Parrondo's paradox
A more explanatory description is: Parrondo devised the paradox in connection with his analysis of the Brownian ratchet, a thought experiment about a machine that can purportedly extract energy from random heat motions popularized by physicist Richard Feynman.
If you start playing Game A exclusively, you will obviously lose all your money in 100 rounds.
Similarly, if you decide to play Game B exclusively, you will also lose all your money in 100 rounds.
Now if we tilt the whole profile towards the right, as shown in Figure 2, it is quite clear that both these cases will become biased towards B.
The apparent paradox has been explained using a number of sophisticated approaches, including Markov chains,[5] flashing ratchets,[6] simulated annealing,[7] and information theory.
In summary, Parrondo's paradox is an example of how dependence can wreak havoc with probabilistic computations made under a naive assumption of independence.
A more detailed exposition of this point, along with several related examples, can be found in Philips and Feldman.
[9] Parrondo's paradox is used extensively in game theory, and its application to engineering, population dynamics,[3] financial risk, etc., are areas of active research.
However, the games need not be restricted to their original form and work continues in generalizing the phenomenon.
[13] In evolutionary biology, both bacterial random phase variation[14] and the evolution of less accurate sensors[15] have been modelled and explained in terms of the paradox.
In ecology, the periodic alternation of certain organisms between nomadic and colonial behaviors has been suggested as a manifestation of the paradox.
The 'paradoxical' effect can be mathematically explained in terms of a convex linear combination.
This question is sometimes asked by mathematicians, whereas physicists usually don't worry about such things.
People drop the word "apparent" in these cases as it is a mouthful, and it is obvious anyway.
The truth is we still keep finding new surprising things to delight us, as we research these games.
