The Quantum Game Interpretation for a Special Phenomenon of Parrondo's Paradox

Abstract Here we contract two associated games that consist of tossing biased coins. By using the discrete-time Markov chain method, game AB, which is played in alternation, is studied by means of theoretical analysis and computer simulation. And we find that this game didn’t have a definite stationary probability distribution and that payoffs of the game depended on the parity of the initial capital. Besides, the quantization method is used in a further study. The results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity.