A deterministic analysis of the computational cost associated with geometric splitting/Russian roulette in Monte Carlo radiation transport calculations is presented. Appropriate integro-differential equations (based on the theory of Monte Carlo errors) are developed for the first and second moments of the tally as well as for the expected value of time per particle history, given that splitting with Russian roulette takes place at one or more internal surfaces of the geometry. The equations are solved using a standard Sn solution technique, allowing for the prediction of computer cost (formulated as the product of sample variance and time per particle history) associated with a given set of splitting parameters. Extensive numerical results relating to the transport model chosen for study (namely, particle transmission through a semi-infinite slab shield composed of an isotropically scattering medium) are presented. Optimum splitting surface locations and splitting ratios are determined. Single-surface results indicate that the threshold slab thickness for which any splitting becomes cost effective varies from ∼2 to >7 mean-free-paths, depending on the degree of scattering in the medium. When splitting is cost effective, it is so over a wide range of surface locations. Benefits of such an analysis are particularly noteworthy for transport problems in which splitting is apt to be extensively employed (e.g., deep-penetration calculations).