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.
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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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