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Abstract: In Parrondo’s paradox, a winning strategy is formed either by playing two losing games randomly or alternating them periodically. The paradox is commonly analyzed using stochastic matrices. In this paper, we modify the stochastic matrices to allow a more systematic introduction of bias into fair processes, while retaining the use of simple matrix operations throughout the analysis. [Copyright &y& Elsevier]

Abstract: Parrondo’s Paradox has gained a fair amount of attention due to it being counter-intuitive. Given two stochastic processes, both of which are losing in nature, it is possible to have an overall net increase in capital by periodically or randomly alternating between the two processes. In this paper, we analyze the paradox with a different approach, in which we start with one process and seek to derive its complementary process. We will also state the conditions required for this to occur. Possible applications of our results include the development of future models based on the paradox. [Copyright &y& Elsevier]