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Parrondo's paradox indicates a paradoxical situation in which a winningexpectation may occur in sequences of losing games. There are many versions ofthe original Parrondo's games in the literature, but the games are played bytwo players in all of them. We introduce a new extended version of games playedby three players and a three-sided biased dice instead of two players and abiased coin in this work. In the first step, we find the part of the parametersspace where the games are played fairly. After adding noise to fairprobabilities, we combine two games randomly, periodically, and nonlinearly andobtain the conditions under which the paradox can occur. This generalized modelcan be applied in all science and engineering fields. It can also be used forgenetic switches. Genetic switches are often made by two reactive elements, butthe existence of more elements can lead to more existing decisions for cells.Each genetic switch can be considered a game in which the reactive elementscompete to increase their molecular concentrations. We present three geneticnetworks based on a new generalized Parrondo's games model, consisting of twonoisy genetic switches. The combination of them can increase network robustnessto noise. Each switch can also be used as an initial pattern to construct asynthetic switch to change undesirable cells' fate.

A new generalization of Parrondo's games to three players and its application in genetic switches