International Journal “Information Theories and Applications”, Vol. 24, Number 4, © 2017 383 AUTOMATON MODEL OF ONE STATISTICAL RULE Tariel Khvedelidze Abstract: In the paper, a construction (algorithm of behavior) of a finite automaton in a stationary random environment with three possible reactions (win, loss, indifference) is proposed. It is constructed on the basis of a known statistical rule from the theory of recurrent events: "either a series of successes of length , or a series of failures of length  ". With methods of the theory of random walks, a formula is obtained for the generating function of the probability of changing the action of the finite automaton under consideration. It is shown that the sequence of finite automata of the construction under consideration converges to the corresponding infinite (with countably many states) automaton of the same structure and its possible behavior is investigated. Keywords: finite automaton, stationary random environment, behavior algorithm, generating function, expediency of behavior. ITHEA keywords: G.3 Probability and Statistics Introduction The problem of the behavior of a finite automaton in a binary stationary random environment was formulated and developed by M. L. Tsetlin [1]. The environment in the simplest case reacts to the actions of the automaton in two ways: either "punishes" or "encourages" the automaton with certain probabilities. The automaton a priori information about the medium does not have an. Тhen different authors the proposed various constructions of asymptotically optimal sequences of automata in both binary and non-binary stationary random environment (see, for example, [2-7]). For automata belonging to such a sequence, the mathematical expectation of the win increases with an increase in the memory capacity of the automaton and tends to the maximum possible in a given stationary random environment. In the interest of technical applications, the synthesis problems of automata optimal at various criteria in a binary and ternary stationary random environment were investigated in [8-9]. However, studies related to the study of the behavior of automata in both binary and non-binary stationary random environments have shown that the construction of an automaton that is best for some feature in any medium is unrealistic. Therefore, it is necessary to construct structures and develop