Lottery odds calculator. How the odds are worked out, step by step.
One Saturday Lotto line has a 1 in 8,145,060 chance of the jackpot, because 6 numbers from 45 can be picked 8,145,060 ways. Our lottery odds calculator shows that working for every game.
How lottery odds are calculated: count every possible line
Lottery odds are calculated by counting how many different lines a game allows, then seeing how many of them you hold. Everything else is detail.
C(n,k), read as "n choose k", is the number of different ways to pick k numbers from n when the order does not matter. A lottery line is exactly that: a set of numbers, in any order.
Saturday Lotto asks you to pick 6 numbers from 45. Multiply 45 × 44 × 43 × 42 × 41 × 40, then divide by 6 × 5 × 4 × 3 × 2 × 1 to remove the orderings that count as the same line. The answer, C(45,6), is 8,145,060.
Only one of those lines matches the draw, so one line has a 1 in 8,145,060 chance of the jackpot. Oz Lotto works the same way with 7 from 47, which is why its jackpot is 1 in 62,891,499.
Plenty of calculators print the final number and stop. A figure you cannot check is a figure you have to take on trust, so ours shows each step.
Lottery odds calculator, plus four tools for the next question
The calculator answers "what are my chances?". These tools answer what people ask next: how does that compare, how many tickets would it take, and who might I share a win with.
Lottery odds calculator
Works out jackpot and any-prize odds from a game's published rules, with every step of the working shown, so you can check the arithmetic yourself.
Odds comparison visualiser
Puts the odds of different games side by side on one visual scale, so 1 in 8,145,060 and 1 in 134,490,400 stop looking like similar numbers.
How many tickets to win
Shows how many tickets it would take for a win to become more likely than not. For any jackpot on this page, that number runs into the millions.
Cost-per-chance comparator
Compares what each game charges for the same chance of a prize. Shorter odds per line and better value per chance are two different questions.
Number-sharing risk checker
Checks how crowded your chosen numbers are likely to be with other players. It does not change your odds; it shows how many people you might split a jackpot with.
Jackpot odds against any-prize odds, worked from the same rules
Jackpot odds count one line out of every possible line. Any-prize odds add up every prize division, which is why Powerball Australia is 1 in 134,490,400 for the jackpot and about 1 in 44 for any prize.
Read the game's published rules
We start from the operator's own rules: how many numbers you pick, how many balls sit in each barrel, and what each prize division needs. Powerball Australia draws 7 numbers from 35, plus a Powerball from a separate barrel of 20.
Count every possible entry
C(n,k) gives the ways to choose k numbers from n. A second barrel multiplies the count, so Powerball Australia's C(35,7) is multiplied by 20 to reach 134,490,400 entries. One entry has a 1 in 134,490,400 jackpot chance.
Add the divisions for any prize
Any-prize odds add up the chance of every prize division, from the jackpot down to the smallest prize. The Lott lists its lowest Powerball tier, matching 2 numbers plus the Powerball, at 1 in 66. Together the divisions come to about 1 in 44.
Test against the operator's table
An automated test compares every figure we compute with the odds table the operator publishes. Our Oz Lotto jackpot figure of 1 in 62,891,499 matches the table Lotterywest publishes.
Date it, and redo it when rules
Each table shows when it was last checked, here October 2026. When a game changes its rules, as Oz Lotto did in May 2022 by moving from 7 from 45 to 7 from 47, we work the odds out again.
Every claim is backed by a calculation shown on the page or a linked primary source; anything that cannot be sourced stays off the site.
Why two tickets double your odds and still change almost nothing
Two different Saturday Lotto lines give you 2 chances in 8,145,060 instead of 1. Your odds have doubled, and almost every possible line is still one you do not hold.
Check whether a ticket is worth
Frequently Asked Questions
- Does the game I choose matter more than the number of tickets?
- Yes, by a wide margin. One Saturday Lotto line has a 1 in 8,145,060 jackpot chance. One Powerball Australia entry has 1 in 134,490,400. Choosing a game moves your jackpot odds far more than adding a second line to the same draw does.
- How many tickets would make a jackpot more likely than not?
- You would need different lines covering more than half of every possible line in a single draw. In Saturday Lotto that is more than half of 8,145,060 lines. Our How many tickets to win tool works out the figure for any game.
- Do syndicates or system entries change the arithmetic?
- No. A syndicate raises the group's odds and splits any prize the same way. A system entry is a bundle of standard games: a Saturday Lotto System 8 is 28 of them, so the extra chance is exactly proportional to the extra cost.
- Do hot or cold numbers improve my chances?
- No. Every ball has the same chance in every draw. Our hot-and-cold generator builds lines from real draw counts and shows those counts, and our randomness tester runs a chi-square test on the same history so you can see whether any pattern is more than chance.
- Which Australian lotto has the best jackpot odds?
- Of the national draws, Saturday Lotto and Weekday Windfall have the shortest jackpot odds at 1 in 8,145,060. Set for Life is 1 in 38,320,568, Oz Lotto 1 in 62,891,499 and Powerball 1 in 134,490,400.
- Why does your US Powerball any-prize figure differ slightly from other sites?
- Rounding. The official Powerball site gives the overall odds of any prize as 1 in 24.87, which our table shows as 1 in 24.9. The Colorado Lottery rounds the same game to 1 in 25. The jackpot is 1 in 292,201,338 either way.
- Are the odds tools free?
- Yes. All 25 tools are free, run in your browser and need no account. You can check any figure on this page without signing up for anything.
Found a figure that disagrees with the operator? Tell us.
Corrections and questions about any odds on this page come straight to us. Send the game, the figure and where you saw a different one.
Every reported error is checked against the operator's source and fixed.