Keno Odds and the Math Behind the Paytable

Keno odds never change from one game to the next. A standard game holds 80 numbers, draws 20 of them, and lets you pick anywhere from 1 to 20 spots. Hit all five spots on a 5-spot ticket and you beat 1 in 1,551. Hit all ten on a 10-spot ticket and you beat 1 in 8,911,711. Those figures are locked by the draw and identical at every operator running the 80/20 format.

The payout is not locked. Each operator publishes its own paytable, and that table on its own decides how much of the game's risk gets paid back. Two keno games with identical odds can return 88% or 95%. The keno rules guide covers ticket types and variants; this page is the math.

Keno odds by number of picks

For a ticket with k spots, the chance of matching exactly m of them is:

> P(m) = [ C(k, m) × C(80 − k, 20 − m) ] ÷ C(80, 20)

C(a, b) is the number of ways to choose b items from a. C(80, 20) — every possible draw — is 3,535,316,142,212,174,320. The middle term counts the drawn numbers that land on spots you didn't pick.

Run that for the top prize on each ticket size:

Derived from the 80-ball, 20-draw format using the formula above. Figures rounded.

Most players care about the whole spread, not just the jackpot line. Here is every outcome on a 10-spot ticket:

Column sums to 100% before rounding. The same formula produces the equivalent table for any pick size.

How keno payouts are calculated

The paytable lists one multiplier per hit count, per ticket size, and nothing else feeds into your return. Points to check before you play:

• "For 1" versus "to 1." Most keno paytables quote for-one, meaning your stake is inside the number shown. A 700-for-1 win on a $1 ticket returns $700 total; 700-to-1 would return $701.
• Zero-hit consolation prizes. Large tickets often pay something for matching nothing, because missing everything on a 10-spot happens 1 in 21.8 games. That tier is a real part of the return, not a novelty.
• Multiplier add-ons. Some games sell a random multiplier as a separate wager with its own probabilities. Price it separately; it does not improve the base ticket.
• Liability caps. Lottery-style keno frequently caps the total paid across a single drawing, so several top-prize tickets can split one pool. The headline prize is a maximum, not a guarantee.

Your theoretical return is the sum, across every hit count, of probability multiplied by payout. Nothing else.

House-edge calculation

Take a 5-spot ticket with an illustrative paytable of 3× for three hits, 15× for four and 700× for five, all quoted for-one:

Illustrative paytable; probabilities are exact for the 80/20 format.

Return to player: 88.5%. House edge: 11.5%, or about $11.50 per $100 staked over the long run.

Now change one cell. Lift the five-hit multiplier from 700× to 800× and the total return climbs to 94.9% — the edge falls from 11.5% to 5.1% on a single number. Keno paytables differ between operators more than almost any other casino game, which is why a generic house-edge figure for keno is close to meaningless. Run the sum on the table in front of you.

Why more picks rarely mean more value

Pick count does not push the house edge in a predictable direction. Some operators price small tickets tightest, some price large ones tightest, and only the paytable tells you which. What pick count reliably changes is variance.

On a 10-spot ticket, paying tiers usually start at five hits. That happens 6.47% of the time — 1 in 15.5 games, ignoring any zero-hit consolation. On a 4-spot ticket paying from two hits, something lands 25.9% of the time, or 1 in 3.9. Same game, same draw, wildly different session experience.

There is a second trap in the big tickets. On the 10-spot, the top two tiers can supply a large share of the posted return while arriving once every 163,381 and 8,911,711 games. Strip them out and what you actually experience across a realistic number of rounds sits well below the advertised RTP. The same gap between headline return and lived return shows up in Plinko's risk levels and in the ticket-size choice in online bingo.

Has anyone ever hit 10 numbers on keno?

Yes, and the arithmetic explains why. One 10-spot ticket wins the top prize once in 8,911,711 attempts, but keno draws run every few minutes in venues and continuously online across many jurisdictions. Assume a system sells one million 10-spot tickets a week: the expected rate is one 10-of-10 roughly every nine weeks. Raise the volume and the wait shortens proportionally.

The near-misses are far more common than players expect. Nine of ten lands 1 in 163,381 — about 55 times more often than the full sweep. Eight of ten lands 1 in 7,384. Those two tiers are where most of a 10-spot ticket's realistic upside actually sits, so their multipliers matter more to your return than the jackpot line does.

How much is 3 out of 5 numbers on keno?

Three hits on a 5-spot ticket occurs 8.39% of the time — 1 in 11.9 games. It is the most frequent paying result on that ticket by a wide margin, arriving about 130 times more often than a full 5-of-5.

The cash amount depends entirely on the operator. Because the outcome is common, paytables price the tier low, often near a straight return of the stake. That low multiplier still carries real weight: in the worked example above, the three-hit tier supplied 28% of the ticket's total return while paying just 3×.

To check any keno game yourself, multiply 0.0839 by its three-hit multiplier, do the same for the other tiers, and add them up. If the total sits below about 0.90, you are looking at a paytable with a double-digit edge.

For the full rules, ticket variants and how the game runs from draw to settlement, read Keno: Rules, Odds and How to Play.