This is an attempt to discuss the following question: When is a random choice better than a deterministic one? That is, if we have an original deterministic setup, is it wise to exploit randomization methods for its solution? There exist numerous situations where the positive answer is obvious; e.g., stochastic strategies in games, randomization in experiment design, randomization of inputs in identification. Another type of problems where such approach works successfully relates to treating uncertainty, see Tempo R., Calafiore G., Dabbene F., ``Randomized algorithms for analysis and control of uncertain systems,'' Springer, New York, 2013. We will try to focus on several research directions including optimization problems with no uncertainty and compare known deterministic methods with their stochastic counterparts such as random descent, various versions of Monte Carlo etc., for convex and global optimization. We survey some recent results in the field and ascertain that the situation can be very different.