Keno Odds: The Full Probability Table
Every keno probability, computed exactly: single-pick odds of 1 in 4, a 1 in 8,911,711 ten-spot sweep, and the full catch distribution for every ticket size from 1 to 10 spots.
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The short answer
Every keno probability comes from one formula, the hypergeometric distribution, and Wild Academy computed all of them exactly for this page (2026). Any single number you pick has a 1 in 4 chance of being drawn. Sweep a 10-spot ticket and you've hit a 1 in 8,911,711 event, matching the Virginia Lottery's published odds.
How are keno odds calculated?
Keno odds are calculated with the hypergeometric distribution, a counting formula that compares 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)
It's less intimidating than it looks. C(a, b) just means "the number of ways to choose b things from a." The top of the fraction counts the tickets that catch exactly k: choose k of your numbers from the 20 that get drawn, and the other n−k from the 60 that stay in the pool. The bottom counts every possible ticket. Divide, and you have the probability. If "catch" and "spot" are unfamiliar words, the keno terms glossary defines both in a sentence.
Run it for the ticket everyone asks about: a 10-spot where all ten numbers hit. 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 ten-number tickets. Divide those and you get 1 in 8,911,711.
That bottom number also explains a famous mistake. You'll see "keno odds are 1 in 1.6 trillion" circulating online, and the 1.6 trillion is real: it's C(80,10), the count of every possible 10-number ticket. But it isn't your odds, because 184,756 of those tickets win, not just one. Anyone quoting 1 in 1.6 trillion counted the tickets and forgot to count the winners.
Every keno odds calculator on the internet runs this same formula. Our own keno odds calculator lets you pick any ticket size and wager, then see the exact probability and expected payout for every catch. The tables below are its complete output for every standard ticket size, computed as exact fractions rather than rounded decimals. If you want the game rules behind the math first, start with our pillar on keno explained.
What are the odds of hitting all 10 numbers in keno?
The odds of hitting all 10 numbers in keno are 1 in 8,911,711, a probability of 0.0000112%. That's Wild Academy's exact calculation (2026) from the formula above, and official sources agree: the Michigan Lottery's Club Keno materials list the 10-spot top catch at 1 in 8.91 million.
For scale: if you played 1,000 games a day, every single day, you'd expect one solid 10-spot roughly every 24 years. It happens to someone eventually. It's just not a plan.
Here's the complete probability picture for a 10-spot ticket, per the same calculation:
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 |
Read the middle rows, because that's where you'll actually live. The single most likely outcome is catching exactly 2, and about 56% of all 10-spot draws catch either 2 or 3. Michigan's published 1 in 19.4 for catching 5 of 10 matches our row exactly. And notice the quiet oddity at the top: catching zero (1 in 21.8) is four times more likely than catching six (1 in 87), which is why several lotteries pay a consolation for a blank ticket.
If 1 in 8.9 million sounds beatable, casinos will happily sell you a longer shot. Wild Academy's calculation (2026) puts a perfect 20-spot ticket at 1 in 3,535,316,142,212,174,320, roughly 1 in 3.5 quintillion. Same formula: that's simply 1 divided by C(80,20), and Wikipedia's keno entry lists the same figure. No venue has existed long enough to expect one.
Solid-catch odds by ticket size
A clean sweep runs from 1 in 4 on a single number to 1 in 8,911,711 on ten, and each added spot multiplies the difficulty by roughly four to six and a half times. Here are Wild Academy's exact solid-catch odds (2026) for every ticket size:
Spots played | Probability of catching all | Odds |
|---|---|---|
1 | 25% | 1 in 4 |
2 | 6.01% | 1 in 16.6 |
3 | 1.39% | 1 in 72 |
4 | 0.31% | 1 in 326 |
5 | 0.064% | 1 in 1,551 |
6 | 0.013% | 1 in 7,753 |
7 | 0.0024% | 1 in 40,979 |
8 | 0.00043% | 1 in 230,115 |
9 | 0.000072% | 1 in 1,380,688 |
10 | 0.0000112% | 1 in 8,911,711 |
The multiplier itself grows as tickets get bigger. Going from 3 to 4 spots makes the sweep about 4.5 times harder; going from 9 to 10 makes it 6.5 times harder. Each new pick has to land among the 20 drawn numbers too, and your earlier catches have already used some of them up.
The popular 7-spot sits at 1 in 40,979, rare enough to feel like an event, common enough that regulars have seen one. Whether a likelier sweep on a smaller ticket is worth anything, though, depends on what it pays relative to these odds. That trade-off is the keno house edge, and it gets its own article.
The full keno probability table
Below is the complete distribution: the probability of every catch count for every ticket from 1 to 10 spots. All values are Wild Academy's calculation (2026), computed as exact fractions from P(k) = C(20,k) × C(60,n−k) / C(80,n) and rounded for display. One orientation tip before you scroll: the most likely outcome always sits near a quarter of your picks, because 20 of the 80 numbers are drawn.
1 to 3 spots
Spots | Catch | Probability | Odds |
|---|---|---|---|
1 | 0 | 75% | 1 in 1.3 |
1 | 1 | 25% | 1 in 4 |
2 | 0 | 56.01% | 1 in 1.8 |
2 | 1 | 37.97% | 1 in 2.6 |
2 | 2 | 6.01% | 1 in 16.6 |
3 | 0 | 41.65% | 1 in 2.4 |
3 | 1 | 43.09% | 1 in 2.3 |
3 | 2 | 13.88% | 1 in 7.2 |
3 | 3 | 1.39% | 1 in 72 |
Even the humble 3-spot sweep is a 1 in 72 event, and you'll catch nothing at all on 42% of 3-spot draws.
4 and 5 spots
Spots | Catch | Probability | Odds |
|---|---|---|---|
4 | 0 | 30.83% | 1 in 3.2 |
4 | 1 | 43.27% | 1 in 2.3 |
4 | 2 | 21.26% | 1 in 4.7 |
4 | 3 | 4.32% | 1 in 23.1 |
4 | 4 | 0.31% | 1 in 326 |
5 | 0 | 22.72% | 1 in 4.4 |
5 | 1 | 40.57% | 1 in 2.5 |
5 | 2 | 27.05% | 1 in 3.7 |
5 | 3 | 8.39% | 1 in 11.9 |
5 | 4 | 1.21% | 1 in 82.7 |
5 | 5 | 0.064% | 1 in 1,551 |
On a 5-spot ticket, about 90% of draws catch two or fewer.
6 and 7 spots
Spots | Catch | Probability | Odds |
|---|---|---|---|
6 | 0 | 16.66% | 1 in 6.0 |
6 | 1 | 36.35% | 1 in 2.8 |
6 | 2 | 30.83% | 1 in 3.2 |
6 | 3 | 12.98% | 1 in 7.7 |
6 | 4 | 2.85% | 1 in 35 |
6 | 5 | 0.31% | 1 in 323 |
6 | 6 | 0.013% | 1 in 7,753 |
7 | 0 | 12.16% | 1 in 8.2 |
7 | 1 | 31.52% | 1 in 3.2 |
7 | 2 | 32.67% | 1 in 3.1 |
7 | 3 | 17.50% | 1 in 5.7 |
7 | 4 | 5.22% | 1 in 19.2 |
7 | 5 | 0.86% | 1 in 116 |
7 | 6 | 0.073% | 1 in 1,366 |
7 | 7 | 0.0024% | 1 in 40,979 |
Catching 4 of 7 (1 in 19.2) is about as likely as catching 5 of 10, which shows how much three extra misses forgive.
8 and 9 spots
Spots | Catch | Probability | Odds |
|---|---|---|---|
8 | 0 | 8.83% | 1 in 11.3 |
8 | 1 | 26.65% | 1 in 3.8 |
8 | 2 | 32.81% | 1 in 3.0 |
8 | 3 | 21.48% | 1 in 4.7 |
8 | 4 | 8.15% | 1 in 12.3 |
8 | 5 | 1.83% | 1 in 54.6 |
8 | 6 | 0.24% | 1 in 423 |
8 | 7 | 0.016% | 1 in 6,232 |
8 | 8 | 0.00043% | 1 in 230,115 |
9 | 0 | 6.37% | 1 in 15.7 |
9 | 1 | 22.07% | 1 in 4.5 |
9 | 2 | 31.64% | 1 in 3.2 |
9 | 3 | 24.61% | 1 in 4.1 |
9 | 4 | 11.41% | 1 in 8.8 |
9 | 5 | 3.26% | 1 in 30.7 |
9 | 6 | 0.57% | 1 in 175 |
9 | 7 | 0.059% | 1 in 1,690 |
9 | 8 | 0.0033% | 1 in 30,682 |
9 | 9 | 0.000072% | 1 in 1,380,688 |
A 9-spot ticket catches four or fewer on roughly 96 of every 100 draws.
10 spots
The full 10-spot distribution is in the section above. Its headline rows: catching zero is 1 in 21.8, and catching all ten is 1 in 8,911,711.
Why do published "overall odds" differ between states?
Because "overall odds of winning" measures a different event in every state: the chance of landing any paid catch tier, and each lottery's paytable pays different tiers. The draw math never changes. The tier menu does, and the low tiers, especially zero-catch consolations, dominate the headline number.
Here's a worked demonstration. The 10-spot games in Maryland, Ohio and Massachusetts all pay on catches of 5 through 10, plus a consolation for catching zero, per the prize structures published by the Maryland Lottery, Ohio Lottery and Massachusetts Lottery (2026). Add up those tiers in our 10-spot table and the chance of winning something is about 1 in 9.1. Strip out just the zero-catch tier and it falls to 1 in 15.5. Same game, same draw, same probabilities: one consolation line moves the "overall odds" by 70%. In fact, on those tickets roughly two of every five "wins" come from catching nothing at all.
Ticket menus widen the gap further. Massachusetts sells 11-spot and 12-spot games most states don't offer, so its odds lines can't be compared ticket-for-ticket with a 10-spot-max state. And a paytable that added a lower tier, say 4 of 10 at 1 in 6.8, would swing its overall-odds line harder than any jackpot change ever could.
So when two states print different overall odds for the "same" spot count, check the tier lists before suspecting different math. And treat the stat itself with mild suspicion: a 1 in 9 chance of "winning" is mostly a 1 in 9 chance of a small consolation tier. What each of those tiers actually pays, and how to compare two paytables before you buy, is covered in keno payout charts explained.
Can you improve your keno odds?
No. Every draw pulls 20 of 80 numbers at random, so every possible ticket faces exactly the tables above. "There is no strategy that will change the chance of winning," Mark Bollman, a mathematics professor at Albion College, told GBH News in 2023. "All 20-number combinations are equally likely."
That verdict covers every popular angle. Hot numbers, cold numbers, birthdays, board patterns: Wizard of Odds is just as blunt that in a fair game "it makes no difference which numbers you choose." We stress-test that folklore against real draw data in best keno numbers: myth vs math. Staking tricks don't touch the tables either; keno betting systems runs those numbers.
The one lever you do control is ticket size. Pick fewer numbers and sweeps get likelier; pick more and you're buying a longer shot at a rarer catch tier. Your expected haul stays at a quarter of your picks either way: play ten spots and two or three catches is the normal draw, not the disappointing one.
One instinct worth retiring: the draw has no memory. A number that hasn't appeared in twenty games is still exactly 1 in 4 on the next draw, the same as one that just hit twice in a row. The tables on this page are the whole game. Nothing you do between draws edits them.
Play it smart: no pick, pattern, or system moves a single row of these tables, so price keno as entertainment using the odds above and never budget around a 1 in 8,911,711 outcome. This article is education, not financial or gambling advice. 18+/21+ depending on your jurisdiction.
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
- Ohio Lottery — KENO — retrieved July 2026
- Massachusetts Lottery — Keno — retrieved July 2026
- GBH News — Is Keno in Massachusetts fair? — retrieved July 2026
- Wizard of Odds — Keno — retrieved July 2026
Frequently asked questions
What are the odds of hitting all 10 numbers in keno?
The odds are 1 in 8,911,711, a probability of 0.0000112%. Wild Academy computed this exactly with the hypergeometric formula: C(20,10) = 184,756 winning combinations out of C(80,10) = 1,646,492,110,120 possible ten-number tickets. Official published odds agree; the Michigan Lottery lists the 10-spot top catch at 1 in 8.91 million. Playing 1,000 games a day, you'd expect one solid hit roughly every 24 years.
What are the odds of hitting 7 out of 7 in keno?
A solid 7-spot is a 1 in 40,979 shot, a probability of 0.0024%, per Wild Academy's exact calculation (2026). Catching 7 on a bigger ticket is far easier because the extra picks are allowed to miss: 7 of 10 comes in at about 1 in 621. Typical 7-spot draws are much humbler, though; you'll catch two or fewer on roughly three of every four games.
How are keno odds calculated?
With the hypergeometric distribution: P(k) = C(20,k) × C(60,n−k) / C(80,n), where n is how many numbers you pick and k is how many you catch. The top counts the tickets that land exactly k of the 20 drawn numbers; the bottom counts every possible ticket. Every keno odds calculator runs this formula, and the tables in this article are its exact output for all standard ticket sizes.
Which spot count has the best odds in keno?
It depends on which odds you mean. Sweeping your whole ticket is likeliest on small ones: 1 in 4 on a single number, 1 in 72 on three, 1 in 8,911,711 on ten, per Wild Academy's calculation (2026). Odds of winning any prize depend on which catch tiers a paytable pays, including zero-catch consolations. Whether any spot count is good value is a house-edge question, not an odds question.
What are the odds of catching zero numbers in keno?
It depends on ticket size. Miss odds shrink as you pick more: a single number misses 75% of the time, a 5-spot blanks 22.7% of the time (1 in 4.4), and a 10-spot blanks just 4.58% of the time (1 in 21.8), per Wild Academy's exact calculation (2026). A big-ticket blank is rare enough that several state lotteries pay a small consolation for catching nothing.
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About the author
Betting & Casino Math Writer
Sofia writes the odds track — betting odds formats, implied probability, house edge, and RTP — and the Myth vs Math pieces that test popular casino tricks against the arithmetic.
