Keno Rules and Odds: A Complete Mathematical Guide to the Lottery Game
Keno represents one of the oldest gambling games still played in modern casinos, with origins tracing back over 2,000 years to ancient China. According to legend, proceeds from early keno games helped fund the construction of the Great Wall. Today, this lottery-style game attracts players with its simple gameplay and potentially large payouts. However, understanding the mathematics reveals why experienced gamblers approach keno with considerable caution.
Unlike table games such as blackjack or craps where optimal strategy can reduce house edges below 1%, keno typically carries edges ranging from 20% to 40%. This guide examines why keno's mathematics make it one of the least favorable games in any casino, while explaining the rules for those who choose to play for entertainment.
How Keno Works: The Basic Rules
Keno gameplay is remarkably straightforward, which contributes to its enduring popularity. The game uses a pool of 80 numbers, from which 20 numbers are randomly selected each round. Players choose their own numbers (called "spots") before the draw, and payouts depend on how many of their selections match the drawn numbers.
Example keno board: Blue = Player selections, Green = Matched numbers
Step-by-Step Gameplay
- Select Your Spots: Choose between 1 and 20 numbers from the 80-number field. Most players select 4-10 numbers.
- Place Your Wager: Bet amounts typically range from $1 to $20 per game, though this varies by casino.
- Watch the Draw: The casino randomly selects 20 numbers using a ball machine or random number generator.
- Check for Matches: Compare your selections to the drawn numbers. Matching numbers are called "catches."
- Collect Winnings: Payouts depend on how many catches you achieve relative to spots selected, according to the pay table.
The Mathematics of Keno Probability
Keno probability calculations use hypergeometric distribution, the same mathematical framework governing lottery games. Unlike games with replacement (where probabilities remain constant), each number drawn in keno changes the probability landscape for subsequent draws.
Research published through the American Mathematical Society confirms that calculating keno odds requires combinatorial mathematics that accounts for the interdependence of selections within a finite pool.
Keno Probability Formula
P(catching k numbers) = [C(n,k) × C(80-n, 20-k)] / C(80,20)
Where: n = spots selected, k = catches, C(a,b) = combinations of a items taken b at a time
Probability by Spot Selection
The following table shows the probability of various outcomes when picking different numbers of spots:
| Spots | Catches | Probability | Odds |
|---|---|---|---|
| 1 Spot | 1 | 25.00% | 1 in 4 |
| 0 | 75.00% | 3 in 4 | |
| 4 Spots | 4 | 0.31% | 1 in 326 |
| 3 | 4.32% | 1 in 23 | |
| 2 | 21.26% | 1 in 4.7 | |
| 6 Spots | 6 | 0.013% | 1 in 7,753 |
| 5 | 0.31% | 1 in 323 | |
| 4 | 2.85% | 1 in 35 | |
| 3 | 12.98% | 1 in 7.7 | |
| 10 Spots | 10 | 0.000011% | 1 in 8,911,711 |
| 8 | 0.0054% | 1 in 18,471 | |
| 6 | 0.52% | 1 in 193 | |
| 5 | 5.14% | 1 in 19 | |
| 0 | 4.58% | 1 in 22 |
The House Edge Problem
Keno's fundamental issue lies in its extraordinarily high house edge. While every casino game maintains a mathematical advantage, keno's edge dwarfs virtually every other option. According to gaming commission reports from the Nevada Gaming Control Board, keno typically returns 70-80% to players, meaning the house retains 20-30% of every dollar wagered.
House Edge Comparison: Keno vs. Other Casino Games
To put this in perspective: with a 25% house edge, playing $100 over an extended session mathematically results in losing $25 to the house. Compare this to blackjack with basic strategy, where the same $100 of action yields an expected loss of only $0.50. The difference is staggering.
Why Is Keno's Edge So High?
Several factors contribute to keno's elevated house edge:
- Low Game Speed: Traditional keno draws occur every 5-10 minutes, meaning players make fewer decisions per hour. Casinos compensate with higher margins per game.
- Operating Costs: Live keno requires runners, writers, and dedicated infrastructure that table games don't need.
- Entertainment Value: Players tolerate higher edges because keno allows socializing, dining, or watching sports while playing.
- Jackpot Structure: Large potential payouts (hitting 8+ spots) require funding from the majority of losing tickets.
Reality Check: Expected Loss
If you play 100 keno games at $1 each with a 25% house edge, your expected loss is $25. Over a year of casual play (1,000 games), expect to lose $250. No strategy can change this mathematical reality. As explained in our article on why betting systems fail, the house edge cannot be overcome through pattern selection or staking modifications.
Understanding Pay Tables
Keno pay tables vary significantly between casinos and even between different games within the same casino. Comparing pay tables is the only meaningful decision players can make, as it directly affects the house edge.
Sample 6-Spot Pay Table Comparison
| Catches | Probability | Pay Table A | Pay Table B | Difference |
|---|---|---|---|---|
| 6 of 6 | 0.013% | $1,500 | $1,800 | +$300 |
| 5 of 6 | 0.31% | $80 | $100 | +$20 |
| 4 of 6 | 2.85% | $4 | $5 | +$1 |
| 3 of 6 | 12.98% | $1 | $1 | $0 |
| House Edge | 28.5% | 24.2% | -4.3% | |
Pay Table B offers substantially better value with an edge over 4 percentage points lower. Over 1,000 games at $1 each, this difference translates to saving approximately $43. While both options remain poor value compared to table games, choosing better pay tables is the only optimization available.
Common Spot Selections Analyzed
Players can choose anywhere from 1 to 20 spots, though most select between 4 and 10. Each spot count offers different risk/reward profiles:
1-3 Spots
Small, frequent wins. Low volatility but limited upside. 1-spot games often pay 3:1 on a hit.
Low Risk/Low Reward4-6 Spots
Reasonable hit frequency with meaningful payouts. Most popular choice among regular players.
Moderate Balance7-10 Spots
Large potential payouts but very low hit rates. Often require 4+ catches to win anything.
High Volatility15-20 Spots
Astronomical odds against hitting high catches. Mathematically impractical for serious play.
AvoidVideo Keno vs. Live Keno
Modern casinos offer keno in two primary formats, each with distinct characteristics:
Live Keno (Lounge Style)
- Draws occur every 5-15 minutes
- Social atmosphere; players can dine while playing
- Lower hands per hour means slower bankroll depletion
- Pay tables often posted; comparison shopping possible
- House edges typically 25-35%
Video Keno (Machine)
- Instant results; can play 200+ games per hour
- Often better pay tables than live keno
- Higher speed dramatically increases hourly expected loss
- Available 24/7 without waiting for draws
- House edges typically 20-30%
While video keno often offers slightly better odds, the dramatically increased game speed means players lose more money per hour despite the lower house edge. This mirrors the mechanics of slot machine mathematics, where game speed multiplies the impact of house edge.
Hourly Expected Loss Comparison
Live Keno:
6 games/hour × $1 bet × 28% edge = $1.68/hour expected loss
Video Keno:
200 games/hour × $1 bet × 24% edge = $48/hour expected loss
Despite the lower edge, video keno's speed makes it 28x more expensive per hour.
Common Keno Myths Debunked
Like all gambling games, keno attracts numerous misconceptions. Understanding why these myths fail helps players make informed decisions.
Myth: Certain Numbers Are "Hot" or "Due"
Each keno draw uses either a physical ball machine or certified random number generator. As documented by testing laboratories like iTech Labs, these systems produce statistically random outcomes. Past results have zero influence on future draws. The belief that numbers are "due" represents the gambler's fallacy, which we analyze extensively in our psychology of gambling guide.
Myth: Patterns Improve Results
Picking numbers in patterns (corners, diagonals, consecutive sequences) provides no advantage. The probability remains identical regardless of number positioning or relationships. The 80-number field has no memory and no spatial awareness.
Myth: Playing More Spots Increases Winning Chances
While selecting more spots means more potential catches, it also increases the threshold for winning. On a 10-spot ticket, you typically need 4-5 catches to win anything, while a 4-spot ticket pays on 2+ catches. The house edge remains relatively constant regardless of spot selection.
Myth: Quick Picks Are Worse Than Chosen Numbers
Whether you carefully select meaningful numbers or let the machine randomly assign spots, the probability of any given number appearing in the draw remains 20/80 = 25%. Your birthday, lucky numbers, or random selections all face identical mathematical odds.
Keno Strategy: Managing the Unavoidable
Since no strategy can overcome keno's mathematical disadvantage, the only meaningful approach involves damage control:
Practical Approaches
- Compare pay tables before playing
- Set strict loss limits before beginning
- Prefer live keno's slower pace
- Treat keno as entertainment, not investment
- Choose 4-6 spots for balanced volatility
- Use keno as a break from table games
What to Avoid
- Chasing losses with larger bets
- Playing video keno at maximum speed
- Believing in hot/cold number systems
- Selecting 15+ spots (near-impossible odds)
- Ignoring pay table differences
- Playing keno as primary gambling activity
Online Keno Considerations
Online casinos offer keno with generally better pay tables than land-based venues, as they have lower operating costs. However, according to regulations documented by the UK Gambling Commission, online keno must use certified random number generators that produce fair outcomes.
Online Keno Advantages
- Often 5-10% better RTP than land-based keno
- Play at your own pace (no waiting for draws)
- Pay tables clearly displayed for comparison
- Lower minimum bets available
Online Keno Disadvantages
- Easy to play very fast, accelerating losses
- Less social interaction
- Auto-play features can lead to excessive play
- Still carries substantial house edge (15-25%)
Frequently Asked Questions
What is the house edge in keno?
Keno typically carries house edges between 20% and 40%, making it one of the worst bets in any casino. Even favorable online keno games rarely have edges below 15%. For comparison, blackjack with basic strategy has a 0.5% edge, and craps' Pass Line bet has 1.41%. This means keno players lose 15-40 times more per dollar wagered than players of skill-based table games.
What are the odds of hitting all numbers in keno?
The odds depend on how many spots you select. Hitting 10 out of 10 spots occurs approximately once every 8.9 million games. Hitting all 20 spots (if you selected 20) is essentially impossible at odds of 1 in 3.5 quintillion. Even hitting 8 out of 8 carries odds of about 1 in 230,000.
How many spots should I pick in keno?
Most experienced players recommend 4-6 spots as a reasonable balance between hit frequency and meaningful payouts. Fewer spots win more often but pay less; more spots offer larger potential wins but hit rarely. The house edge remains high regardless of spot selection, so the choice comes down to personal preference for volatility.
Is there a winning keno strategy?
No strategy can overcome keno's high house edge. Every number has an equal 25% chance of being drawn. Pattern selection, hot/cold tracking, and betting systems all fail against the mathematics. The only practical strategy involves comparing pay tables, setting loss limits, and treating keno as entertainment with expected losses built in.
Is video keno better than live keno?
Video keno often has slightly better pay tables (lower house edge), but the dramatically faster game speed means players lose more money per hour. A video keno player might play 200 games per hour versus 6 games per hour for live keno. The slower pace of live keno results in less financial exposure despite often having worse odds per game.
Conclusion: The Keno Reality
Keno offers the appeal of lottery-style gambling with potentially large payouts from small wagers. Its relaxed pace suits players who want gambling entertainment while dining or socializing. However, the mathematics are unambiguous: keno carries one of the highest house edges in any casino, typically 20-40%.
For players who understand and accept these odds, keno can provide entertainment value. The key is approaching the game with realistic expectations. Unlike blackjack where proper strategy reduces the house edge below 1%, or craps where the Free Odds bet has zero house edge, keno offers no mathematical path to advantage play.
If you choose to play keno, compare pay tables, set strict loss limits, prefer the slower pace of live keno, and never chase losses. Most importantly, budget keno as entertainment expense rather than an investment or income-generating activity. The mathematics guarantee long-term losses for all players regardless of number selection, pattern recognition, or betting system employed.
Disclaimer: This article is for educational purposes only and does not constitute gambling advice. Keno is a negative expectation game with extremely high house edges. All gambling carries risk of financial loss. Never gamble with money you cannot afford to lose. If gambling is affecting your life negatively, please visit our responsible gambling resources for help.