I've picked up a project from someone else who has created a spreadsheet that is meant to represent some slot machine mathematics and i'm struggling to understand the math that is used to get certain figures.
The game is built on 3 sets of balls that are draw. 10 balls, 15 balls and 20 balls. Each set has 3 balls drawn from them giving you 3/10, 3/15 and 3/20. These ball sets are unique and individual and have no correlation to each other. From there we're building a set of paytables on those.
The first tier that was created is: Minimum 1 matched from each set which is calculated as:
ball set of 10 = 0.708333333
ball set of 15 = 0.516483516
ball set of 20 = 0.403508772
Then he multiplied all of those together to get a probability to calculate the rest of that line in the table.
I need to understand how he got those 3 figures that make up 1 probability figure.
Thanks!
In the first case, you are drawing 3 balls from a group of 10, and you want to calculate the chance that at least one of them is one of the 3 'winning' balls.
This is (1-P(none of them 'winning')) = $1-(\frac{7}{10})(\frac{6}{9})(\frac{5}{8}) = 0.708333333$
The other numbers are calculated similarly.