Getting the groups worked out in keno math

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Understanding the math of keno can be challenging. Fortunately there are ways available (pun intentional) to compute the number possible in any given ticket.

For simplicity let’s use an all king ticket (a group of one indicated by circling the one number chosen) of 8.

How many ways does a ticket such as this have? To find out how many are possible you need to know the number of groups you have. 

In this example we have 8 groups of one number each. If you know what an exponent or power of a number means you are all set.

The formula for calculating how many ways are possible is 2 to the nth power -1; n is the number of groups, which is the exponent used. Thus we have 2 to the eighth power which means 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256. From this we subtract 1 to get 255. There are 1 eight, 8 sevens, 28 sixes, 56 fives, 70 fours, 56 threes, 28 twos, and 8 ones, which total 255.

Notice the symmetry. There are the same number of sevens and ones, sixes and twos, and fives and threes. The reason is this: If you choose five numbers three must be left over. Choose six numbers and two are left over. Choose seven numbers and one is left over.

How do we know there are the total number of ways as I listed? We shall go into those calculations in a future column. Hint: If you know Pascal’s Triangle or Binomial Theorem it helps but it is not necessary. Until then, best of luck to you in Keno Math 101.

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: [email protected]

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