  We study the likelihood which relative minima of random polynomial potentials
support the slow-roll conditions for inflation. Consistent with
renormalizability and boundedness, the coefficients that appear in the
potential are chosen to be order one with respect to the energy scale at which
inflation transpires. Investigation of the single field case illustrates a
window in which the potentials satisfy the slow-roll conditions. When there are
two scalar fields, we find that the probability depends on the choice of
distribution for the coefficients. A uniform distribution yields a $0.05\%$
probability of finding a suitable minimum in the random potential whereas a
maximum entropy distribution yields a $0.1\%$ probability.
