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Science Frontiers ONLINE No. 128: MAR-APR 2000 |
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Two games played with coins illustrate the effect. One game employs a weighted coin such that the probability of winning is much less than 50%. If played alone, your capital decreases steadily in a rather smooth curve, with a small win now and then but many small losses. The second game requires two weighted coins and is also a losing proposition by itself. Here, though, the graph of your assets vs. the number of games played is a sawtooth. There are sharp increases and downturns, but with an average downward trend.
Switching between the two games in a random manner has the effect of locking in a win before the next loss comes along. It's a ratchet effect. Your overall capital will rise, at least it does according to the equations, though your intuition cannot help but doubt it. No wonder this Is called Parrondo's paradox!
(Harmer, Gregory P., and Abbott, Derek; "Losing Strategies Can Win by Farrondo's Paradox," Nature, 402:864, 1999. Anonymous; "Losing to Win," Science News, 157:47, 2000.)
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