Gathering is a fundamental coordination problem in cooperative mobile robotics. In short, given a set of robots with arbitrary initial location and no initial agreement on a global coordinate system, gathering requires that all robots, following their algorithm, reach the exact same but not predetermined location. Gathering is particularly challenging in networks where robots are oblivious (i.e., stateless) and the direct communication is replaced by observations on their respective locations. Interestingly any algorithm that solves gathering with oblivious robots is inherently self-stabilizing. In this paper, we significantly extend the studies of deterministic gathering feasibility under different assumptions related to synchrony and faults (crash and Byzantine). Unlike prior work, we consider a larger set of scheduling strategies, such as bounded schedulers, and derive interesting lower bounds on these schedulers. In addition, we extend our study to the feasibility of probabilistic gathering in both fault-free and fault-prone environments. To the best of our knowledge our work is the first to address the gathering from a probabilistic point of view.