Parrondo's paradox

Parrondo's paradox, a paradox in game theory, has been described as:

A combination of losing strategies becomes a winning strategy.

It is named after its creator, Juan Parrondo, who discovered the paradox in 1996.

A more explanatory description is:

There exist pairs of games, each with a higher probability of losing than winning, for which it is possible to construct a winning strategy by playing the games alternately.

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. However, the paradox disappears when rigorously analyzed. Winning strategies consisting of various combinations of losing strategies were explored in biology before Parrondo's paradox was published.

Example: Watering a plant

Now consider the case of a potted houseplant. There are two games that can be played with the plant:

Game A: pour a continuous stream of water into the pot.
Game B: pour no water into the pot.

From the point of view of keeping the plant alive, both are losing games; over time, the plant will either take on too much water and rot, or it will dry up. Paradoxically, however, the plant can be kept alive by judiciously switching between the games, alternately watering the plant and turning off the water.

Example: Pedestrian

Consider the situation of a pedestrian trying to get to a grocery store. The pedestrian can play two games:

Game A: cross every street regardless of traffic.
Game B: stand still.

If the pedestrian plays only A, then they will eventually be struck by a vehicle. However, if they only play B, then they will never move from their position, failing to get to their destination. Parrondo's paradox suggests a solution: counterintuitively, if the pedestrian waits at every red light for traffic to pass, but crosses the street when the light turns green, then they may safely make their way to the grocery store.