Electrical measurements, dc and ac, show that (AgI)(x)(HgS)(0.5-x/2)(As2S3)(0.5-x/2) glasses, 0.0 x0.6, exhibit drastic changes in ionic conductivity sigma(i) with silver iodide additions. The ionic transport increases by 13 orders of magnitude with increasing silver content from similar to 0.002 to similar to 23 at.%, and the activation energy decreases from 1.05 to 0.35 eV. Two distinctly different ion transport regimes above the percolation threshold concentration, x(c) approximate to 30ppm, were distinguished. The critical percolation regime at low silver content ( 2-5 at.% Ag) is characterized by a random distribution of silver-related entities and obeys a power-law composition dependence of sigma(i). The ion transport parameters depend on the host network connectivity, represented by the average coordination number , via the critical fictive temperature T-0; the calculated T-0 value is comparable to the glass transition temperature for the glassy (HgS)(0.5)(As2S3)(0.5) host matrix. In contrast, in the modifier-controlled domain, the silver-related entities are nonrandomly distributed. The high Ag+ ionic mobility results from interconnected tetrahedral (AgI2/2S2/2)(n) chains in the silver iodide content range 0.20.5.