This paper addresses the dynamics and the convergence of ordinal comparison in the simulation of stochastic discrete event systems. It examines properties of dynamic behaviours of ordinal comparison in a fairly general framework. Most importantly, it proves that for some important classes of discrete event systems, the probability of obtaining a desired solution using an ordinal comparison approach converges at exponential rate while the variances of the performance measures converge at best at rate O(1/t2), where t is the simulation time. Heuristic arguments are also provided to explain that exponential convergence rate holds for more general systems.