A randomized model verification strategy for RANSAC is presented. The proposed method finds, like RANSAC, a solution that is optimal with user-controllable probability n. A provably optimal model verification strategy is designed for the situation when the contamination of data by outliers is known, i.e. the algorithm is the fastest possible (on average) of all randomized RANSAC algorithms guaranteeing 1 - n confidence in the solution. The derivation of the optimality property is based on Wald?s theory of sequential decision making. The R-RANSAC with SPRT, which does not require the a priori knowledge of the fraction of outliers and has results close to the optimal strategy, is introduced. We show experimentally that on standard test data the method is 2 to 10 times faster than the standard RANSAC and up to 4 times faster than previously published methods.