Probability in Keno
Keno is a popular game of chance that shares similarities with both bingo and lottery. It is easy to play, making it accessible to a broad audience, from casual gamers to more serious gamblers. This article aims to demystify the workings of Keno, providing a comprehensive overview of its rules, gameplay, and the mathematical principles that underpin its operation.
What is Keno?
Keno is a game where players bet by selecting numbers (typically between 1 and 80). After all players make their bets, 20 numbers are drawn randomly. The amount of money players win is determined by how many numbers they guess correctly.
How to Play Keno
- Choosing Your Numbers: The first step in playing Keno is for the player to select numbers from 1 to 80. The exact number of choices allowed can vary by casino or online platform, but players typically choose between 1 and 20 numbers.
- Placing Your Bet: Once you have chosen your numbers, you place your bet. In most cases, the minimum and maximum bets are established by the house.
- The Draw: After bets are placed, the game proceeds to the draw. Twenty numbers are randomly selected as the winning numbers. This can be done through a ball machine similar to those used in lotteries or through a computerized random number generator.
- Checking for Wins: Players compare the numbers they selected with the numbers drawn. The more numbers that match, the larger the prize. The structure of payouts varies, with large jackpots typically offered for matching a high number of numbers.
Understanding Keno Odds
The odds of winning in Keno vary significantly depending on the number of numbers you select and the specific rules of the game you’re playing. The game is known for having a high house edge, often ranging from 20% to 30%. This means that, on average, players lose $20 to $30 for every $100 wagered, which is higher compared to many other casino games.
Mathematically, the probability of hitting all 20 numbers in a standard game (where 20 numbers are drawn from a pool of 80) is astronomically low, at approximately 1 in 3.5 quintillion. Even matching fewer numbers, like 10 out of 10, carries daunting odds of 1 in 8.9 million.
Strategies for Playing Keno
While Keno is predominantly a game of luck, some players adopt strategies to enhance their experience:
- Choosing Consecutive Numbers: Some players believe in the pattern strategy, selecting numbers that follow each other.
- Number Picking Strategies: Whether it’s lucky numbers, birthdays, or patterns on the card, some players have preferred methods for selecting numbers.
- Bet Sizing: Adjusting bet sizes based on wins and losses, though it doesn’t change the house edge, can affect the volatility of your game experience.
Mathematics
There are some interesting mathematics behind Keno. There are many questions to be answered: What is the chance of winning in Keno? How big is the house edge in Keno?
The chances of hitting a certain number of correct numbers in Keno is shown below.
| Number of matching numbers | Chance |
| 0 | 1/843.380 |
| 1 | 1/46.446 |
| 2 | 1/20.115 |
| 3 | 1/8.009 |
| 4 | 1/4.877 |
| 5 | 1/4.287 |
| 6 | 1/5.258 |
| 7 | 1/8.826 |
| 8 | 1/20.055 |
| 9 | 1/61.420 |
| 10 | 1/253.801 |
| 11 | 1/1,423.822 |
| 12 | 1/10,968.701 |
| 13 | 1/118,084.920 |
| 14 | 1/1,821,881.628 |
| 15 | 1/41,751,453.986 |
| 16 | 1/1,496,372,110.872 |
| 17 | 1/90,624,035,964.712 |
| 18 | 1/10,512,388,171,906.553 |
| 19 | 1/2,946,096,785,176,811.500 |
| 20 | 1/3,535,316,142,212,174,320.000 |
As can be seen, the chance of hitting 20 correct numbers is close to zero. This has led to that casino and lotteries even do not have to consider the case of someone hitting 20 correct numbers in general, since it is so extremely unlikely. However hitting 1 to 8 numbers is very likely, and is in general what occurs. For example hitting 8 numbers has a 5% chance, which means that on average you will get this 5% of the time. In simple terms, if you played Keno 100 times, you would get this roughly 5 times (on average).
Conclusion
Keno is a fun and straightforward game that offers the chance of winning large prizes for a small initial bet. While it has a high house edge, its simplicity and the excitement of possibly hitting a big win continue to attract a wide audience. Remember, Keno should be played for entertainment, not as a way to make money. As with any form of gambling, it’s important to play responsibly.
References
Mark Bollman (2014). Basic Gambling Mathematics: The Numbers Behind the Neon. CRC Press. pp. 40–41.