Keno is one of the most famous gambling games. It was created in China 2,000 years ago by a general to collect money for the war and now is played worldwide. The most common Keno is played with 80 numbers and 20 are drawn.
Let’s see in what consist:
We have a concrete number of numbers (we will use the 20/80 for the examples) and each the players choose a different range of numbers (picks)
Depending on the number of picks selected the payouts will be different.
Let’s take the 20/80 version. We have 80 numbers and 20 are drawn.
We pick 1 number. The probabilities to hit the number are 20 / 80 = 25%
That was easy, but how can we calculate how many hits would we have for 20 picks?
Let’s work.
We have to calculate the number of combinations for 2 picks:
Total Numbers: 80
Numbers drawn: 20
Picks: 2
To calculate the number of combinations of 2 numbers from a total of 80 we have to do:
Combinations (numbers,picks) = numbers! / picks! x (numbers – picks)!
! = Factorial
For the example= 80! / 2! x (80-2)! = 3,160 combinations
Ok, so we have the total combinations of 2 elements for a total of 80 numbers (3,160 combinations). Now we have to calculate the number of combinations that would we good for our picks:
Combinations (drawn,picks) = 20! / 2! x (20-2)! = 190 combinations
So now we have the total combinations of 2 elements that are good for us (190 combinations).
Then the probability to hit 2 picks is = 190 / 3,160 = 6,01%
Now imagine that we bet to 20 picks, here you can see the probabilites for each number of hits:
You can see that you have a 96,62% of probability to pick between 2-8 numbers.
Alex Zubizarreta
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