The ratio ${\ensuremath{\mu}}_{N}$ of the cross section for circularly polarized light to that for linearly polarized is numerically investigated for
N-photon ionization of atomic hydrogen. For
N<4, it appears that the gain factor is greater than unity. For $N\ensuremath{\ge}4$, the ratio ${\ensuremath{\mu}}_{N}$ is generally smaller than unity and decreases when the multiphoton order
N increases.