The instability of earth-rock dams is related to numerous stochastic parameters; however, conventional stability analysis often overlook the impacts of multiple parameters on earth-rock dams, such as reservoir water level, soil shear strength, and earthquakes. To comprehensively analyze the failure probability and damage modes of earth-rock dams, a case study of the dam in a pumped storage hydropower station was conducted. Based on pseudo-static method, plastic limit analysis, finite element discretization concepts, stochastic programming theory, and Monte Carlo simulation, we proposed a novel algorithm for the reliability analysis of earth-rock dams, considering the variability of soil shear strength parameters. Then, the failure probabilities of different sections of the dam were calculated based on the unit failure probability theory to assess the reliability of the whole dam. The results show that after supporting the downstream slope of the dam, the failure probability under normal water level and seismic condition were reduced by 1.90% and 17.56%, respectively, indicating that the supporting piles sustained the reinforcement effect under seismic conditions. Compared with the conventional methods (finite element method and Bishop’s method), the calculation efficiency of the proposed algorithm was increased by 98.31%, with a mere average relative error of 3.32% for the safety factor. This suggests that the algorithm can accurately and efficiently predict the failure probability and failure zones of earth-rock dams, providing a reliable tool for the engineering design and safety assessment.