The Grid Giant Star Survey (GGSS) is a partially filled, all-sky survey to identify K-giant stars with low levels of radial velocity (RV) variability. Previously, we studied histograms of the RV variability obtained in the early phase of the GGSS (Bizyaev et al.). This part of the survey has been conducted with a very limited number of observations per star and a rough accuracy. We apply Monte Carlo simulations to infer a fraction of RV-stable stars in the sample. Our optimistic estimate is that 20% of all considered K giants have RV variability under 30 m s(-1). Different assumptions of intrinsic RV variability for our stars give 12% - 20% of RV-stable K giants in the sample studied.