The structure and energies of neutral Mg(NH3)(n) clusters have been investigated by experiment and theory, the ionization energy (IE) thresholds of these clusters being the probe of the differential solvation. Experimentally, the IE's of the magnesium atoms solvated by ammonia have been investigated by tunable laser ionization of clusters prepared in a simple pick-up source. IE's of clusters Mg(NH3)(n) have been measured for n=1 up to 37. The solvation of the magnesium ion is more efficient than that of the closed shell neutral Mg atom, resulting in a steep decrease of the ionization energy of ammonia clusters of increasing sizes (1.3 eV for n=1, 2.2 eV for n=2, and 2.9 eV for n=3). The stepwise decrease becomes smaller for higher order clusters (n > 20) but the asymptotic value does not appear to be reached even at n=37, suggesting a still developing electrostatic stabilization of the ion clusters at these sizes. Quantum chemical calculations have been performed which reveal the unique features of the solvation of the neutral closed shell Mg atom. The formation of neutral clusters is dominated by singly coordinated cyclic subunits containing three ammonias, while the ion is best stabilized by triply coordinated magnesium. The experimental ionization energies are in excellent agreement with the calculated values, indicating a "locally adiabatic" process. The very low ionization energy limit or asymptote, 2.3 eV, measured for the largest clusters can be simply rationalized by electrostatic interactions in the ion cluster, without having to invoke charge separation in the neutral aggregate.