The number of ambient divisions is rounded down the the nearest perfect square below the number specified. At deeper levels of the ray tree, the number of divisions (and super-samples) is further reduced by 0.5^N, where N is the number of bounces. This is all in the name of saving caclulation time while maintaining a constant contribution to accuracy. The 0.5 value was selected as a compromise average reflectance value, which is higher than it should be in some cases and lower than it should be in others.
If you set -aa 0, then the actual surface reflectance or transmittance is used rather than 0.5, since the values are not cached or re-used.