This paper deals with the design of an on-board control strategy for Electric Vehicle recharging under the hypothesis of missing knowledge of the future energy price and the presence of vehicle to grid capability. For this purpose the charging session is modeled as a finite horizon Markov Decision Process and the optimal charging policy is computed according to Reinforcement Learning techniques, the learning phase makes use of the revenues received when taking actions in states represented by the current level of charge, the leftover charging time and the last realization of energy price. Simulation results show the effectiveness of the proposed approach with respect to the fulfillment of driver preferences in charging and the diversification of the control action during charging for the exploitation of the vehicle to grid concept.