 ways, or 1 in 56.66.
How do bonus balls change the odds?
When the bonus is drawn from a separate drum, the jackpot odds are multiplied by the bonus combinations: 5 of 69 plus 1 of 26 gives C(69, 5) · 26 = 292,201,338. The calculator assumes this separate-drum setup; a bonus drawn from the same drum as the main numbers is a different calculation.
Does buying more tickets help?
Each different ticket adds one combination, so 10 tickets give 10 chances in 13,983,816 in a 6/49 game — still about 1 in 1.4 million. Picking “unpopular” numbers does not change the odds of winning, only how many people might share a prize.
Are some numbers more likely than others?
No. In a fair draw every combination, including 1-2-3-4-5-6, is exactly as likely as any other.