Lottery Odds Calculator
Exact jackpot odds for any pick-from-pool lottery with bonus ball.
What it does
Lottery odds are combinations: how many distinct tickets exist determines the chance one line wins. A 5 from 69 game holds 11,238,513 main lines, and the bonus ball multiplies that count once more.
The tool above takes the pick count, pool size, and bonus pool (zero for none). It returns the jackpot odds per line with the main combinations and bonus share beside them.
The default mirrors Powerball: 5 from 69 with a 1 in 26 bonus ball is 11,238,513 x 26 = 1 in 292,201,338. A classic 6 from 49 with no bonus is 1 in 13,983,816 by the same counting.
The game matrix follows official Powerball rules with the combination math taught in Khan Academy statistics units. Both agree every line holds equal odds no matter which numbers it carries.
How to use
- Enter how many main numbers one line plays.
- Enter the pool they are drawn from.
- Enter the bonus pool size, or 0 when the game has none.
- Read jackpot odds first for the per line chance.
- Multiply by your lines count for the ticket level chance.
Formula
- pool choose pick
- Distinct main lines ignoring order.
- bonus
- Multiplier when a separate ball must also match.
- 1 in
- One winning line per this many tickets.
Order never matters in these games, which is why combinations (not permutations) count the lines. Bonus balls draw from a separate pool, so they multiply rather than combine.
Worked example
Example: Powerball 5/69 + 1/26
Pick 5, pool 69, bonus 26.
- Main: 69 choose 5 = 11,238,513 lines.
- Bonus: 1 in 26 must also match.
- Jackpot: 11,238,513 x 26 = 292,201,338.
- Per line: 1 in 292,201,338.
- Tool shows 1 in 292,201,338, 11,238,513, 1 in 26.
Reference table
| Game | Matrix | Jackpot odds |
|---|---|---|
| Powerball | 5/69 + 1/26 | 1 in 292,201,338 |
| Mega Millions style | 5/70 + 1/25 | 1 in 302,575,350 |
| Classic 6/49 | 6/49, no bonus | 1 in 13,983,816 |
Limits
- Jackpot tier only; lower tiers pay better odds.
- Ignores splits between multiple winners.
- Ignores taxes and annuity versus cash gaps.
- Expected value stays negative at normal jackpots.
Common mistakes
- Treating lucky numbers as likelier than any other line.
- Reading near misses as being due.
- Buying more lines per draw instead of budgeting draws.
- Confusing jackpot odds with any prize odds.
- Pricing the annuity total as cash in hand.
Try it yourself
Quick checks. Answers sit tucked under each question.
6/49 no bonus?
49 choose 6 = 13,983,816: 1 in 13,983,816.
5/70 + 1/25?
12,103,014 x 25 = 1 in 302,575,350.
Two Powerball lines?
Still 1 in 292,201,338 each; together 2 in 292,201,338.
Questions
What are Powerball odds?
1 in 292,201,338 per line: 11,238,513 main combos times the 1 in 26 bonus.
Do quick picks win more?
They win proportionally to sales share. Every combination holds equal odds.
Do past numbers matter?
No. Draws are independent, so overdue numbers hold the same odds.
What does 6/49 pay in odds?
1 in 13,983,816 for the jackpot without a bonus ball.
Should I split lines across draws?
Odds per dollar match either way; budgeting beats timing schemes.
Is the lottery a good bet?
As math, no: expected value runs negative. Play for fun money only.