Keno Odds Calculator
18+ only. Contains affiliate links — we may earn a commission. Not for residents of the US, UK, France, Germany, Netherlands, Spain, Austria, Australia, Ontario or Vietnam. Not legal or financial advice.
Choose a 40-ball or 80-ball board, how many distinct balls are drawn and how many distinct numbers you pick. The table covers every hit count from zero to all your picks. It assumes a uniformly random draw without replacement; number patterns do not improve the odds.
Example inputs: replace with your own figures
Result
| Expected hits | 0.25 |
|---|
| Hits | Probability |
|---|---|
| 0 | 75% |
| 1 | 25% |
18+ · Educational tool. All calculations run in your browser. Examples are not casino rates.
Educational draw model only. Displayed decimals are rounded. No Keno payout table, operator odds or verified casino rules are supplied.
How it is calculated
- For board N, draw D, picks p and hits h: P(h) = C(p, h) × C(N − p, D − h) / C(N, D). C(a, b) is zero when b exceeds a.
- Possible hits range from max(0, D + p − N) to min(p, D). Other hit counts are shown with zero probability. Draws and picks must each be between 0 and N.
- On a 40-ball board with 10 drawn and 1 pick, P(1 hit) = 10/40 = 25%; P(0 hits) = 75%. Expected hits = p × D/N, which is not the chance of receiving a prize.
- No payout table is assumed. To calculate RTP you also need the total-return multiplier for each hit count: RTP = Σ P(h) × m(h). Keno draws are dependent within a round, unlike independent Plinko turns.
18+ · No formula removes the house edge. Do not chase losses; set limits and only use money you can afford to lose. Help and limits.
Related reading
- Mines: another without-replacement model
- Plinko: independent turns
- Probability versus payout
- Calculate RTP with your payout table
Frequently asked questions
Does choosing consecutive numbers change the probability?
No, provided every draw of distinct numbers is equally likely. Only the board size, draw count and pick count matter.
Why are some table entries zero?
You cannot hit more than the draw or pick count, and a large draw may make zero hits impossible. All hit counts remain visible so these constraints are explicit.
Does a 25% hit chance mean 25% RTP?
No. Hit probability and return are different quantities. RTP also needs the payout for every outcome.
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