What a keno bet returns depends on two things: how likely each catch is, and what the paytable pays for it. This calculator handles both. It uses the hypergeometric distribution to give the exact probability of catching 0 through all of your numbers, then turns your casino’s paytable into Return to Player (RTP), house edge and hit frequency.
Pool size and draw count are adjustable, so standard 80-number keno with 20 drawn and shorter formats such as 40 numbers with 10 drawn run through the same tool.
| Catch | Probability | 1 in X | Likelihood |
|---|
| Catch | Probability | Payout | Push | RTP Share |
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How to Use the Calculator
- Set the game. Enter how many numbers you pick, how many are in the pool and how many the house draws, then press Calculate Keno Odds.
- Read the odds table. Each row is one catch level with its probability and its “1 in X” equivalent.
- Add the paytable. Type the payout next to every catch that pays and leave the rest blank.
- Choose “for 1” or “to 1” to match how the casino writes its payouts, then press Calculate RTP & House Edge. The RTP Share column shows how much of the return each catch supplies.
The Math Behind Keno Odds
Let N be the numbers in the pool, n the numbers you pick, D the numbers drawn and k the numbers you catch. The probability of catching exactly k is:
P(catch k) = C(n, k) × C(N−n, D−k) ÷ C(N, D)
C(a, b) is the number of ways to choose b items from a. Standard keno is N = 80 and D = 20; a 40-number game drawing 10 is N = 40 and D = 10. The calculator evaluates the formula for every catch level, so the results are computed probabilities and do not come from simulated draws.
How RTP and House Edge Are Calculated
RTP is the sum, over every paying catch, of its probability multiplied by the total amount it returns per unit wagered:
RTP = Σ [P(catch k) × total return for catch k]
House Edge = 1 − RTP
Take a Pick 6 bet in standard keno with an illustrative paytable of 3, 4, 70 and 1,600 for 1:
| Catch | Probability | Odds | Payout | RTP share |
|---|---|---|---|---|
| 6 of 6 | 0.01% | 1 in 7,753 | 1600 for 1 | 20.64% |
| 5 of 6 | 0.31% | 1 in 323 | 70 for 1 | 21.67% |
| 4 of 6 | 2.85% | 1 in 35 | 4 for 1 | 11.42% |
| 3 of 6 | 12.98% | 1 in 7.7 | 3 for 1 | 38.95% |
The shares add up to an RTP of 92.67% and a house edge of 7.33% (the rows above are rounded). The bet returns something on 16.16% of draws. The smallest prize supplies the largest share of the return, and the two top catches, which together land about once in 310 draws, supply 42.31 percentage points of it. Raise or lower any one payout in the calculator and the RTP Share column shows where the return moved.
If a paytable works out above 100% RTP, the calculator labels the result as a player edge.
“For 1” vs “To 1” Payouts
A payout of 5 for 1 means a $1 bet comes back as $5 in total, stake included. A payout of 5 to 1 means $5 profit plus the $1 stake, so $6 in total. The Pick 6 table above gives the same 92.67% when entered in “to 1” mode as 2, 3, 69 and 1,599.
Mixing up the two formats shifts every paying row by one full stake, which is enough to move the RTP by the whole hit frequency: 16.16% in this example.
Pick 10 in Standard Keno
Pick 10 draws players with its top prize, but the full distribution shows where results land in practice:
| Catch | Probability | Odds |
|---|---|---|
| 0 of 10 | 4.58% | 1 in 21.8 |
| 1 of 10 | 17.96% | 1 in 5.6 |
| 2 of 10 | 29.53% | 1 in 3.4 |
| 3 of 10 | 26.74% | 1 in 3.7 |
| 4 of 10 | 14.73% | 1 in 6.8 |
| 5 of 10 | 5.14% | 1 in 19.4 |
| 6 of 10 | 1.15% | 1 in 87.1 |
| 7 of 10 | 0.16% | 1 in 621 |
| 8 of 10 | 0.01% | 1 in 7,384 |
| 9 of 10 | under 0.01% | 1 in 163,381 |
| 10 of 10 | under 0.01% | 1 in 8,911,711 |
Catching 2 or 3 numbers accounts for 56.27% of all draws. Five or more comes up 6.47% of the time. All 10 is a 1 in 8,911,711 event: at one draw per minute around the clock, that is one expected hit in about 17 years.
Catch-All Odds by Pick Size
For standard 80/20 keno, each extra number makes a full catch several times less likely, while missing every number becomes rarer:
| Pick size | Catch all | Catch all, % | Catch none, % |
|---|---|---|---|
| Pick 1 | 1 in 4 | 25.00% | 75.00% |
| Pick 2 | 1 in 16.6 | 6.01% | 56.01% |
| Pick 3 | 1 in 72.1 | 1.39% | 41.65% |
| Pick 4 | 1 in 326 | 0.31% | 30.83% |
| Pick 5 | 1 in 1,551 | 0.06% | 22.72% |
| Pick 6 | 1 in 7,753 | 0.01% | 16.66% |
| Pick 7 | 1 in 40,979 | under 0.01% | 12.16% |
| Pick 8 | 1 in 230,115 | under 0.01% | 8.83% |
| Pick 9 | 1 in 1,380,688 | under 0.01% | 6.37% |
| Pick 10 | 1 in 8,911,711 | under 0.01% | 4.58% |
None of this ranks pick sizes by value. Two casinos can run the same Pick 6 with different payouts for 4, 5 and 6 catches, and the RTP follows the payouts.
Standard 80/20 vs 40/10 Keno
A game that draws 10 numbers from 40 hits the same fraction of the pool as standard keno, a quarter, so a 10-number ticket averages 2.5 catches in both. The distributions still differ:
| Pick 10 | 80 numbers, 20 drawn | 40 numbers, 10 drawn |
|---|---|---|
| Expected catches | 2.50 | 2.50 |
| Catch 0 | 4.58% | 3.54% |
| Catch 2 or 3 | 56.27% | 59.89% |
| Catch 5 or more | 6.47% | 4.98% |
| Catch all 10 | 1 in 8,911,711 | 1 in 847,660,528 |
The 40/10 game bunches results closer to the average: fewer blanks, fewer high catches, and a full catch that is about 95 times rarer. A paytable written for 80/20 keno would therefore produce a different RTP in the 40/10 game, which is why the RTP section always works from the format you entered.
Frequently Asked Questions (FAQ)
Does playing the same numbers every game improve my odds?
No. Every fair keno draw is independent of the one before it, so a set of numbers you have played for years has the same chance as a set picked at random a second ago. Only the count of numbers you pick changes the probabilities.
What is the house edge on keno?
Keno has no single house edge. The edge comes from the paytable, and paytables differ between casinos, between pick sizes at the same casino, and between game versions. Enter the payouts for your game in the paytable section and the calculator returns the theoretical RTP and house edge for that exact bet.
How do I enter my keno paytable?
Calculate the odds for your pick, pool and draw size first. Then type the payout next to each catch that pays and leave the others blank. Pick “for 1” if the listed number is the total you get back, or “to 1” if it is profit on top of your stake. In “to 1” mode, tick Push for a catch that only refunds the bet.
Is RTP the same as my chance of winning?
No. Hit frequency is how often a bet returns anything; RTP is how much comes back on average per unit wagered. In the Pick 6 example on this page the bet pays on 16.16% of draws, yet the RTP is 92.67%, because the rare 5-of-6 and 6-of-6 catches carry almost half of the return.
What are the odds of catching zero numbers?
In standard 80/20 keno it is 75.00% for Pick 1, 22.72% for Pick 5 and 4.58% for Pick 10. The more numbers you pick, the harder it is to miss all of them. If your paytable pays for catching zero, enter that payout in the Catch 0 row.
Does this calculator work for non-standard keno games?
Yes, for pools of 20 to 80 numbers, up to 40 numbers drawn and up to 40 picked. Both the probability table and the RTP section use the values you enter, so a 40-number game with 10 drawn is calculated directly.
What if I pick more numbers than the house draws?
Then catching all of your numbers cannot happen, and the calculator labels that result as impossible. The remaining catch levels are calculated as usual, and the paytable rows for impossible catches are switched off.
What does the hypergeometric distribution mean?
It is the probability model for drawing from a fixed pool without putting anything back. Keno fits it exactly: the pool is fixed, your picks are the numbers that count as hits, and no ball can be drawn twice. Because each drawn ball changes what is left in the pool, the chances cannot be found by multiplying one fixed probability.