  The 1/N expansion of the two-particle irreducible effective action offers a
powerful approach to study quantum field dynamics far from equilibrium. We
investigate the effective convergence of the 1/N expansion in the O(N) model by
comparing results obtained numerically in 1+1 dimensions at leading,
next-to-leading and next-to-next-to-leading order in 1/N as well as in the weak
coupling limit. A comparison in classical statistical field theory, where exact
numerical results are available, is made as well. We focus on early-time
dynamics and quasi-particle properties far from equilibrium and observe rapid
effective convergence already for moderate values of 1/N or the coupling.
