This paper presents a novel learning automaton, βtype, which consists of 2-state Bayesian estimators. The β-type learning automaton is presently among the fastest learning automata known, which was proposed in our earlier works. However, compared with the βtype learning automaton and the conventional learning automata, the β-type learning automaton deteriorates from the viewpoint of memory usage and other resources, for example, since computational and energy resources of some applications are limited, such as the wireless sensor networks, reducing memory footprint and performance optimization are very important issues. So, in this study, we propose the β-type learning automaton with minimum resources, 2-state Bayesian estimators. Then, the efficiency of proposed β-type learning automaton is shown through several simulation results under some random environments.