**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 .

*Example*:

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%.