What is a keno odds calculator?
A keno odds calculator gives the exact chance of catching a given number of your picks. In standard keno, 20 numbers are drawn from 80. If you pick 10 spots, the chance of exactly 5 hits is 5.14% (1 in 19.4), and the chance of 5 or more is 6.47%. The numbers come from counting combinations, so they are exact for the rules you enter.
Odds are only half of the picture in keno, because the paytable decides what each hit is worth. A calculator for the odds cannot say if a game is good value, but it can show how fast the chance of the top hits falls. That is the quickest way to see why the big prizes are rare, and why the expected number of hits is small. With 10 spots and 20 of 80 drawn, you hit 2.5 numbers on average.
How do you use the keno odds calculator?
- Enter the numbers in the pool. Standard keno uses 80.
- Enter the numbers drawn. Standard keno draws 20.
- Enter the spots you pick. Most games allow 1 to 10, and some allow up to 20.
- Enter the hits you want. This is how many of your picks you want to see drawn.
- Read the large number. It is the chance of exactly that many hits. The panel gives the chance of that many or more, and a table of every number of hits.
Example: Pool 80, 20 drawn, 10 spots, 5 hits. Ways to hit exactly 5 = C(10,5) x C(70,15). All draws = C(80,20). The chance is 5.14%, or 1 in 19.4.
How are keno odds calculated?
Keno follows the hypergeometric distribution. If N numbers are in the pool, n are drawn and you pick K, the chance of exactly h hits is C(K, h) x C(N – K, n – h) / C(N, n). Here C(K, h) is the number of ways to choose which of your picks are hit and C(N – K, n – h) is the number of ways for the rest of the draw to miss your other picks. The calculator uses exact whole numbers. The same counting is how Wikipedia lists the odds for a 20-spot ticket, where catching none has odds of 1 in 843.38.
| Step | Working | Result |
|---|---|---|
| All draws | C(80, 20) | 3,535,316,142,212,174,320 |
| Ways to hit exactly 5 of 10 | C(10, 5) x C(70, 15) | 252 x 70-choose-15 |
| Chance of exactly 5 | ways / all draws | 5.14% |
| Odds | all draws / ways | 1 in 19.4 |
What does a 10-spot ticket look like?
The table shows every possible number of hits for a 10-spot ticket. The most likely result is 2 hits, not the 5 hits that often earn a first prize. Hitting 6 or more happens about once in 76 tickets, and hitting all 10 is 1 in 8,911,711.
| Hits | Odds | Chance |
|---|---|---|
| 0 | 1 in 21.8 | 4.58% |
| 1 | 1 in 5.6 | 17.96% |
| 2 | 1 in 3.4 | 29.53% |
| 3 | 1 in 3.7 | 26.74% |
| 4 | 1 in 6.8 | 14.73% |
| 5 | 1 in 19.4 | 5.14% |
| 6 | 1 in 87.1 | 1.15% |
| 7 | 1 in 621 | 0.16% |
| 8 | 1 in 7,384 | 0.01% |
| 9 | 1 in 163,381 | 0.0006% |
| 10 | 1 in 8,911,711 | under 0.0001% |
How does the number of spots change the chance of hitting all of them?
Picking more spots raises the top prize but makes catching every one far less likely. The table gives the chance of hitting all of your spots. The jump from 5 to 10 spots changes the odds from about 1 in 1,551 to about 1 in 8.9 million.
| Spots picked | Odds of hitting every spot | Chance |
|---|---|---|
| 1 | 1 in 4.0 | 25.00% |
| 2 | 1 in 16.6 | 6.01% |
| 3 | 1 in 72.1 | 1.39% |
| 4 | 1 in 326 | 0.31% |
| 5 | 1 in 1,551 | 0.06% |
| 6 | 1 in 7,753 | 0.01% |
| 8 | 1 in 230,115 | 0.0004% |
| 10 | 1 in 8,911,711 | under 0.0001% |
This is why paytables for larger tickets look generous at the top. A big headline prize on a 10-spot ticket is a prize for an event that happens about once in 9 million tickets. What a ticket is worth is the chance of each hit times its prize, added up. The odds here are one half of that sum, and the paytable is the other half.
What does the calculator leave out?
- The paytable. It gives the odds of hits, not the value of a ticket.
- The house edge. It depends on the paytable, and it can be large. Check the game’s published return.
- Game variants. Some games add bonus numbers or multipliers.
- Picking strategy. The numbers drawn are random, so no pick is luckier than another.
- Several tickets. It treats one ticket at a time.
What mistakes do people make with keno odds?
- Chasing “hot” numbers. The draw has no memory.
- Thinking more spots is better. More spots means a lower chance of every top hit.
- Reading the top prize as typical. The table shows how rare it is.
- Playing fast. Draws come every few minutes in many venues, so spend adds up quickly.
- Skipping the paytable. Two games with the same odds can pay very differently.
What should you try next?
Change the spots from 10 to 5 and compare the chance of hitting them all. Then check how the same counting works for bingo with the bingo odds calculator. To see what a regular session costs on average, use the expected loss calculator, and to set a budget first, use the Safer play toolkit.
How to read the result
The large number is the chance of exactly the number of hits you chose, with the "1 in" odds under it. The panel gives the chance of that many hits or more and a table of every possible number of hits with its odds. The results are exact counts. They tell you how likely each hit is, not what it pays, and the paytable decides whether a ticket is good value.
How it is calculated
With N numbers in the pool, n drawn and K picked, the chance of exactly h hits = C(K, h) x C(N - K, n - h) / C(N, n), where C(a, b) is the number of ways to choose b items from a. This is the hypergeometric distribution. The calculator uses exact whole numbers, and the chance of h or more is the sum of the chances from h to the maximum.
Worked example
Worked example
Pool 80, 20 drawn, 10 spots, 5 hits. Ways = C(10,5) x C(70,15). All draws = C(80,20). Chance of exactly 5 hits = 5.14%, or 1 in 19.4. Chance of 5 or more = 6.47%. The average number of hits is 10 x 20 / 80 = 2.5.
Limits
The calculator gives hit odds, not prizes. It does not use a paytable, so it cannot say if a game is good value, and it does not model bonus numbers, multipliers or progressive prizes. It treats one ticket and a fair draw where every number is equally likely, so no pick is luckier than another. The house edge depends on the paytable, which the operator publishes. Results are exact for the inputs, and are not predictions.