New paradoxical games based on Brownian ratchets

Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged – namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the current capital of the player. Here we present new games where all the rules depend only on the history of the game and not on the capital. This new history-dependent structure significantly increases the parameter space for which the effect operates.