# The Parrondo Paradox

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Parrondo's paradox is a surprising statement about the combination of certain probabilistic events. We start with two games A and B that, individually, are losing games. But we define game C as follows: Flip a fair coin and play A if the coin comes up heads and B if it comes up tails. Then C can be a winning game.

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Contributed by: Stan Wagon (July 2011)

(Macalester College)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In the Demonstration, the lengths of the games are 500 flips and the results are averaged over 100 repetitions. Snapshots 1 and 2 show that games A and B are losing games. Snapshot 3 shows that the combination ABBAB is a winning game.

For more information on the paradox, which arose from some considerations of physics, see Parrondo's paradox or the *MathWorld* Parrondo's paradox (Wolfram *MathWorld*) entry. For detailed analysis of the games discussed here, see [1].

Reference

[1] D. Velleman and S. Wagon, "Parrondo's Paradox," *Mathematica in Education and Research*, 9(3–4), 2001 pp. 85–90.

## Permanent Citation