A dynamical Langevin model is employed to evaluate the excess of the neutron emission in the fission of heavy nuclei ²⁴⁰Cf, ²⁴⁶Cf, ²⁵⁴Cf, ²⁴⁰U relative to the standard statistical-model prediction at various saddle-to-scission friction strengths. It is shown that when the neutron-to-proton ratio N/Z of the system increases, the sensitivity of the excess to the friction decreases substantially, and it almost disappears for ²⁴⁰ U. We suggest that using those compound systems with low N/Z favors an accurate determination for the saddle-to-scission friction strength based on the measurement of the pre-scission neutron multiplicity.