The game of Keno is composed of 80 numbers from which 20 are randomly picked by the Operator. The Bettor determines what he is going to play by indicating the quantity of numbers he is going to choose. Generally, the Bettor chooses a game of from 1 to 20 numbers (commonly referred to as "spots") and plays that particular game. The Bettor wins if he the numbers he selects are a subset of the 20 numbers picked by the Operator.
My assignment is to develop a slot machine based on the Keno concept but fixed on 9 Spot (Bettor chooses 9 numbers). The program generates 20 random unique numbers (0 < n < 81) which are stored in an array (Operator Numbers). The random number generator is reset and 9 more random unique numbers are generated (0 < n < 81) and are stored in a second array (Bettor Numbers). The numbers in the second array can match the numbers in the first array as the random number generator is reset after the first array.
The slot machine will award credits by counting the matches of Bettor numbers to Operator numbers. After determining the total possibilities and then probabilities of matched numbers I came up with the following table ( attached image1.jpg) :
Formulas for determining possibilities:
Spot 0: ((20!/20!)/(0!))x((60!/51!)/(9!)) = 14,783,142,660
Spot 1: ((20!/19!)/(1!))x((60!/52!)/(8!)) = 51,172,416,900
Spot 2: ((20!/18!)/(2!))x((60!/53!)/(7!)) = 73,379,314,800
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Spot 9: ((20!/11!)/(9!))x((60!/60!)/(0!)) = 167,960
Total: (80!/71!)/(9!) = 231,900,297,200
I got the probability of each Spot by dividing each Spot possibilities by the Total possibilities.
I experimented with the pay amount for each Spot until I got a modest return (12%).
The Slot machine has 9 squares which represent the Spot 9 keno game. A red square represents a matched number.
Here is a screenshot of the working Slot machine showing 3 matched numbers (attached image2.png):
The slot machine has now been extended to allow more options as in the image attached (image3.png):
The Keno game is extended such that numbers 1 to 50 are Red, 51 to 70 are Black and 71 to 80 are Blue. Are the possibilities for each Spot going to change? I need assistance in coming up with the new paytable with the relevant possibilities and probabilities.
Thank you.
My assignment is to develop a slot machine based on the Keno concept but fixed on 9 Spot (Bettor chooses 9 numbers). The program generates 20 random unique numbers (0 < n < 81) which are stored in an array (Operator Numbers). The random number generator is reset and 9 more random unique numbers are generated (0 < n < 81) and are stored in a second array (Bettor Numbers). The numbers in the second array can match the numbers in the first array as the random number generator is reset after the first array.
The slot machine will award credits by counting the matches of Bettor numbers to Operator numbers. After determining the total possibilities and then probabilities of matched numbers I came up with the following table ( attached image1.jpg) :
Formulas for determining possibilities:
Spot 0: ((20!/20!)/(0!))x((60!/51!)/(9!)) = 14,783,142,660
Spot 1: ((20!/19!)/(1!))x((60!/52!)/(8!)) = 51,172,416,900
Spot 2: ((20!/18!)/(2!))x((60!/53!)/(7!)) = 73,379,314,800
.
.
Spot 9: ((20!/11!)/(9!))x((60!/60!)/(0!)) = 167,960
Total: (80!/71!)/(9!) = 231,900,297,200
I got the probability of each Spot by dividing each Spot possibilities by the Total possibilities.
I experimented with the pay amount for each Spot until I got a modest return (12%).
The Slot machine has 9 squares which represent the Spot 9 keno game. A red square represents a matched number.
Here is a screenshot of the working Slot machine showing 3 matched numbers (attached image2.png):
The slot machine has now been extended to allow more options as in the image attached (image3.png):
The Keno game is extended such that numbers 1 to 50 are Red, 51 to 70 are Black and 71 to 80 are Blue. Are the possibilities for each Spot going to change? I need assistance in coming up with the new paytable with the relevant possibilities and probabilities.
Thank you.
