A global reactor performance code employing Monte Carlo techniques has been developed to study the “probability of ignition” and has been applied to several configurations of a compact, high-field ignition tokamak to determine the relative benefits of raising the plasma current and peaking the density profile. Probability distributions for the critical physics parameters in the code are estimated using existing experimental data. An energy confinement scaling representing a 1 to 2.5 times improvement over the L mode is assumed; the range of this multiplier was chosen to reflect the uncertainty in extrapolating the energy confinement time to the high field ignition regime. Even with fairly broad input probability distributions, the probability of ignition improves significantly with increasing plasma current and density profile peaking. Raising the plasma current by 2 MA has about the same impact as raising the peak-to-average density ratio from ∼1 to ∼3. With either this density peaking or a plasma current ≥11 MA, the probability of ignition is computed to be ≥40%. In other cases, values of Q (the ratio of the fusion power to the sum of the ohmic and auxiliary input powers) of the order of 10 are generally obtained. Comparisons of our empirically based confinement assumptions with two theory-based transport models yield conflicting results.