Parrondo games with strategy

Abstract

The notion of a strategy in the multi-player version of the Parrondo game is reviewed. We calculate the gain for the greedy strategy as a function of the number N of players, including exact analytic results for N < 4 and in the limit N --> infinity. We show that the greedy strategy is optimal for N = 1 and N = 2 but, not for N = 3. In the limit N --> infinity our analysis reveals a very rich behavior including the possibility of phase transitions as a function of the chosen strategy.