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No. 128: MAR-APR 2000

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How to Win by Loosing (twice)

It's all exceedingly counterintuitive. If you switch randomly between two games of chance, each of which is guaranteed to empty your pockets if played separately, you can actually win. This phenomenon can be proved mathematically, but we will not inflict this upon our readers, even if we understood it.

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.)

From Science Frontiers #128, MAR-APR 2000. � 1997 William R. Corliss

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