Why Keno Odds Are What They Are
Keno odds aren't arbitrary — they come directly from combinatorics, the branch of math that counts how many ways events can occur. Every keno probability can be calculated exactly from first principles, with no estimation or simulation required.
The key insight: there are a fixed number of ways to draw 20 numbers from 80, and a fixed number of those ways result in exactly k of your N chosen numbers being included. Dividing one by the other gives the probability.
The Formula
Keno uses the hypergeometric distribution — the standard model for drawing without replacement from a finite population. The formula for hitting exactly k matches when you pick N spots:
Hypergeometric Formula for Keno
P(k matches) = C(N, k) × C(80 − N, 20 − k) / C(80, 20)
N = number of spots you picked | k = number of matches | C(n, r) = "n choose r" = n! / (r! × (n−r)!)
Breaking Down the Formula
- C(N, k) — The number of ways to choose exactly k winning numbers from your N picks. These are the "hits."
- C(80 − N, 20 − k) — The number of ways the remaining draw slots (20 − k) are filled from the numbers you didn't pick (80 − N of them). These are the "non-hits."
- C(80, 20) — The total number of possible draws. This is a single enormous number: 3,535,027,396,898,400 — over 3.5 quadrillion possible draws.
4-Spot Probability Table
When you pick 4 spots, there are only 5 possible outcomes (0 through 4 matches):
| Matches | Probability | 1 in X Odds | Typical Payout ($1) |
|---|---|---|---|
| 0 matches | 30.83% | 1 in 3.2 | — |
| 1 match | 43.27% | 1 in 2.3 | — |
| 2 matches | 21.26% | 1 in 4.7 | $1 |
| 3 matches | 4.32% | 1 in 23 | $5 |
| 4 matches (jackpot) | 0.31% | 1 in 326 | $120 |
The most likely outcome for a 4-spot player is 1 match (43%), followed by 0 matches (31%). A full jackpot happens about once every 326 games.
6-Spot Probability Table
| Matches | Probability | 1 in X Odds | Typical Payout ($1) |
|---|---|---|---|
| 0 matches | 16.60% | 1 in 6.0 | — |
| 1 match | 36.39% | 1 in 2.7 | — |
| 2 matches | 30.83% | 1 in 3.2 | — |
| 3 matches | 12.98% | 1 in 7.7 | $1 |
| 4 matches | 2.85% | 1 in 35 | $4 |
| 5 matches | 0.31% | 1 in 323 | $100 |
| 6 matches (jackpot) | 0.013% | 1 in 7,753 | $1,500 |
For a 6-spot player, 1 or 2 matches covers nearly 67% of all games. The jackpot (all 6) occurs roughly once every 7,753 games.
8-Spot Probability Table
| Matches | Probability | 1 in X Odds | Typical Payout ($1) |
|---|---|---|---|
| 0 matches | 8.31% | 1 in 12 | — |
| 1 match | 26.62% | 1 in 3.8 | — |
| 2 matches | 32.83% | 1 in 3.0 | — |
| 3 matches | 21.54% | 1 in 4.6 | — |
| 4 matches | 8.15% | 1 in 12 | — |
| 5 matches | 1.83% | 1 in 55 | $12 |
| 6 matches | 0.24% | 1 in 423 | $80 |
| 7 matches | 0.017% | 1 in 6,232 | $1,000 |
| 8 matches (jackpot) | 0.00043% | 1 in 230,115 | $15,000 |
Notice that 8-spot players hit 0–4 matches the vast majority of the time (97.4%). The jackpot is 30x harder to hit than a 6-spot jackpot, but pays 10x more.
10-Spot Probability Table
| Matches | Probability | 1 in X Odds | Typical Payout ($1) |
|---|---|---|---|
| 0 matches | 3.94% | 1 in 25 | — |
| 1 match | 16.21% | 1 in 6.2 | — |
| 2 matches | 28.64% | 1 in 3.5 | — |
| 3 matches | 28.54% | 1 in 3.5 | — |
| 4 matches | 17.46% | 1 in 5.7 | — |
| 5 matches | 6.70% | 1 in 15 | $5 |
| 6 matches | 1.60% | 1 in 63 | $20 |
| 7 matches | 0.23% | 1 in 621 | $140 |
| 8 matches | 0.023% | 1 in 7,384 | $1,000 |
| 9 matches | 0.0012% | 1 in 163,381 | $5,000 |
| 10 matches (jackpot) | 0.0000112% | 1 in 8,911,711 | $100,000 |
Hitting all 10 spots is one of the rarest events in lottery gaming — nearly 9 million to 1 odds. For context, you'd need to play one game every 4 minutes for over 68 years on average before hitting it once.
House Edge Explained
The house edge in keno is typically 20–35% — significantly higher than most other casino games. Here's how it compares:
| Game | Typical House Edge | Player RTP |
|---|---|---|
| Keno | 20–35% | 65–80% |
| Slot Machines | 4–8% | 92–96% |
| American Roulette | 5.26% | 94.7% |
| Baccarat | 1.06% (banker bet) | 98.9% |
| Blackjack (basic strategy) | ~0.5% | ~99.5% |
| State Lotteries (jackpot) | ~50% | ~50% |
Where Does the House Edge Come From?
The house edge arises from the gap between true odds and paytable payouts. Consider a 6-spot jackpot: the true odds are 1 in 7,753, meaning a "fair" payout would be $7,753 for a $1 bet. Instead, most paytables pay $1,500. That gap — $6,253 per occurrence — is the source of the house's profit.
This happens at every prize level. For 3 matches in a 6-spot game (which pays $1), the true odds are 1 in 7.7. A fair payout would be $7.70. The $1 payment represents a significant house edge at that tier too. Sum up all tiers and you get the overall RTP — typically 65–75%.
The Most Common Misunderstanding: "Due" Numbers
Because keno draws are independent — completely random, with no memory of past draws — no number is ever "due" to appear. If the number 42 hasn't appeared in 50 draws, it has exactly the same probability of appearing in the next draw as any other number: 20/80 = 25%.
This is called the Gambler's Fallacy — the mistaken belief that past random outcomes influence future ones. In keno (and all RNG-based games), they do not.
The Gambler's Fallacy in Keno
There are no "hot" or "cold" numbers in keno. Every draw is independent. "Due" numbers don't exist. Frequency charts showing past draws are entertainment, not strategy — they cannot predict future outcomes.
Why Play Keno With These Odds?
It's a fair question. Keno has a higher house edge than most casino games. So why do millions of people play it?
- Entertainment value: For many players, $20 of keno is an evening of entertainment — a bargain compared to other forms of entertainment.
- Jackpot potential: A $1 bet can return $100,000 on a 10-spot hit. That kind of upside isn't available in blackjack or roulette.
- Low minimum bet: You can play many games for $1 each — a very low entry price.
- Simplicity: No strategy to learn, no skill required, no pressure. Just pick numbers and watch.
- Social play: Lottery keno at a bar or restaurant is a shared activity — watching the draw together is part of the experience.
See the Odds for Yourself
Use our interactive odds calculator to get exact probabilities and "1 in X" odds for any spot count and match combination.
Open Odds Calculator