In this work, the utility of PCMO RRAMs as an enabler for large scale stochastic recurrent neural networks like Boltzmann machines is proposed. The parameters affecting the set-time stochasticity are identified. With HRS andVSetfixed,tSetdistribution is fully determined across cycles and time. The asymmetric nature of stochasticity between set and reset is highlighted. Deterministic and gradual state control in the Reset operation allows HRS controllability to enable drift-free set stochasticity over many iterations. The reduced drift enables the solution of problems greater than 1000 nodes for the max-cut graphical optimization using Boltzmann machines which is 20×higher than electrical-input only method of stochasticity generation. Further, HRS controllability allows tuning out of the device-to-device variability effects improving solution quality by 10×compared to a system with realistic variations. The properties of PCMO RRAM neuron as a stochastic neuron with a controllable internal state makes it the choice of device for implementing stochasticity and weights in large scale Boltzmann machines.