We have performed Monte Carlo simulations of the Ag+ cation and of the Ag atom in water. We have used the Kozack and Jordan polarizable water potential. The pairwise solute-water potentials and the three-body cation-water potential are based on MP2 calculations. We get for the hydration enthalpy of Ag+ the value -5.65 +/- 0.15 eV, in good agreement with the experimental value: -5.5 +/- 0.1 eV. For the ionization free energy of Ag, we have tested three available methods (thermodynamic perturbation, overlapping distribution, and self-consistent histograms methods) and found out that they yield very close results. The redox potential of the Ag+/Ag couple is estimated to be -2.3 V/NHE. Since our potentials include no empirical data, the agreement with the electrochemical value, -1.9 V/NHE, and the thermochemical value, -2.1 V/NHE, is satisfactory.