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: