The selection of an optimal cluster head (CH) node, acting as an intermediary between the base station and ancillary nodes, is a pivotal challenge in mobile Ad Hoc networks, significantly impacting network performance and efficiency. This study introduces a novel approach for CH node selection in Mobile Ad Hoc Networks (MANETs), aiming to bolster network efficiency. This approach selects the head of a nodes cluster based on the Connectivity Probability (CP), derived from the Poisson probability and each node's residual energy. The Poisson distribution, governed by a key parameter, lambda, serves to determine the likelihood of a specific outcome. In the context of this study, lambda signifies the average distance between any given node and the base station, measured relative to their communication range. Considering the direct influence of a node's residual energy on connection probability, the product of these two parameters is computed to ascertain CP. Nodes demonstrating the highest CP values are considered prime candidates for CH selection. The efficacy of the proposed algorithm was evaluated against established protocols, namely the LEACH and R-LEACH. Simulation results suggest that the proposed algorithm significantly improves network performance, extending the network lifetime by over 6 times and 3 times that of LEACH and R-LEACH, respectively. It also enhances network stability by approximately 7 times compared to LEACH and over 2 times that of R-LEACH. Furthermore, the algorithm notably improves throughput, exhibiting an increase by approximately 7 times relative to both protocols. In conclusion, the proposed algorithm offers a promising strategy for CH node selection in MANETs, potentially benefitting a wide gamut of applications.