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The Parrondo effect describes the seemingly paradoxical situation in which two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24 (2000)]. Here we generalize this analysis to the case where both games are history-dependent, i.e. there is an intrinsic memory in the dynamics of each game. New results are presented for the cases of both random and periodic switching between the two games.doi:10.1103/physreve.67.056128 pmid:12786241 fatcat:3p35javtjvg2ni36an4pclsp4q