Keno is one of the highest house-edge games in any casino, but that does not mean every bet is equal. The difference between a Pick 4 and a Pick 10 is enormous — not just in jackpot size, but in how likely you are to win anything at all.
This calculator uses the hypergeometric distribution to compute the exact mathematical probability of every possible outcome for any Pick strategy. No simulations, no approximations — just the precise odds.
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The Math Behind Keno Odds
Standard keno uses a pool of 80 numbers. The house draws 20. You pick between 1 and 20 numbers (your “spots”). The question is: of the 20 numbers drawn, how many will match yours?
This is a classic hypergeometric probability problem. The formula for catching exactly k numbers out of your n picks when 20 are drawn from 80 is:
P(catch k) = C(n, k) × C(80−n, 20−k) ÷ C(80, 20)
Where C(a, b) is the combination function — the number of ways to choose b items from a. The calculator computes this for every possible value of k, from 0 (catching nothing) up to your full pick count.
Example: The Pick 10 Trap
Pick 10 is one of the most popular keno bets because the jackpot for catching all 10 numbers can be enormous. But look at the actual probabilities:
Catch 10/10: 1 in 8,911,711 — roughly equivalent to a small state lottery. You could play one keno game every minute for 17 years straight and statistically expect to hit this once.
Catch 5/10: 1 in 19.4 — this is the most likely winning outcome, but at most casinos a Pick 10 with 5 catches pays only 2× to 3× your bet.
Catch 0/10: 1 in 21.8 (4.58%) — you have nearly a 1-in-22 chance of none of your numbers being drawn. Some casinos actually pay a small consolation prize for catching 0 on Pick 10, since it is surprisingly rare to whiff completely.
The most common result on Pick 10 is catching 2 or 3 numbers (combined probability: 56.3%), which almost never pays anything.
Catch-All Odds by Pick Size
How your pick size affects the odds of catching every number:
Pick 1: 1 in 4 (25.0%) — one in four games, you win. Simple and transparent.
Pick 3: 1 in 72.1 (1.39%) — manageable. You will hit this a few times in a long session.
Pick 5: 1 in 1,551 (0.064%) — a typical casino session is 20–30 games. You will almost certainly not catch all 5 tonight, but over months of regular play it is plausible.
Pick 7: 1 in 40,979 (0.0024%) — now we are firmly in “hope” territory. You need to play thousands of games.
Pick 10: 1 in 8,911,711 — this is the lottery-odds zone. The jackpot needs to be massive to justify this bet mathematically.
Pick 15: 1 in 428 billion — for perspective, the odds of being struck by lightning in your lifetime are about 1 in 15,000.
Strategic Advice: Why Pick 4–7 Often Has the Best RTP
Keno house edges vary dramatically depending on the casino and the pick size. However, a consistent pattern emerges across most paytables: Pick 4 through Pick 7 tend to offer the best Return to Player (RTP).
The reason is structural. For low picks (1–3), the payouts must be small because wins are frequent — and casinos need their edge. For high picks (8–15), the catch-all jackpot is so rare that casinos can afford to offer eye-catching top prizes while still maintaining 25–30% house edges on the overall bet.
In the middle range (4–7), the partial catches (catching most but not all of your numbers) occur often enough that they contribute meaningfully to RTP. A Pick 6 that pays 75× for catching 6/6 and 4× for catching 5/6 has two revenue-generating outcomes instead of just one.
Before placing any keno bet, check the specific paytable at your casino. The same Pick 6 can have anywhere from 60% to 95% RTP depending on the venue.