Keno odds calculator
Odds are exact for a draw of 20 numbers from 80. Payouts differ by game and state, so check the pay table of the game you play.
Key facts
- In Australian keno, 20 numbers are drawn from 1 to 80, as set out in the Queensland Keno Rule 2010.
- Chance of matching k of your s numbers = C(20, k) x C(60, s - k) / C(80, s).
- Picking 1 number gives a 1 in 4 chance; catching all 10 of 10 spots is 1 in 8,911,711.
- On a 10 spot game you are more likely to catch none of your numbers (4.58%) than 6 or more (1.32%).
- Heads (11 or more of the 20 drawn numbers in 1 to 40) has a 39.84% chance, tails the same, and evens 20.32%.
How to use the keno odds calculator
Pick how many numbers you play, from 1 to 20. The calculator lists every possible result, from matching all your numbers down to matching none, with the exact chance and the odds as "1 in" a number. It does not show prizes, because pay tables differ between games and states. Use it next to the prize table for the game you play.
How keno odds are calculated
Keno odds come from a counting formula called the hypergeometric distribution. The draw takes 20 numbers from 80, so 20 numbers are "hits" and 60 are "misses". If you pick s numbers, the chance of matching exactly k of them is:
C(20, k) x C(60, s - k) / C(80, s)
C(n, r) is the number of ways to choose r items from n. Take a 4 spot game where you need all four. There are C(20, 4) = 4,845 ways to pick four numbers from the 20 drawn, and C(80, 4) = 1,581,580 ways to pick any four from 80. So the chance is 4,845 / 1,581,580, or 1 in 326.
Keno odds of winning the top catch, by spot
The more numbers you pick, the harder it gets to match all of them. Each extra spot multiplies the difficulty.
| Numbers picked | Chance of matching all | Odds |
|---|---|---|
| 1 | 25% | 1 in 4 |
| 2 | 6.01% | 1 in 17 |
| 3 | 1.39% | 1 in 72 |
| 4 | 0.31% | 1 in 326 |
| 5 | 0.064% | 1 in 1,551 |
| 6 | 0.013% | 1 in 7,753 |
| 7 | 0.0024% | 1 in 40,979 |
| 8 | 0.00043% | 1 in 230,115 |
| 9 | 0.000072% | 1 in 1,380,688 |
| 10 | 0.000011% | 1 in 8,911,711 |
| 15 | 1 in 428,010,179,098 | |
| 20 | about 1 in 3.5 x 10^18 |
Every result on a 10 spot game
A 10 spot game shows how the chances spread out. On average you catch a quarter of your numbers, because 20 of the 80 are drawn: 2.5 numbers on a 10 spot.
| Numbers matched | Chance | Odds |
|---|---|---|
| 10 | 0.000011% | 1 in 8,911,711 |
| 9 | 0.00061% | 1 in 163,381 |
| 8 | 0.0135% | 1 in 7,384 |
| 7 | 0.161% | 1 in 621 |
| 6 | 1.148% | 1 in 87 |
| 5 | 5.143% | 1 in 19 |
| 4 | 14.732% | 1 in 7 |
| 3 | 26.740% | 1 in 4 |
| 2 | 29.526% | 1 in 3 |
| 1 | 17.957% | 1 in 6 |
| 0 | 4.579% | 1 in 22 |
Just over half of all 10 spot tickets (52.06%) catch 2 numbers or fewer. Matching none of your 10 (4.58%) happens more than three times as often as matching 6 or more (1.32%).
Heads or tails odds
Heads or tails is a bet on where the 20 drawn numbers fall. Under section 17 of the Queensland Keno Rule 2010, heads wins when 11 or more of the 20 drawn numbers are between 1 and 40, tails wins when 11 or more are between 41 and 80, and evens wins when the draw splits exactly 10 and 10.
| Bet | Wins when | Chance |
|---|---|---|
| Heads | 11 or more of the 20 drawn are 1 to 40 | 39.84% |
| Tails | 11 or more of the 20 drawn are 41 to 80 | 39.84% |
| Evens | Exactly 10 from each half | 20.32% |
Evens comes up about 1 game in 5. That is why heads and tails each win less than 40% of the time, not 50%.
Pundit tip: odds tell you how often a catch happens, not whether a game is good value. A game that pays often but pays small can still return less than one that rarely pays. Always read the prize table next to these odds.
Keno odds in Australia: what the rules say
The Queensland Keno Rule 2010, published on the TAB's help site, sets out the game: 20 numbers drawn from 1 to 80, a Keno Classic game with a $1 minimum wager, jackpots on 7, 8, 9 and 10 spot wagers, and prizes paid from the prize tables in a schedule of prizes. For Keno Classic, it allocates 10% of 7, 8, 9 and 10 spot wagers to jackpot growth.
The odds on this page are the same in any keno game that draws 20 from 80. What changes between games is the prize table, and the prize table decides the return.
From keno odds to the real cost
To find what a keno game returns, multiply the chance of each catch by the prize for that catch and add them up. The total, divided by the bet, is the game's return to player; the rest is the house's share. The expected value calculator does the same sum for a single bet. Do it once with a real pay table and you will see why the big catches, at 1 in millions, add very little to the average return.
That is the same logic as a poker machine's RTP, and doubling your bet after a loss does not change it; the Martingale calculator shows why the average never moves. The pokies calculator shows what a given return costs per hour. For how keno works online, read our guide to online keno in Australia. Every calculator is on our bet calculators page, and free, confidential help is listed on our gambling help page.
Frequently asked questions
What are the odds of winning keno?
It depends on how many numbers you pick and how many you need to match. Picking 1 number, you match it 1 time in 4. Picking 10, you catch 5 or more 6.47% of the time and all 10 about 1 in 8.9 million. Whether a catch wins money depends on the game's prize table.
What is the best number of spots to play in keno?
There is no best spot count for winning more often in the long run, because the prize table, not the odds, sets the return. Fewer spots win small amounts more often; more spots win rarely but can pay more. Compare the prize table with the odds before you choose.
What are the odds of getting all 20 numbers in keno?
On a 20 spot game, matching all 20 is 1 in C(80, 20), which is about 1 in 3.5 quintillion (3.5 x 10^18). Catching none of your 20 numbers is far more likely, at 1 in 843.
How does the keno odds calculator work?
It uses the hypergeometric formula for 20 numbers drawn from 80: for each possible catch it counts the ways to match that many of your numbers and miss the rest, then divides by all the ways to draw 20 numbers. The results are exact, not simulated.
Are keno odds the same in every state?
The draw is 20 numbers from 80, so the chance of each catch is the same wherever the game uses that format. Prize tables and jackpots can differ by game and state, so the return is not the same everywhere.
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