text: Keno odds are long with 15 spots, but worth it
  
  January 19, 2016 3:00 AM
  by
  
  Little has been written on tickets greater than 10 spots as the odds are exceeding high to hit all the numbers – sometimes even greater than the recent huge Powerball lottery, and for a lot less money.
  
  The odds on tickets of 10 spots or more:
  
  • 10 out of 10: nearly 9 million to 1.
  
  • 11 out of 11: over 62.3 million to 1.
  
  • 12 out of 12: over 471 million to 1.
  
  • 13 out of 13: over 4 billion to 1.
  
  • 14 out of 14: nearly 40 billion to 1.
  
  • 15 out of 15: nearly 430 billion to 1.
  
  Source (Smart Keno Play by Keith L. Hall & Ronald L. Vikmyhr).
  
  Why play such a long odds ticket?
  
  First, almost all the payouts are taken by the smaller number of hits in a typical cycle, though this may take years (actually millions of them) on the average – less than 1/1000 of 1% of the return is in the 15 out of 15 due to its rarity. In reality you are looking for the large intermediate hits that have much lesser, but still high odds.
  
  Another reason is, when you have a way ticket composed of 15 numbers, in case your hits are scattered all through the ticket rather than in your marked groups. Let’s say you are playing a 3-3-3-3-1-1-1 because you have read my previous columns and know that in downtown Las Vegas 7 spots have very good top end pays at some casinos.
  
  You know you have to hit a king and two of the groups of three to get your solid 7. Thus you have two groups of 3 chosen from four groups of 3 = (4!)/(2!2!) = (4 X 3 X 21!)/(2!2!) = (4 X 3)/(2 X1) = 12/2 = 6 ways for your two groups of three. Being there are three kings you have 6 X 3 = 18 possible 7 spots with this ticket.
  
  Odds Calculations from the Keno Calculator by The Wizard of Odds, Michael Shackleford on wizardofodds.com/keno using his keno calculator.
  
  Yes, there are 18 7-spots
  
  The ticket used is a 15-spot example from Smart Keno Play as mentioned above. Confirming there are 18 seven spots possible on a 3-3-3-3-1-1-1 ticket from “The Book of Ways” by William Holmes.
  
  Now that you have your seven-spot ticket from 15 total numbers, there are a lot of possible 7 spots possible but only 18 will be a solid hit due your groupings. There are (15!)/(8!7!) = (15 X 14 X 13 X 12 X 11 X 10 X 9 X 8!)/(8!7!) = (15 X 14 X 13 X 12 X 11 X 10 X 9 )/( 7!) = 32,432,400/5,040 = 6,435 possible 7 spots and just 18 of them will be a solid hit.
  
  By playing the 15 spot you still will get paid if your spot hits are scattered all around. Granted, it may not be a large play but as you can see, most of the ways of hitting 7 out of 15 will be scatter pays, and as the late Vulcan, Mr. Spock, of blessed memory would say, 6,417 out of 6,435 to be exact will be non-solid hits.
  
  Thus, this is a good reason to play the 15-spot in addition to your 18 7-spots. Best place to play, undoubtedly, the Deano rate at The D, which returns the most percentage-wise, where you even get a small pay on 0, 1, or 2 spots hit.
  
  Don’t shrug off those who play a higher number of spots, they may have a very good reason for doing so. We are all out to win and just may have different ways to accomplish that big triumph.
  
  See you next week, over and out!
  
  Pesach Kremen is a former UNLV Masters Gaming student, has won and placed in multiple local keno tournaments, and has written several academic papers on keno. Email: PesachKremen@GamingToday.com