What is Parrondo's Paradox?

The magical craps system featured in GOD DOESN’T SHOOT CRAPS is based on a recent breakthrough in advanced mathematics and physics called “Parrondo’s Paradox.”

Developed by Professor Juan M. R. Parrondo of the Complutense University of Madrid, the theory states that two “losing” games can be combined into a single winning outcome.


Simply stated, it is accomplished through the use of ratchets – the familiar saw-toothed mechanical device used in elevators and self-winding wristwatches. A ratchet is used to allow movement in one direction but to prevent it in another. Every child, for example, knows that by shaking a can of mixed nuts you can get the heavier Brazil nuts to move to the top because the smaller nuts help “ratchet” their movement upward.

Dr. Parrondo discovered that the same principle can be applied to gambling games. To prove it, he created two coin-flipping games that were designed to lose by virtue of using weighted coins.

When you play these games separately, your bankroll will gradually diminish to zero. But if you alternate or “flash” between the two games, the occasional winnings of one game will be trapped by the ratchets of the second game. In other words, you can lose at both games and still emerge an overall winner!

Can this theory be applied to casino games? Dr. Parrondo says no. But GOD DOESN’T SHOOT CRAPS says yes! And the book-within-a-book included in the novel (“WIN BY LOSING”) shows exactly how it’s done.

But “Parrondo’s Paradox” has implications that go far beyond casino gambling. The theory can be used to explain why some investors make money in a falling stock market. Why random events in the “primordial soup” led to the origins of life. How the chaotic movements of quantum particles at the subatomic level combine to create the logical order of the universe. Even how Bill Clinton’s poll numbers seemed to go higher the more he misbehaved!

To learn more about “Parrondo’s Paradox,” click on the links below to see articles in The New York Times, Nature, and Science News.


NEW YORK TIMES: "Paradox in Game Theory: Losing Strategy That Wins"

NATURE: "Good news for losers"

SCIENCE NEWS: "Losing to Win"