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Doyne Farmer illustrates how understanding complex systems can help predict seemingly random events, such as outcomes in roulette. By applying physics principles to the roulette game, he and his team constructed wearable computers that allowed them to gain an edge over the casino, achieving around a 20% advantage. This computer played a vital role in measuring the ball's velocity and predicting its landing spot. Farmer's experience in predicting outcomes has informed his subsequent work in economics and climate science, demonstrating that chaos and complexity can offer insights beyond traditional methods.