Beyond Parrondo's paradox

The Parrondo's paradox is a counterintuitive phenomenon where individually-losing strategies can be combined in producing a winning expectation. In this paper, the issues surrounding the Parrondo's paradox are investigated. The focus is lying on testifying whether the same paradoxical effect can be reproduced by using a simple capital dependent game. The paradoxical effect generated by the Parrondo's paradox can be explained by placing all the parameters in one probability space. Based on this framework, it is able to generate other possible paradoxical effects by manipulating the parameters in the probability space.