Polarons and their associated transport properties are a field of great current interest both in chemistry and physics. In order to further our understanding of these quasi-particles, we have carried out first-principles calculations of self-trapped holes (STH) in the model compounds AgCl and AgBr, where extensive experimental information exists. Our calculations confirm that the STH solely stabilizes in AgCl but with a binding energy of only 165 meV, an order of magnitude smaller than that found for the Vk center in KCl. Key contributions to this stabilization energy come from the local relaxation along breathing (a1g) and Jahn-Teller (eg) modes in the AgCl6 4-unit. In order to study the transfer of the STH among silver sites we (i) use first-principles calculations to obtain the hopping barrier of the STH to first and second neighbors, involving eight distinct paths, using firstprinciples and (ii) construct a simple model, based on Slater-Koster parameters, that highlights the similarity of polaron transfer with magnetic superexchange. This allows one understanding why the movement of STH to second neighbors is highly enhanced with respect to closer ones. In agreement with experimental data and the model, the present calculations prove the existence of a dominant mechanism of polaronic motion that corresponds to the displacement of the STH to the next nearest sites in the <100> direction and a small barrier of 37 meV. This mechanism is dominated by the covalency inside a AgX6 4-complex (X:Cl;Br) thus explaining why the STH is not stabilized in AgBr following the increase of covalency due to the ClBr substitution. The present calculations confirm that ~10% of the charge associated with the STH in AgCl is lying outside the AgCl6 4-complex. This fact is behind the differences between optical and magnetic properties of the STH in AgCl and those observed in KCl:Ag 2+ .2