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.