It was shown in Sadiq (2013) that succession parameters under the Aunu permutation patterns can be used as vertices of the graph model resulting from different transition of the automata scheme employed. This paper generates a graph model using the Aunu permutation patterns governed by some properties as embedded in method of construction of a typical game of chance scheme. A finite automata model was constructed from the game of chance using the (123) avoiding class of the Aunu permutation patterns.Furthermore, the paper illustrated some useful relationship between the field of automata theory and Combinatorics; it also highlights some important applications of the Aunu Permutation Patterns in graph theory.