# Parrondo's paradox with a three-sided coin

phys.org | 7/11/2018 | Staff
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Physicists have demonstrated that Parrondo's paradox—an apparent paradox in which two losing strategies combine to make a winning strategy—can emerge as a coin game with a single coin in the quantum realm, but only when the coin has three states (heads, tails, and a side) rather than the conventional two.

In general, Parrondo's paradox, also called a Parrondo's game, only works when the two losing strategies are somehow dependent on each other and are combined in such a way as to change the conditions that lead to them losing. Ever since it was discovered by physicist Juan Parrondo in 1996, Parrondo's paradox has found applications in engineering, finance, and evolutionary biology, among other areas.

#### Ways - Parrondo - Game - Wikipedia - Entry

One of the simplest ways to implement a Parrondo's game is described in this Wikipedia entry. Suppose you have \$100, and you can choose to play any combination of two games. In the first game, you lose \$1 every time you play. In the second game, you win \$3 if you have an even number of dollars left, and you lose \$5 if you have an odd number of dollars left. If you only play the first game or only play the second game, you will eventually lose all your money, so playing each game by itself is a losing strategy. However, if you alternate between the two games, starting with the second game, then you will win \$2 for every two games you play, so the two losing strategies can combine into a winning strategy.

In the new study, physicists Jishnu Rajendran and Colin Benjamin at the National Institute of Science Education and Research, HBNI, in India, have demonstrated a Parrondo's game using a three-state coin, which they represent with a qutrit, a quantum system with three states.

#### Parrondo - Games - Context - Benjamin

"Parrondo's games have been seen in a classical context," Benjamin told...