Penning ionisation (PI) processes involving pairs of Rydberg alkali-metal atoms, excited to different quantum states and experiencing dipole.dipole interactions, have a wide range of important properties in atomic physics.Within the framework of the semiclassical approximation, we have used both numerical and analytical approaches to examine the Penning autoionisation width dependence on the state quantum numbers in a quasi-molecule formed by the interacting partner atoms.We described the characteristics of optimal quantum numbers that lead to enhanced PI widths for the interacting Rydberg atom pairs of all alkali-metal atoms. The excited states of atoms in these pairs are asymmetric, resulting in a large atomic shell size difference: Inspired by Efimov et al (2016 J. Phys. B: At. Mol. Opt. Phys. 49 125302), we call such a pair eTom f and eJerry f (for ebig f and esmall f). Compared to symmetric pairs, the optimal asymmetric pairs display a significant (by several orders of magnitude) increase in the PI rate. This property makes PI a relevant source for producing charged particles in cold Rydberg systems that spontaneously evolve into cold plasma. Contrary to hydrogen atoms examined in (Efimov et al 2016 J. Phys. B: At. Mol. Opt. Phys. 49 125302), the difference in quantum defects in alkali-metal atoms results in a strong Penning width dependence on the orbital quantum numbers l of the quasi-molecule. In particular, alkali-metal atoms exhibit two PI channels associated with bound.bound optical transitions showing Δl = ±1-individual and closely spaced (doublet-like) configurations of optimal pairs. Furthermore, we demonstrate that the presence of Forster resonances can lead to a notable (up to five times) increase in the PI efficiency.