The theoretical analysis and computer simulation on Parrondo's history dependent games

Abstract This paper is based on Parrondo's history-dependent game model that has been put forward by P.Arena. Using discrete-time Markov chains and computer simulation, we analyse the parrondo's paradox when games ABC…ABC played periodically and the parameter M=4. And then we find the volume of parameter space for which the paradox takes effect. Meanwhile we simulate the different sequences for mixing games A, B and C by computer and find an interesting phenomenon that when the total time of playing game A,B and C is an even number, the mixing game's payoff dependents on the original capital's parity.