Keno Odds Calculator: Exact Probabilities for Every Ticket
A free keno odds calculator that computes the exact probability and expected payout for any ticket size from 1 to 10 spots. Powered by the hypergeometric distribution — the same math casinos use.
On this page
| Catches | Probability | Odds | Payout | EV |
|---|---|---|---|---|
| 0 / 5 | 22.7% | 1 in 4 | — | $0.0000 |
| 1 / 5 | 40.6% | 1 in 2 | — | $0.0000 |
| 2 / 5 | 27.0% | 1 in 4 | — | $0.0000 |
| 3 / 5 | 8.39% | 1 in 12 | $2 | $0.1679 |
| 4 / 5 | 1.21% | 1 in 83 | $20 | $0.2418 |
| 5 / 5 | 0.0645% | 1 in 1.6K | $300 | $0.1935 |
| Expected return per $1 wager | $0.6032 | 39.7% edge | ||
With a 5-spot ticket and a $1 wager, your expected return is $0.6032 per game — a house edge of 39.7%.
Probabilities computed from the hypergeometric distribution: P(k) = C(20,k) × C(60,n−k) / C(80,n). Payouts shown are typical multi-game keno rates and vary by casino. Your actual return depends on the specific paytable.
The short answer
Every keno probability can be computed exactly. The calculator above takes your ticket size (1 to 10 spots) and wager amount, then shows the probability of every possible outcome — from catching nothing to sweeping the board. It also shows the payout and expected value for each catch, so you can see exactly what the house edge is before you play.
The math behind it is the hypergeometric distribution, the same formula every casino and state lottery uses to set its paytables. No approximation, no simulation — these are exact numbers.
Key takeaway: Keno's house edge ranges from about 4% to over 30% depending on the paytable and ticket size. The calculator makes this visible: compare the "Expected return" row at the bottom against your wager to see exactly how much the house keeps per game.
How to use the calculator
- Pick your spots — tap a number from 1 to 10. This is how many numbers you're selecting on your ticket.
- Set your wager — choose from $0.25 to $20.
- Read the table — each row shows one possible outcome (catching 0, 1, 2... up to all your spots). Green-highlighted rows are the ones that pay.
- Check the bottom line — the expected return per wager and the house edge percentage.
How the math works
Keno draws 20 numbers from a pool of 80. You pick between 1 and 10 numbers before the draw. The probability of catching exactly k of your n picks is:
P(k) = C(20, k) × C(60, n−k) / C(80, n)
where C(a, b) is the number of ways to choose b items from a (a binomial coefficient). The formula counts: how many ways can k of your numbers land inside the 20 drawn, multiplied by how many ways can the rest of your numbers land outside the 20, divided by the total ways to draw any 20 from 80.
This is called the hypergeometric distribution because you're sampling without replacement — each number can only appear once. For the full derivation and a complete table of every probability for every ticket size, see our keno odds probability table.
What does the expected value mean?
Expected value (EV) is what you'd earn on average if you played the same ticket millions of times. For each outcome, multiply the probability by the payout, then add them all up. The total is your expected return per wager.
For example, a 5-spot $1 ticket might return about $0.68 on average. That means for every dollar wagered, the house keeps roughly 32 cents. That's the house edge — and it's why keno is one of the most expensive games in the casino compared to blackjack (0.5% edge) or craps (1.4% edge).
The calculator shows this number explicitly so there's no guesswork. Different spot counts have different house edges because casinos set each paytable independently. Our keno house edge guide explains why the range is so wide (1% to 40%) and which ticket sizes tend to be the best value.
Do "lucky numbers" change the odds?
No. Every number from 1 to 80 has exactly the same probability of being drawn. The hypergeometric formula depends only on how many numbers you pick and how many you catch — not which specific numbers they are. Whether you play 7-11-22 or 3-44-67, the odds are identical.
This is a common misconception we cover in depth in our best keno numbers: myth vs math guide. The calculator proves it: change your numbers in a real game and the probabilities in this table don't move.
How does this compare to lottery keno?
State lottery keno games (Ohio, Maryland, Massachusetts) use the same 80-number pool and 20-number draw, so the probabilities are identical. The only thing that differs is the paytable — state lotteries often pay slightly different amounts per catch than online casinos. The calculator shows typical multi-game keno payouts; your casino or lottery may vary.
For state-specific payout tables, see our keno payout charts guide which includes Ohio, Maryland, and Massachusetts side by side.
What should I learn next?
- Keno Explained: Full rules from scratch if you're brand new
- Keno Odds Probability Table: The complete table with exact fractions for every ticket
- Keno House Edge: Why the edge ranges from 1% to 40% and which tickets are the best value
- Keno Payout Charts: Real paytables from state lotteries and online casinos
- Keno Mastery Course: The full structured course, lesson by lesson
About the author
Casino & Crypto Fundamentals Writer
Elena writes Wild.io Academy’s bonus and fine-print guides — what casino offers really cost and how wagering requirements work — plus the crypto beginner track, from what cryptocurrency is to buying your first coins.