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Noise is known to disrupt a preferred act or motion. Yet, noise and broken symmetry in asymmetric potential, together, can make a directed motion possible, in fact essential in some cases. In Biology, in order to understand the motions of molecular motors in cells ratchets are imagined as useful models. Besides, there are optical ratchets and quant...
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... questions to ask, will the resulting game be always winning with any proportion of A or B played? To look for an answer, we simulated the combined games where game A is played with probability and game B with ( ) in random order. For each value of , the simulation is done to check the resulting mean capital for reasonably long time steps to make sure of the trend, i.e., if the combined game is winning or losing. But interestingly, it is observed that with any arbitrary amount of randomness, the combined game is not always winning. For a certain range of values of , the game appears to be winning and for higher or lower values than that, the combined game is losing which means the paradox does not occur. The numerical result is displayed below. The preliminary understanding is that too much or too little presence of game A influences the capital in such a way that the triggering of the good coin in game B turns less and less. Game A pushes the value of capital towards or away from the multiple of 3, which the game B cannot do alone. The mechanism in B changes the capital toward multiple of 3 more likely (mathematical argument is given in [2]) and that is the bad coin is played more often when game B is played only. These pathological scenarios are checked with detailed numerical investigations [ Figure 4]. ...
