Multi player Parrondo games with rigid coupling

In the original Parrondo game, a single player combines two losing strategies to a winning strategy. In this paper we investigate the question what happens, if two or more players play Parrondo games in a coordinated way. We introduce a strong coupling between the player such that the gain or loss of all players in one round is the same. We investigate two possible realizations of such a coupling. For both we show that the coupling increases the gain per player. The dependency of the gain on the various parameters of the games is determined. The coupling can not only lead to a larger gain, but it can also dominate the driving mechanism of the uncoupled games. Which driving mechanism dominates, depends on the type of coupling. Both couplings are set side by side and the main similarities and differences are emphasised.