A Hartman-sensor-based, adaptive optics system is analyzed using numerical simulation. The same simulation was used to quantify the lucky shot concept. One-dimensional, isoplanatic wavefronts were generated, containing the known spatial and statistical properties of atmospheric-turbulence-degraded wavefronts. The quality of the corrected wavefronts was analyzed as a function of different combinations of sensor (lenslet) number and correcting mirror number. It is shown that it is possible to reduce the number of correcting mirrors with no great loss of image quality. As a consequence of the wavefront simulation, it is shown that the lucky shot occurrence probability is very low.