This paper presents a probabilistic reliability assessment model to address several challenges presented by modern power systems with increasing shares of variable renewable energy and storage. The model includes a two-stage structure to simulate steady-state and post-contingency conditions that allows for a more realistic assessment of system reliability. Computational efficiency is enhanced through filtering of Monte Carlo samples and parallel computing. We first analyze how outage sample size affects reliability assessment outcomes across systems with different resource adequacy levels, showing that smaller sample sizes lead to greater variability in reliability metrics. Through a case study analysis of an "ERCOT-like" system we demonstrate reasonable convergence in expected unserved energy outcomes with approximately 25,000 daily outage samples. We then assess three different sample filtering methods and show that filtering based on total firm generation margin closely approximates the full sample result while simulating dispatch for 10% or less of the daily samples. Finally, we implement an imperfect foresight post-contingency redispatch model and show that assuming perfect foresight overestimates system reliability. This paper highlights the importance of incorporating imperfect foresight with careful selection of sample size and efficient sample filtering when conducting reliability assessments for evolving power systems.