The role of three irrational numbers PI, neper and feigenbaum constant as a new switching strategies in the Parrondo's paradox

Parrondo's paradox is a paradox in game theory that is inspired by the mechanical properties of ratchets. According to original formulation of Parrondo's paradox, two separate losing games can be combined to win via a random or periodic strategy. In this paper the role of irrational numbers (e, π and Feigenabum constant δ) as a new switching strategy for combination of two losing games on Parrondo's paradox was investigated and the effects of this new strategy on the final gain of Parrondo's paradox was compared to random strategy. Results showed that the highest final gain of Parrondo's paradox is related to the “e” switching strategy and also except for random switching strategy, digit 5 causes the maximum final gain in all strategies.