Distributed algorithms that are resilient to failures can either be deterministic or probabilistic. Take for example the consensus problem.
Paxos is deterministic in the sense that given the assumption it makes, it always works.
In constrast, randomized consensus works with a given probability.
What is the advantage of designing and using a deterministic algorithm?
The assumptions upon which deterministic algorithms rely have also a probability of holding in the reality (what is called their assumption coverage). Hence, there is always a probability that a deterministic algorithm does not work in the reality.