The effect of the ionic polarizability on the solvation of positive and negative ions in water is investigated using molecular dynamic simulations. The NEMO many-body interaction potential for the water molecules is used, and a variety of values for the polarizability of the ions are considered. The increase of the polarizability leads to a larger electrical field at the ion through (i) a shrinking of the solvation shell around the ion and (ii) an increased probability of an asymmetric location of the ion in the cage. For the positive ions, whose polarizabilities are generally smaller than those of negative ions, these effects are visible only for the highest polarizability studied. However, for a given polarizability, the electrical field at an ion as well as its preference for an asymmetric location is larger for cations than for anions. The induced dipole moments in the first hydration layer are also investigated.