Keno Download
Before making a keno download, make sure to calculate the probabilities.
By doing so, you greatly increase your chances of success in online
casinos. 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.
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