Mean reversal for stochastic hybrid systems

Consider two discrete time Markov chains on a finite state space with +/- 1 win or lose payoff subject to transition between the states. We introduce a class of processes whose cumulative expected payoffs are decreasing in time but, whenever the processes are chosen at random by flipping a fair coin, the expected payoff for the randomized process becomes increasing in time. The seemingly counterintuitive long time run mean reversal generalizes the idea of combining two losing games into a winning one, known as Parrondo's Paradox. (c) 2007 Elsevier Ltd. All rights reserved.