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Keno Odds: The Probability Table
Every keno probability comes from one formula, the hypergeometric distribution. A single number is a 1 in 4 shot; sweeping a 10-spot ticket is 1 in 8,911,711.
Keno odds are calculated with the hypergeometric distribution, a counting formula comparing your picks against the 20 numbers drawn from a pool of 80. The chance of catching exactly k of your n picks is:
P(k) = C(20, k) × C(60, n−k) / C(80, n)
C(a, b) means "the number of ways to choose b things from a." The top of the fraction counts tickets that catch exactly k, choosing k of your numbers from the 20 drawn and the rest from the 60 that stay in the pool; the bottom counts every possible ticket. For a 10-spot sweep, there are C(20,10) = 184,756 ways to pick ten numbers entirely inside the 20 drawn, out of C(80,10) = 1,646,492,110,120 possible tickets. Divide those and you get 1 in 8,911,711.
That bottom number causes a famous mistake. "Keno odds are 1 in 1.6 trillion" circulates online, and the 1.6 trillion is real, it's C(80,10), the count of every possible ticket. But it isn't your odds, because 184,756 of those tickets win, not just one.
What does the full 10-spot catch distribution look like?
Here's the full catch distribution for a 10-spot ticket:
Catch | Probability | Odds |
|---|---|---|
0 | 4.58% | 1 in 21.8 |
1 | 17.96% | 1 in 5.6 |
2 | 29.53% | 1 in 3.4 |
3 | 26.74% | 1 in 3.7 |
4 | 14.73% | 1 in 6.8 |
5 | 5.14% | 1 in 19.4 |
6 | 1.15% | 1 in 87 |
7 | 0.16% | 1 in 621 |
8 | 0.014% | 1 in 7,384 |
9 | 0.00061% | 1 in 163,381 |
10 | 0.0000112% | 1 in 8,911,711 |
The single most likely outcome is catching exactly 2, and about 56% of all 10-spot draws catch either 2 or 3. Catching zero (1 in 21.8) is actually four times more likely than catching six (1 in 87), which is why several lotteries pay a small consolation for a blank ticket.
How does a sweep get harder as ticket size grows?
And solid-sweep odds by ticket size, from a single number up through ten:
Spots played | Probability of catching all | Odds |
|---|---|---|
1 | 25% | 1 in 4 |
3 | 1.39% | 1 in 72 |
5 | 0.064% | 1 in 1,551 |
7 | 0.0024% | 1 in 40,979 |
10 | 0.0000112% | 1 in 8,911,711 |
Each added spot multiplies the difficulty by roughly four to six and a half times, and the multiplier itself grows as tickets get bigger. A perfect 20-spot casino ticket, by the same formula, collapses to roughly 1 in 3.5 quintillion.
"Overall odds of winning" figures differ between states not because the draw math changes, but because each lottery's paytable pays different catch tiers, and low tiers, especially zero-catch consolations, dominate the headline number. One consolation line alone can move a state's published "overall odds" by 70%.
Can you do anything to improve these odds?
None of this can be improved. Every draw pulls 20 of 80 numbers at random, so every possible ticket faces exactly the tables above; hot numbers, cold numbers, and betting systems don't touch a single row. The lever you do control is ticket size: fewer spots means likelier sweeps of smaller prizes, more spots means longer shots at rarer, bigger ones. For how these numbers translate into definitions like "spot" and "catch," see the keno glossary; for how they fit into the bigger picture of what keno costs, start with what is keno.
Sources
- Virginia Lottery — Keno — retrieved July 2026
- Michigan Lottery — Club Keno — retrieved July 2026
- Wikipedia — Keno — retrieved July 2026
- Maryland Lottery — Keno Prize Structure — retrieved July 2026
- Wizard of Odds — Keno — retrieved July 2026
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