Lottery Odds Calculator
Exact jackpot odds for any pick-n-from-m lottery, with or without a bonus ball, plus the odds of every smaller prize tier — computed with exact combinatorics.
Lottery Odds Calculator: with the default inputs, jackpot odds is 1 in 13,983,816.
How many balls you choose from, e.g. 49 in a 6/49 game.
Size of a separate pool for one extra ball (26 for Powerball). Leave at 0 if there isn't one.
- Jackpot probability
- 0.0000071511%
- Main-pool combinations
- 13,983,816
- Total possible tickets
- 13,983,816Main combinations × the bonus pool, if there is one.
- Odds of matching one fewer number
- 5 of 6: 1 in 54,200.8
- Odds of matching at least half your numbers
- 3+ of 6: 1 in 53.7
Assumptions
- All balls are equally likely and drawn without replacement from the main pool.
- A bonus ball is drawn from a separate, independent pool, so it multiplies the number of outcomes.
- Counts are exact binomial coefficients computed with arbitrary-precision integers.
- Prize tiers ignore game-specific rules such as bonus-ball prize splits, multipliers and rollovers.
| Numbers matched | Tickets that do this | Odds | Probability |
|---|---|---|---|
| 6 | 1 | 1 in 13,983,816 | 0.000007% |
| 5 | 258 | 1 in 54,200.8 | 0.001845% |
| 4 | 13,545 | 1 in 1,032.4 | 0.096862% |
| 3 | 246,820 | 1 in 56.7 | 1.76504% |
| 2 | 1,851,150 | 1 in 7.6 | 13.237803% |
| 1 | 5,775,588 | 1 in 2.4 | 41.301945% |
| 0 | 6,096,454 | 1 in 2.3 | 43.596498% |
The "tickets that do this" column adds up to 13,983,816, every possible ticket. A bonus ball, if any, is not included in this table — it only splits the top row further.
How this is worked out
The formula
Number of possible tickets (order does not matter): C(n, k) = n! ÷ (k! (n − k)!) With a separate bonus pool of size b, total outcomes = C(n, k) × b. Jackpot probability = 1 ÷ total outcomes. Matching exactly j of your k numbers (hypergeometric): ways = C(k, j) × C(n − k, k − j), out of C(n, k) tickets.
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Numbers in the main pool
- How many balls you choose from, e.g. 49 in a 6/49 game.from 1 to 100 · whole numbers only · defaults to 49
- Numbers you pick
- A number.from 1 to 20 · whole numbers only · defaults to 6
- Bonus ball pool
- Size of a separate pool for one extra ball (26 for Powerball). Leave at 0 if there isn't one.from 0 to 100 · whole numbers only · defaults to 0
What you get back
- Jackpot oddsmain answer
- Jackpot probability
- Main-pool combinations
- Total possible tickets
- Main combinations × the bonus pool, if there is one.
- Odds of matching one fewer number
- Odds of matching at least half your numbers
What this assumes
- All balls are equally likely and drawn without replacement from the main pool.
- A bonus ball is drawn from a separate, independent pool, so it multiplies the number of outcomes.
- Counts are exact binomial coefficients computed with arbitrary-precision integers.
- Prize tiers ignore game-specific rules such as bonus-ball prize splits, multipliers and rollovers.
About this calculator
Lottery odds are pure combinatorics, and the arithmetic is exact — no estimation, no simulation. This calculator handles any "pick k numbers from a pool of n" game, with or without a separate bonus ball, and gives the odds of every prize tier, not just the jackpot.
How to use it
Enter the size of the main pool and how many numbers you pick. If the game draws one extra ball from its own separate pool (Powerball's red ball from 26, Mega Millions' gold ball from 25, EuroMillions' Lucky Stars), enter that pool size too. Leave it at 0 for a plain 6-from-49 style draw.
Why order doesn't matter
A lottery ticket is a set, not a sequence — drawing 3, 17, 42 is the same ticket as 42, 3, 17. So the count is the binomial coefficient C(n, k), not a permutation. For 6 from 49 that is 49! ÷ (6! × 43!) = 13,983,816. One ticket, one chance in nearly fourteen million.
Adding a bonus ball from a separate pool multiplies the total, because the bonus is drawn independently. Powerball's 5 from 69 gives C(69, 5) = 11,238,513 combinations; times the 26 red balls gives 292,201,338.
Reading the prize tiers
The table uses the hypergeometric distribution: to match exactly j of your k numbers you must choose j from the k winning numbers and the remaining k − j from the n − k losers. Two things usually surprise people:
- Matching zero numbers is by far the most likely outcome in most games — 43.6% of 6/49 tickets match nothing at all.
- The odds improve enormously as you drop tiers. Matching 3 of 6 in a 6/49 game is about 1 in 57, roughly 245,000 times easier than the jackpot.
What the numbers do and don't mean
- Every combination is equally likely. 1-2-3-4-5-6 has exactly the same chance as any scatter of numbers. Picking it is a bad idea only because thousands of other people do, so you would share the prize.
- Buying more tickets scales linearly, not magically. Ten tickets take you from 1 in 14 million to 1 in 1.4 million — still far less likely than being struck by lightning this year.
- There is no such thing as a due number. Draws are independent; past results carry no information.
- Odds are not expected value. Whether a ticket is a fair bet depends on the jackpot size, the number of other players (rollovers get shared), tax, and the annuity-versus-lump-sum discount. Jackpot odds alone never answer "is it worth it?"
- Wheeling systems and number-picking software change which combinations you cover, never the odds per combination.
Frequently asked questions
▸What are the odds of winning a 6 from 49 lottery?
1 in 13,983,816. That is C(49, 6), the number of different six-number tickets you can make from 49 balls.
▸What are the odds of winning Powerball?
1 in 292,201,338 — C(69, 5) = 11,238,513 white-ball combinations multiplied by the 26 possible red balls.
▸Does buying more tickets meaningfully improve my chances?
Only in proportion. Ten tickets give ten chances in 14 million rather than one, which is a real tenfold improvement on a vanishingly small number.
▸Are some number combinations luckier than others?
No. Every combination is equally likely. Avoiding popular patterns like 1-2-3-4-5-6 or birthday-heavy picks does not change your odds of winning, only your odds of sharing the prize.
▸Why is matching zero numbers so common?
Because most of the pool is not in the draw. In a 6/49 game there are 43 non-winning numbers, and C(43, 6) ÷ C(49, 6) ≈ 43.6% of all tickets match none of them.
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