**3-reel slot machines**

**2. Case B – different numbers of stops and symbol
distributions on the reels**

** 2.6
Event –
Any combination of two specific symbols**

The probability of
is
,
where are
the basic probabilities of the two symbols occurring on the reels respectively ( is
the probability of symbol no. *i* occurring on reel no. *j*).

* Example*:

Find the probability of any combination of red seven and blue seven symbols occurring on a payline of a 3-reel slot machine having 56, 56, and 60 stops on reels 1, 2, and 3 respectively and the following distributions of the two symbols on these reels respectively: 2, 2, 2 for red seven; 2, 1, 1 for blue seven.

The basic probabilities are: and . The sought probability is:

.

** 2.7 Event
–
Any combination of at least one of three specific symbols**

The probability of
is
,
where are
the basic probabilities of the three symbols occurring on each reel
respectively. Denoting ,
for *j* from 1 to 3, we can write
and
use the tables and the results of section 2.1.

*Example*:

Find the probability of any combination of bar-type symbols (single, double, and triple bar) occurring on a payline of a 3-reel slot machine with 50, 50, and 60 stops on reels 1, 2, and 3 respectively, and the following distributions of the bar-type symbols on these reels respectively: 2, 2, 1 for single bar; 2, 1, 1 for double bar; 1, 1, 1 for triple bar.

We have: , , The sought probability is: