Keno odds depend on two things: how many of your chosen numbers appear in the draw, and which match counts the game’s paytable rewards. For a draw of 20 numbers from 80, the chance of matching exactly r of k selected spots is C(k,r) × C(80−k,20−r) ÷ C(80,20). To find the chance of winning any prize, add the probabilities for every match count that the local paytable marks as a win.
What do Keno odds measure?
There are two different probabilities players often mean by “Keno odds”:
- Exact-match probability: the chance that a draw contains a particular number of your selected spots, such as exactly five.
- Overall odds of winning: the chance of receiving any prize under a particular game’s paytable. This combines the probabilities of all match counts that pay.
These are not interchangeable. The chance of matching all your spots is only one possible outcome; an overall-odds figure can include several lower match counts, and some games pay for zero matches. The Ohio Lottery and Virginia Lottery both describe games drawing 20 numbers from a pool of 80, but their 10-spot paytables produce different overall odds: Ohio lists 1 in 9.05, while Virginia lists 1 in 3.9. Those figures describe those jurisdictions’ games, not Keno universally. See the Ohio Lottery Keno page and Virginia Lottery Keno page.
How to calculate the chance of an exact number of matches
For a game that draws 20 distinct numbers from 80, let k be the number of spots you select and r the number of those spots that appear in the draw. The probability of exactly r matches is:
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P(exactly r matches) = C(k,r) × C(80−k,20−r) ÷ C(80,20)
C(n,m), read “n choose m,” counts the ways to select m items from n. The numerator counts draws that contain exactly r of your k chosen numbers and fill the other 20−r drawn positions with numbers you did not choose. The denominator counts all possible 20-number draws. This is a hypergeometric model: numbers are drawn without replacement.
For example, to calculate the probability of exactly five matches when you choose 10 spots, use k = 10 and r = 5: C(10,5) × C(70,15) ÷ C(80,20). The formula gives the probability of that exact result—not the chance of any prize. A combinations-based Keno probability example is also provided in GambleAware NSW’s Part B: Keno.
How to find the chance of winning any prize
- Identify the exact game and wager. Check the operator’s current rules for the draw format, spot count, paytable, and any optional features.
- List every winning match count. Include zero matches if the paytable awards a prize for it.
- Calculate each exact-match probability. Use the formula for each winning value of r with the game’s pool size and draw size.
- Add those probabilities. The sum is the chance of winning any prize for that spot selection, assuming the draw follows the stated format.
For instance, Ohio’s 10-spot example lists prizes for 10, 9, 8, 7, 6, 5, or 0 matches. Its overall odds are based on those paid outcomes, rather than on the probability of hitting all 10 spots alone. A different paytable can count different outcomes as wins, even when the draw format is the same.
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Why published Keno odds differ
The draw format determines the probability of each match count; the paytable determines which of those outcomes count as wins and what they pay. Compare the actual rules rather than treating an overall-odds figure as a feature shared by every Keno game.
| Example | Draw format | 10-spot overall odds | Qualification |
|---|---|---|---|
| Ohio Lottery | 20 drawn from 80 | 1 in 9.05 | Ohio’s current page gives this figure for its 10-spot example; listed prize values are based on a $1 wager. The operating procedure is effective October 18, 2025. Ohio Lottery Keno |
| Virginia Lottery | 20 drawn from 80 | 1 in 3.9 | Virginia’s official Keno page gives this figure for its 10-spot example and its own prize table. Virginia Lottery Keno |
The difference does not contradict the combinations formula: overall odds depend on which results each game pays. When comparing games or bet styles, check the pool and draw size, whether you want jackpot odds or any-prize odds, paid match tiers, cost per draw, optional features, and any top-prize caps or multipliers.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Check the cost as well as the odds
Odds describe the likelihood of an outcome, not the amount you must wager or the value of a prize. In Ohio, displayed prizes are based on a $1 wager; the Lottery says to multiply the listed prize by the wager for wagers over $1. That scaling instruction should not be confused with a different probability for matching numbers. Check the current rules for the exact wager and prize conditions.
Optional features can change the total cost without changing the base game’s match-count formula. Delaware’s KENO Bonus feature costs the same amount as the KENO wager, so a $1 KENO wager plus Bonus costs $2 total. It is a separate feature, not an adjustment to the base game’s odds. Details are on the Delaware Lottery’s What Is KENO? page.
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What the formula does—and does not—tell you
The formula applies when each possible set of the stated number of drawn spots is equally likely. If a game uses a different pool size or draws a different number of spots, replace 80 and 20 with that game’s parameters. The formula gives probabilities for match counts; it does not by itself identify winning outcomes, prize amounts, or the chance of winning under a particular paytable.
Under this uniform-draw model, choosing one set of numbers rather than another does not improve the probability of a given match count. A number pattern or previous result does not alter the combinations counted by the formula. For a decision about a real game, rely on its current official rules and paytable rather than a general Keno odds chart.
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