Start With the Draw, Not the Payout
Every keno pay table rests on one mechanical fact: the game draws a fixed set of numbers from a larger pool, and your ticket marks a smaller set of spots. The pay table is not invented by a marketing team. It is built backwards from the probability of catching each possible number of spots, then shaped by the house edge the operator wants to hold.
Once you see that order, the arithmetic stops looking mysterious. You are not calculating what the casino feels like paying. You are calculating what a given catch is worth as a share of all possible draws, then adjusting that fair value downward by a fixed percentage.
The Combination Formula Behind Every Catch
Keno is a hypergeometric game. The draw selects numbers without replacement, and your ticket either matches a drawn number or it does not. The probability of catching exactly k of your n chosen spots when the game draws 20 numbers from a pool of 80 is built from three combination counts.
The first count is the number of ways to choose your k hits from your n spots. The second is the number of ways to fill the remaining 20 minus k drawn numbers from the 80 minus n numbers you did not pick. The third is the total number of possible 20-number draws from 80. Divide the product of the first two by the third, and you have the probability of that exact catch.
Combinations use the standard formula: the number of ways to choose r items from a set of s items is s factorial divided by r factorial times (s minus r) factorial. A scientific calculator or spreadsheet function handles this cleanly. The important part is keeping the three counts separate and consistent.
| Term | What It Counts | Why It Matters |
|---|---|---|
| Hits from your spots | Ways to choose k matching numbers from your n picks | Sets the numerator for that catch level |
| Misses from the rest | Ways to choose the remaining drawn numbers from numbers you did not pick | Completes the draw so it totals 20 |
| Total possible draws | Ways to choose any 20 numbers from the full 80 | Denominator for every probability |
From Probability to a Fair Payout
Suppose you mark four spots. The probability of catching all four is the number of ways to choose all four from your four, multiplied by the number of ways to choose the remaining sixteen drawn numbers from the seventy-six you did not pick, all divided by the total ways to choose twenty from eighty. That probability is small. Catching three of four is more likely, catching two more likely still, and catching zero the most likely outcome of all.
A fair game would pay each catch level the inverse of its probability, minus the stake. If a catch happens once in one hundred draws, a fair return on a one-unit ticket would be ninety-nine units of profit. Real keno pay tables pay less than that fair amount. The gap between the fair payout and the listed payout, multiplied by the probability of that catch, is the contribution that catch level makes to the house edge.
Where the House Edge Enters the Table
The operator chooses a target hold, then scales every listed prize downward until the weighted sum of payouts equals one minus that hold. The pay table is the output of that scaling, not the input. This is why two keno games with identical draw mechanics can show different prizes for the same catch.
House edge and return to player are complements: they sum to 100% for the same game under the same pay table. If a keno game returns a small fraction of coin-in over the long run, the house edge is the rest. That edge is built into the listed prizes, not applied as a separate fee at the end of a session.
| Element | Fixed by the Game | Chosen by the Operator |
|---|---|---|
| Number pool | 80 numbers drawn from | Not adjustable per table |
| Draw size | 20 numbers per draw | Not adjustable per table |
| Probability of each catch | Determined by spots marked | Not adjustable |
| Prize for each catch | Not fixed | Scaled to hit target hold |
| House edge | Not fixed | Set through the prize scale |
Why Catch Zero Is Part of the Calculation
A complete pay table calculation includes every possible outcome from zero catches to a full hit. Many tables list no prize for zero or one catch on a multi-spot ticket, but those outcomes still carry probability. Their expected value is zero, yet they must be counted because they are the most frequent results on most tickets.
Leaving zero-catch outcomes out of the weighted sum would overstate the return. The house edge calculation only works when the probabilities of all catch levels sum to one and every level contributes its actual weighted value, including the levels that pay nothing.
Reading a Published Pay Table in Reverse
You rarely need to calculate a pay table from scratch, because the operator prints it. What you can do is reverse-engineer the structure. Look at the prizes for adjacent catch levels on the same ticket. If catching four pays many times more than catching three, the probability gap between those outcomes is large. If two catch levels pay identical prizes, the operator has flattened that part of the scale.
The listed prizes are per unit staked. A table that shows a prize for four hits on a four-spot ticket is telling you the multiple of your wager returned if that catch occurs. The stake itself is subtracted from that return when you calculate net profit.
Where the Pay Table Lives
In a physical keno lounge, the pay table is printed on the ticket or posted at the writing station. In an online or app-based game, the information panel or rules screen carries the same data. The game information panel is the authoritative source for the exact prize scale in force, because pay tables can vary between game versions even when the draw mechanics are identical.
If a game offers a progressive jackpot for a full catch, the progressive contribution is typically taken out of the game's return before the fixed prizes are set. That changes the pay table arithmetic: the fixed prizes may be slightly lower to fund the growing top prize, and some progressives require a maximum-stake ticket to qualify for the full amount.
FAQ
Do I need to know the combination formula to play keno?
No. The formula explains why the pay table looks the way it does, but the game itself only requires you to mark spots and read the posted prizes. Understanding the arithmetic helps you see that the house edge is built into the prize scale, not something you can overcome by picking numbers differently.
Why do different keno games pay different amounts for the same catch?
Because the operator sets the target hold and scales prizes to reach it. Two games can share the same 80-number pool and 20-number draw while offering different prizes for catching three of five spots. The probability is identical; the chosen house edge is not.
Can I calculate the exact house edge from a printed pay table?
Yes, if the table lists every catch level and you know the stake. Multiply each prize by the probability of that catch, sum the products, and subtract the result from one. The remainder is the house edge for that ticket under that pay table. The calculation requires the full probability distribution, including the outcomes that pay nothing.
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This article is general information about how these mechanics work. It is not legal advice and not a recommendation to gamble or to use any particular operator. Availability and legality differ by jurisdiction — check the rules that apply where you are.