We study galaxies drawn from the semi-analytic models of Guo et al. (2011) based on the Millennium Simulation. We establish a set of four observationally measurable parameters which can be used in combination to identify a subset of galaxy groups which are old, with a very high probability. We therefore argue that a sample of fossil groups selected based on the luminosity gap will result in a contaminated sample of old galaxy groups. By adding constraints on the luminosity of the brightest galaxy, and its offset from the group luminosity centroid, we can considerably improve the age-dating.