Random pyramids are the most widely used texture in monocrystalline silicon solar cells for reducing front-surface reflection and trapping weakly absorbed light. In prior efforts to evaluate the light-trapping performance of random pyramids through optical simulations, the base angle of the pyramids was assumed to be 54.7°, as is expected from the orientation of the crystallographic planes. In this contribution, we benchmark the light-trapping capability of real random pyramids - which have a distribution of base angles - against both ideal, 54.7° random pyramids, and a Lambertian scatterer. We do so by calculating the path length enhancement and fraction of rays remaining trapped as a function of passes through the wafer, and this information is used to calculate short-circuit current density as a function of wafer thickness. Interestingly, the excellent performance of real random pyramids - they are close to Lambertian - arises precisely because they are imperfect and have a distribution of angles.