Keno Odds Calculator
Keno draws a fixed batch of numbers from a pool without replacement, so the chance of matching exactly k of your chosen spots is an exact hypergeometric probability. Enter the pool size (usually 80), how many numbers are drawn (usually 20), how many spots you marked, and the number of matches you want the odds for. The calculator returns the exact probability of hitting exactly k, the odds against that result, and the expected number of matches. Every figure is pure combinatorics with no estimation.
Keno odds formula
P(exactly k) = C(s, k) * C(N - s, d - k) / C(N, d)
where N = pool, d = numbers drawn, s = your spots
Odds against = (1 - P) / P
Expected matches = s * d / N
C(n, r) is the binomial coefficient, the number of ways to choose r items from n. The numerator counts ways to match k of your spots and fill the rest with non-spots; the denominator counts all possible draws.
Standard 80-ball keno facts
- The draw fraction is 20/80 = one quarter, so each spot has a 25 percent chance of being hit.
- A 10-spot ticket expects 2.5 matches on average.
- Hitting all 10 spots on a 10-spot ticket has probability about 0.0000112 percent.
- Matching exactly 5 of 10 spots has probability about 5.14 percent.
- The probability of zero matches on a 10-spot ticket is about 4.58 percent.
Keno odds: frequently asked questions
How are keno odds calculated?
Keno is a draw without replacement, so the chance of matching exactly k of your spots is a hypergeometric probability. It equals C(spots, k) times C(pool minus spots, drawn minus k), all divided by C(pool, drawn), where C is the binomial coefficient. This calculator evaluates that exact expression.
What are the standard keno numbers?
In a typical keno game the pool is 80 numbers and 20 are drawn each round. You choose a number of spots (commonly 1 to 20). This calculator lets you set the pool, the count drawn, your spots, and the number of matches k, so it works for any keno variant.
What does odds against mean?
Odds against a result express how many losing outcomes there are for each winning outcome. If the probability of hitting k is p, the odds against are (1 minus p) divided by p, written as that figure to 1. Lower probability means longer odds.
What is the expected number of matches?
By symmetry the expected number of your spots that are hit equals your spots times the draw fraction (numbers drawn divided by the pool). For an 80-ball game drawing 20, that fraction is one quarter, so a 10-spot ticket expects 2.5 matches on average.
What inputs are valid?
The pool size must be a positive whole number. The numbers drawn and your spots must each be whole numbers no larger than the pool. The matches k must be a whole number that is achievable, meaning at most your spots and at most the numbers drawn. Impossible combinations return n/a.
Official sources
- Nevada Gaming Control Board: Gaming regulations and approved game rules.
- NIST/SEMATECH e-Handbook of Statistical Methods: Hypergeometric distribution.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.