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 → ∞. We show that the greedy strategy is optimal for N=1 and N=2 but not for N = 3. In the limit. N→ ∞ our analysis reveals a very rich behavior including the possibility of phase transitions as a function of the chosen strategy.
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