Hypergeometric catch probabilities for 1–10 spot keno: 20 numbers drawn from 80
| Spots | Catch 0 | Catch 1 | Catch 2 | Catch 3 | Catch 4 | Catch 5 | Catch All |
|---|---|---|---|---|---|---|---|
| 1-Spot | 75.00% | 25.00% | — | — | — | — | 1 in 4.0 |
| 2-Spot | 56.01% | 37.97% | 6.01% | — | — | — | 1 in 16.6 |
| 3-Spot | 41.65% | 43.09% | 13.88% | 1.39% | — | — | 1 in 72.1 |
| 4-Spot | 30.83% | 43.27% | 21.26% | 4.32% | 0.31% | — | 1 in 326 |
| 5-Spot | 22.72% | 40.57% | 27.05% | 8.39% | 1.21% | 0.064% | 1 in 1,551 |
| 6-Spot | 16.60% | 36.35% | 30.83% | 12.98% | 2.85% | 0.310% | 1 in 7,753 |
| 7-Spot | 12.01% | 31.52% | 32.67% | 17.46% | 5.22% | 0.930% | 1 in 40,979 |
| 8-Spot | 8.63% | 26.64% | 32.81% | 21.48% | 8.15% | 1.830% | 1 in 230,115 |
| 9-Spot | 6.14% | 21.79% | 31.64% | 24.65% | 11.48% | 3.280% | 1 in 1,380,688 |
| 10-Spot | 4.28% | 17.33% | 29.53% | 26.74% | 14.73% | 5.140% | 1 in 8,911,712 |
| Spot Count | Hit 0 (Blank) | Hit Half | Hit All | Best Bet |
|---|---|---|---|---|
| 4-Spot | 1 in 3.2 | 1 in 4.7 (2 of 4) | 1 in 326 | Catch 2+ for frequency |
| 5-Spot | 1 in 4.4 | 1 in 11.9 (3 of 5) | 1 in 1,551 | Balanced risk/reward |
| 6-Spot | 1 in 6.0 | 1 in 7.7 (3 of 6) | 1 in 7,753 | Good mid-tier jackpot |
| 8-Spot | 1 in 11.6 | 1 in 422 (4 of 8) | 1 in 230,115 | Jackpot play only |
| 10-Spot | 1 in 23.2 | 1 in 19.4 (5 of 10) | 1 in 8,911,712 | Max jackpot hunting |
Every row is a spot count, meaning the quantity of numbers you mark on the ticket. Every column is a catch, meaning how many of your marked numbers turned up among the 20 the game draws. Read across the 5-Spot row and you can see that catching nothing at all happens 22.72% of the time, catching one number happens 40.57% of the time, and catching all five happens once in every 1,551 tickets on average.
The single most useful habit the card encourages is checking the blank-ticket column before you commit to a spot count. A 10-spot ticket wins nothing at all 4.28% of the time, which sounds encouraging until you notice that the paying catch levels on a 10-spot start at 5 numbers, so the great majority of those tickets still return zero. The blank column is not the losing column. It is only the column where you matched literally nothing.
Keno draws 20 numbers from a field of 80 without replacement, which makes the hypergeometric distribution the correct model. The probability of catching exactly k of your n spots is the number of ways to choose k winners from the 20 drawn, times the ways to choose the remaining n minus k from the 60 undrawn, divided by the ways to choose n from all 80.
These are not estimates or simulation results, and they do not drift. They fall out of the structure of the game, so they are identical in Massachusetts, in Ohio, and on a bar-top machine in Nevada. Anything that varies between venues is on the payout side, never on this card. That is exactly why the card is worth carrying: the odds half of the equation is settled, and it fits on one page.
Odds are only half of the picture. What a catch is worth is set by the operator, and the same 5-of-5 that pays $800 in one game pays $620 in another. Return to player, house edge, and whether a given spot count is worth playing at all depend on that paytable, not on the probabilities here. Pair the card with the state paytable you actually play, or with the comparison sheet, before drawing any conclusion about which game to sit down at.
The card also says nothing about bonus multipliers, Bulls-Eye style add-ons, or the progressive top prizes some states attach to a max bet. Those change the payout schedule and the cost per game, and they are covered on the individual state guides.
Use the print button at the top of the page. The sheet is laid out for US Letter at half-inch margins and drops this explanatory section automatically, so it comes out as one page with the tables and notes only. Printing to PDF from the same dialog gives you a copy you can keep on a phone. If the tables look cramped, check that your browser is not scaling to a percentage other than 100.
Want the same maths for a spot count and catch level not shown here? The keno odds calculator computes any combination exactly, and keno odds explained walks through the formula step by step.