Learn
Keno Math: Hypergeometric Odds Made Simple
Keno probability comes from one formula. The board above counts one catch step by step. Below are the formula, the terms and the odds for every OLG Daily Keno tier.
Loading the simulator
From board to formula
- Pick your spotsYou mark between two and ten numbers on a board numbered one to seventy. Each marked number is a spot.
- Twenty numbers are drawnOLG Daily Keno draws twenty numbers at random from the seventy. A spot that is drawn is a catch.
- Count ways to catch kChoose which k of your spots are drawn: C(spots, k) ways.
- Count ways for the restThe other drawn numbers must come from the numbers you did not mark: C(pool − spots, drawn − k) ways.
- Divide by all drawsC(pool, drawn) is the number of all possible sets of twenty drawn numbers. Good ways divided by all ways gives the odds.
The hypergeometric formula
P(catch k) = C(spots, k) × C(pool − spots, drawn − k) ÷ C(pool, drawn)
Example: For example, ten spots and all ten caught: C(10, 10) × C(60, 10) ÷ C(70, 20) = 1 in 2,147,181.
Terms on the board
- Spot
- A number you mark on the board.
- Catch
- One of your spots that is among the drawn numbers.
- Pool
- All numbers on the board. In OLG Daily Keno: one to seventy.
- Drawn
- How many numbers are drawn each game. In OLG Daily Keno: twenty.
- C(n, k)
- The number of ways to choose k items from n when order does not matter. See combinations explained.
- Hypergeometric
- The odds of getting k matches when numbers are drawn without being put back.
OLG Daily Keno odds by tier
| Tier (catch of spots) | Odds |
|---|---|
| 2 of 2 | 1 in 12.7 |
| 3 of 3 | 1 in 48 |
| 4 of 4 | 1 in 189.2 |
| 5 of 5 | 1 in 780.6 |
| 4 of 5 | 1 in 50 |
| 6 of 6 | 1 in 3,383 |
| 5 of 6 | 1 in 169.1 |
| 7 of 7 | 1 in 15,464 |
| 6 of 7 | 1 in 618.6 |
| 5 of 7 | 1 in 63.1 |
| 8 of 8 | 1 in 74,941 |
| 7 of 8 | 1 in 2,436 |
| 6 of 8 | 1 in 198.8 |
| 9 of 9 | 1 in 387,197 |
| 8 of 9 | 1 in 10,325 |
| 7 of 9 | 1 in 684.8 |
| 6 of 9 | 1 in 85.6 |
| 10 of 10 | 1 in 2,147,181 |
| 9 of 10 | 1 in 47,238 |
| 8 of 10 | 1 in 2,571 |
| 7 of 10 | 1 in 261.1 |
| 0 of 10 | 1 in 38.6 |
Values calculated with the formula. The game conditions print the same odds rounded to whole numbers. Only one prize can be won per selection.
What the numbers show
Catch 10 of 10
1 in 2,147,181The rarest tier: every spot you marked must be among the drawn numbers.
Catch 0 of 10
1 in 38.6With ten spots, catching none of them has odds of 1 in 38.6, and the OLG paytable lists a prize for it.
Catch 2 of 2
1 in 12.7Fewer spots means fewer numbers that must be drawn, so the top tier comes up more often.
Counting combinations
Every keno odds value is built from C(n, k). See how one combination count is done.
Sources
- OLG – Daily Keno Game Conditions · checked Oct 29, 2026
- OLG – Daily Keno past results and odds · checked Oct 29, 2026
- OLG – About Daily Keno · checked Oct 29, 2026
Questions
How are keno odds calculated?
Count the ways to catch k of your spots, multiply by the ways the other drawn numbers miss your spots, then divide by all possible draws. For example: C(10, 10) × C(60, 10) ÷ C(70, 20) = 1 in 2,147,181.
What is a hypergeometric distribution?
It gives the odds of getting k matches when numbers are drawn from a fixed pool without being put back. Keno, where drawn numbers are not returned to the board, follows it exactly.
Why do keno odds depend on the board size?
The pool size and the count of drawn numbers are both in the formula. A bigger pool or fewer drawn numbers makes each catch less likely. More drawn numbers makes catches more likely.
Does picking my own numbers change keno probability?
No. For the same number of spots, every set of numbers has the same odds. Quick pick and your own numbers are equal, and past results do not affect the next draw.
Why do the odds here differ slightly from OLG's?
They are the same odds. OLG's game conditions round them to whole numbers, while this page shows values calculated from the formula with one decimal place.