In system-level simulations, the Monte Carlo (MC) approach is used to approximate the expectation of throughput due to the exponentially growing number of possible interference constellations that an exact solution would require. Utilizing the opportunistic resource fair (ORF) scheduler model in a multi-beam fifth-generation (5G) cellular network scenario, the conventional approach schedules the beams based on individual beam scheduling probabilities for each MC realization. This implementation suffers from inaccuracy and early error saturation, leading to poor performance of the MC approximation. This letter proposes an alternative way to use the joint beam probability distribution for scheduling from a convex optimization problem, which dissolves ambiguities. The simulation results show that the new approach not only provides higher precision and less complexity but also shows some potential to improve the downlink throughput of the user equipments (UEs).