  Recently noticed ability of restart to reduce the expected completion time of
first-passage processes allows appealing opportunities for performance
improvement in a variety of settings. However, complex stochastic processes
often exhibit several possible scenarios of completion which are not equally
desirable in terms of efficiency. Here we show that restart may have profound
consequences on the splitting probabilities of a Bernoulli-like first-passage
process, i.e. of a process which can end with one of two outcomes. Particularly
intriguing in this respect is the class of problems where a carefully adjusted
restart mechanism maximizes probability that the process will complete in a
desired way. We reveal the universal aspects of this kind of optimal behaviour
by applying the general approach recently proposed for the problem of
first-passage under restart.
