Regarding round-off errors as random is often a necessary simplification to describe their behavior. Assuming, in addition, the symmetry of their distributions, we show that one can, in unstable (ill-conditioned) computer calculations, suppress their effect by statistical averaging. For this, one slightly perturbs the argument of fx0 many times and averages the resulting function values. In this text, we forward arguments to support the assumed properties of round-off errors and critically evaluate the validity of the averaging approach in several numerical experiments.