Sufficient conditions are provided in terms of transition kernels under which one game results in a lower variance than another game when both estimate the same quantity. By defining the efficiency of a Monte Carlo game by the inverse of the product of the variance and the number of collisions per history and the computing time per collision, and by using a special approximation, called the separation assumption, for the evaluation of integrals occurring in the analysis, it is shown in a simplified situation that the expected leakage probability method in reaction rate and leakage estimations, although reducing the variance, is less efficient than the analog game with an expectation estimator. The efficiency of a game with survival biasing and Russian roulette is examined, and a simple method is presented for the determination of a quasi-optimum value of the Russian roulette parameter.