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KENO CALCULATOR

Work out the exact probability of matching your Keno spots on a Stake-style 40-number, 10-draw board. Pure hypergeometric odds — not operator pay tables.

Your Keno Ticket
Chance of Exactly m
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Expected Hits
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Chance of Zero Hits
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Stake-style Keno draws 10 numbers from a pool of 40. If you pick n spots, the chance of matching exactly m of them is the hypergeometric probability C(n,m)·C(40−n,10−m) / C(40,10). These are hit odds only; the payout for each hit count is set by the operator, so it is not shown here.

FULL HIT-DISTRIBUTION TABLE (updates with your spot count)

Hits (m)ProbabilityApprox. Odds
021.6572%1 in 5
141.6484%1 in 2
227.7656%1 in 4
37.9330%1 in 13
40.9574%1 in 104
50.0383%1 in 2,611

Default shown for a 5-spot ticket. Change the spot count above to recalculate.

HOW KENO ODDS WORK

Keno is a lottery-style draw. In the Stake-style version used here the game picks 10 winning numbers from a pool of 40. Before the draw you choose n of those 40 numbers (1 to 10 spots). Your result is how many of your picks appear among the 10 drawn.

The maths is the hypergeometric distribution — drawing without replacement. The chance of matching exactly m of your n spots is C(n,m) × C(40−n, 10−m) / C(40,10), where C(40,10) = 847,660,528 is the number of possible draws. For example, on a 5-spot ticket you have about a 21.66% chance of zero hits, and only about a 0.038% chance (roughly 1 in 2,611) of hitting all five. Whatever number of spots you pick, your expected number of hits is always n × 10 / 40 = n/4.

The odds above are fixed by the maths of the draw — there is no pattern or hot number that changes them. What each hit count pays is an operator-specific pay table, so check your casino, and confirm a real draw with the Keno provably fair verifier.

Related Resources

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KENO CALCULATOR FAQ

Keno uses the hypergeometric distribution because numbers are drawn without replacement. With a 40-number pool and 10 drawn, picking n spots, the chance of matching exactly m is C(n,m) × C(40-n,10-m) / C(40,10). This tool computes the full hit distribution for any 1-to-10 spot ticket. It does not calculate payouts, which are operator-specific.
It gets steeply rarer as you add spots. Hitting all your picks is about 25% for a 1-spot ticket, roughly 0.038% (about 1 in 2,611) for a 5-spot ticket, and around 1 in 8.9 million for a 10-spot ticket. Bigger tickets pay far more for a full match precisely because a full match is so unlikely.
On this 40-pool, 10-draw format your expected hits are always your spots divided by four: n × 10/40 = n/4. So a 4-spot ticket averages 1 hit, an 8-spot ticket averages 2 hits. The average is the same story regardless of which numbers you choose — only the spread of outcomes changes.
No. It computes probabilities only. On a provably-fair Keno game the 10 numbers come from a hashed server seed that is revealed only after the round, so the draw cannot be predicted. Use our Keno verifier to check that a past draw was fair.