3-reel slot machines
1. Case A – the same number of stops and symbol distribution on the reels
1.7 Event – Any combination of at least one of three specific symbols
The probability of is , where , , and are the distributions of the three symbols on a reel.
For the numerical probabilities, we can use the table and the results of section 1.1 (event - A specific symbol three times) for .
Find the probability of any combination of seven-type symbols (assume for example that there are red, blue, and black sevens) occurring on a payline of a 3-reel slot machine with 48 stops on each reel, having 2 red, 2 blue and 3 black sevens on each reel.
Take for instance , , and (for any permutation of these values on the denotations, we will reach the same result, as the probability formula is symmetric in these three variables). We take c = 2 + 2 + 3 = 7 and look in the table of section 1.1 at the intersection of row t = 48 with column c = 7, where we find the probability P = 0.00310149 = 0.310149%.