Keno

Last update: Mar. 16, 2009

Keno can be played either live, or on a machine. I refer to the later as “video keno.” The odds are better in video keno, but the rate of play is much slower in live keno, so you may lose less that way on an hourly basis.

The rules of keno are simple. Choose 1 to 10 numbers from the range of 1 to 80. Some casinos also offer a pick-20 option. Next, the casino or machine will draw 20 numbers from the same range of 1 to 80. If one of your picks matches one of the drawn numbers by the casino/machine, it is called a “catch.” The more catches the player has, the more he wins.

9-Spot Survey

In 2001 I did a comparitive study of pick-9 keno games in Las Vegas. The following table presents my results in order or return, from highest to lowest. Since I did this survey, keno has been on the decline, and many of these casinos took out their live keno games.

San Diego Video Keno Survey

Between November 30 and December 1, 2008, I sampled the pay table for 25-cent and $1 video keno pay tables at 11 casinos in San Diego County. Following are the results, sorted first from highest to lowest, and second by alphabetical order.

The La Posta, Santa Ysabel, and Valley View are omitted from the $1 survey, because I couldn't find ordinary keno in that denomination.

Disclaimer: The Barona Casino hired me to perform surveys of San Diego casinos for backjack, roulette, and craps. Research on other games, including video keno, I did at my own initiative.

Other Games Surveyed in San Diego

• Blackjack
• Craps
• Roulette
• Video poker

Computation of Probabilities

The probability of matching x numbers, given that y were chosen, is the number of ways to select x out of y, multiplied by the number of ways to select 20-x out of 80-y, divided by the number of ways to select 20 out of 80.

The "number of ways to select x out of y" means the number of ways, without regard to order, you can select x items out of y to choose from. I shall represent this function as combin(y,x) which you can use in Excel.

For the general case combin(y,x) is y!/(x!×(y-x)!). For those of you unfamiliar with the factorial function n! is defined as 1×2×3×...×n. For example 5!=120. The number of possible five card poker hands would thus be combin(52,5) = 52!/(47!×5!) = 2,598,960.

The overall general formula for the probability of x matches and y marks is combin(y,x)×combin(80-y,20-x)/combin(80,20).

As an example let's find the probability of getting 4 matches given that 7 were chosen. This would be the product of combin(7,4) and combin(73,16) divided by combin(80,20). combin(7,4) = 7!/(4!×3!)= 35. combin(73,16) = 73!/(16!×57!)=5271759063474610. combin(80,20) = 3535316142212170000. The probability is thus (35×5271759063474610)/3535316142212170000 =~ 0.052190967 .

To determine the expected return of an overall number of picks take the dot product of the return and the probability for each number of winning catches. For example the pick 5 at the Atlantic City Tropica pays 1 for 3 catches, 10 for 4, and 800 for 5. Thus the return is 1×combin(5,3)×combin(75,17)/combin(80,20) + 10×combin(5,4)×combin(75,16)/combin(80,20) + 800×combin(5,5)×combin(75,15)/combin(80,20) = 0.72079818915262.

Appendices

• Keno appendix 1 features an analysis of the top/bottom/left/right as as well as edge tickets as played at the Las Vegas Hilton.
  

• Keno appendix 2 features an analysis of Caveman Keno as played on IGT's Game King.
  
• Keno appendix 3 probabilities and returns for basic keno at the Atlantic City Tropicana.
  
• Keno appendix 4 progressive keno at the Orleans. Learn when the meter is high enough to have a positive expectation.
  
• Keno appendix 5 Nevada numbers, a progressive lottery game at some of the Nevada Park Place casinos.
  
• Keno appendix 6Power Keno.
  
• Keno appendix 7 Super Keno.
  
• Keno appendix 8 Top Bottom Keno.
  
• Keno appendix 9High/Low/Middle Keno: Keno game seen at the Lisboa in Macau.
  
• Keno appendix 10Extra Draw Keno.
  
• Keno appendix 11Jumbo Bingo Progressive game at the Station Casinos.
  
• Keno appendix 12Triple Trouble Keno.
  
• Keno props Miscellaneous keno bets.
  
• Probabilities in Keno. A lesson in how to calculate keno probabilities.
  
• Cleopatra Keno
  
• Jackpot Party Keno
  

Links

• German translation of this keno page.
• Online casino comparison of keno paytables.
• expected returns of lots of keno games.

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