True random number generation (TRNG) circuits are presented which employ magnetic tunnel junction (MTJ) elements that can change magnetization state probabilistically in response to application of electrical pulses. Some implementations include pulse generators which apply perturbation sequences to the MTJ elements. The MTJ elements responsively produce randomized outputs related to changes in magnetization states. Probability compensators are included which monitor for deviations in measured probabilities in the randomized outputs from a target probability. The probability compensators make adjustments to the perturbation sequences to influence probabilistic changes in the magnetization states of the MTJ elements and bring the measured probabilities to within a predetermined deviation from the target probability.