This paper draws a parallel between creative cognition and a multi-armed bandit problem involving learning from experience in an uncertain environment. Special emphasis is put on the optimal sequencing of divergent and convergent behavior by showing that divergence must be inhibited at one point to converge toward creative behavior so that excessive divergence is counterproductive. We test this hypothesis with a behavioral experiment, using measures of individual divergence and convergence components of creative potential in high school students. Results confirmed that a mix of divergence and convergence predicted high performance in a bandit task but not in a purely random task or in a simple repetitive task. These predictions are maintained after controlling for sex, personality, incentives, and other factors. As hypothesized, creative cognition was necessary for high performance under the appropriate conditions. However, it was not necessary to get high grades in a traditional school system.