How Lottery Odds Are Worked Out, Game by Game
Where the 1 in 292 million Powerball figure comes from, and the same math applied to Mega Millions, NY Lotto, Take 5, Pick 10, Numbers and Win 4.
Every lottery's headline odds come from one piece of school math: counting how many different tickets are possible. Once you know that, you can check any game's odds yourself and compare games fairly.
Counting combinations
When the order of the balls doesn't matter, the number of ways to choose k numbers from n is written C(n, k) and read "n choose k". For five numbers from 69 it's:
C(69, 5) = (69 × 68 × 67 × 66 × 65) ÷ (5 × 4 × 3 × 2 × 1) = 11,238,513
That's how many different sets of white balls a Powerball ticket can have. The red Powerball comes from a separate drum of 26, so every one of those sets can be paired with 26 different Powerballs:
11,238,513 × 26 = 292,201,338
So a single Powerball play has a 1 in 292,201,338 chance of the jackpot. Nothing else is involved: no history, no hot numbers, no patterns.
The jackpot odds for every game we cover
| Game | How it's drawn | Jackpot odds |
|---|---|---|
| Powerball | 5 from 69 + 1 from 26 | 1 in 292,201,338 |
| Mega Millions | 5 from 70 + 1 from 24 | 1 in 290,472,336 |
| Millionaire for Life | 5 from 58 + 1 from 5 | 1 in 22,910,580 |
| New York Lotto | 6 from 59 | 1 in 45,057,474 |
| Take 5 | 5 from 39 | 1 in 575,757 |
| Pick 10 | Pick 10, 20 of 80 drawn | 1 in 8,911,711 |
| Numbers | 3 digits, 0–9 | 1 in 1,000 |
| Win 4 | 4 digits, 0–9 | 1 in 10,000 |
Mega Millions and Powerball are almost level: Mega Millions has one more white ball (70) but two fewer Mega Balls (24). Millionaire for Life is more than twelve times easier to win than either, because its bonus drum has only five balls.
Smaller prizes use the same idea
For a prize like "match 3 white balls plus the Powerball", you count the ways to hit exactly three of the five winning numbers and miss with your other two:
C(5, 3) × C(64, 2) = 10 × 2,016 = 20,160 ways out of 11,238,513
Multiply by 1/26 for the Powerball and you get about 1 in 14,494. Every game page on this site has a full odds table worked out this way, including the less obvious ones like Pick 10, where matching none of your ten numbers is a winning result.
What the odds don't tell you
Odds describe a single play. Buying ten plays makes you ten times as likely to win, which for Powerball is still about 1 in 29 million. They also say nothing about how much you'll win: jackpots can be shared, and some prizes are pari-mutuel, meaning the pool is divided among winners. And no past result changes the next one. The balls don't know what came out last time, which is the subject of our post on hot and cold numbers.