Some stochastic properties of topological dynamics of semigroup actions

For an iterated function system (IFS), we investigate combinatorial issues relating to the use of random orbits and also we study stochastic properties of random orbits in topological dynamics of semigroup actions. Moreover, we will address some conditions under which a property for typical orbits is satisfied for almost surely chaos game orbits. Also, as consequence, we present several applications of our main result.