Who's Counting: Winning at Losing Games

So far, so what? Game S is simple and results in steady movement down the staircase to the bottom, and game C is complicated and also results in steady movement down the staircase to the bottom. The fascinating discovery of Parrondo is that if you play these two games in succession in random order (keeping your place on the staircase as you switch between games), you will steadily ascend to the top of the staircase.

Connection to Dot-Com Valuations?

Alternatively, if you play two games of S followed by two games of C followed by two games of S and so on, all the while keeping your place on the staircase as you switch between games, you will also steadily rise to the top of the staircase. (You might want to look up M.C. Escher’s paradoxical drawing, Ascending and Descending, for a nice visual analog to Parrondo’s paradox.)

Standard stock market investments cannot be modeled by games of this type, but variations of these games might conceivably give rise to counterintuitive investment strategies. Although a much more complex phenomenon, the ever-increasing valuations of some dot-coms with continuous losses may not be as absurd as they seem. Perhaps they’ll one day be referred to as Parrondo profits.

Professor of mathematics at Temple University, John Allen Paulos is the author of several books, including A Mathematician Reads the Newspaper and, most recently, I Think, Therefore I Laugh. His “Who’s Counting?” column on ABCNEWS.com appears on the first day of every month.

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