In a thermally equilibrated system, electron behavior in a metal is described by the Fermi-Dirac equation. With ultrafast lasers, electrons can be excited into temporary distributions which are not described by the Fermi-Dirac equation and are therefore not at a well-defined temperature. These nonthermal distributions quickly equilibrate through two primary processes: electron-electron scattering and electron-phonon scattering. In most situations, these effects are unnoticeable, since they are completed within 5 ps. A probabilistic numerical model for electron-electron scattering is presented. The model is robust, scaleable, and requires only one parameter. The success of the model suggests future work on a similar electron-phonon scattering model, which would provide a complete description of the elctron distribution during thermalization. Once complete, this model can be tested by measuring the amount of second harmonic light generated by an ultrafast laser in a pump-probe experiment.