Racing algorithms are iterative methods for identifying the best among several options with high probability. The quality of each option is a random variable. It is estimated by its empirical mean and concentration bounds obtained from repeated sampling. In each iteration of a standard racing algorithm each promising option is reevaluated once before being statistically compared with its competitors. We argue that Hoeffding and empirical Bernstein races benefit from generalizing the functional dependence of the racing iteration and the number of samples per option and illustrate this on an artificial benchmark problem.