<p>Oscillator Ising machines (OIMs) and probabilistic bit (p-bit) platforms have emerged as promising non-Von Neumann paradigms for tackling hard computational problems. While OIMs realize gradient-flow dynamics, p-bit platforms operate through stochastic sampling. Although traditionally viewed as distinct approaches, this work presents a theoretically grounded framework for configuring OIMs as p-bit engines. We demonstrate that this functionality can be enabled through a novel interplay between first- and second harmonic injection to the oscillators. Our work identifies new synergies between the two methods and broadens the scope of applications for OIMs beyond combinatorial optimization problems to those that entail stochastic sampling. We further show that the proposed approach can be applied to other analog dynamical systems, such as the Dynamical Ising Machine.</p>