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Contrarian behavior is a kind of self-organization in complex adaptive systems (CASs). Here we report the existence of a transition point in a model resource-allocation CAS with contrarian behavior by using human experiments, computer simulations, and theoretical analysis. The resource ratio and system predictability serve as the tuning parameter and order parameter, respectively. The transition point helps to reveal the positive or negative role of contrarian behavior. This finding is in contrast to the common belief that contrarian behavior always has a positive role in resource allocation, say, stabilizing resource allocation by shrinking the redundancy or the lack of resources. It is further shown that resource allocation can be optimized at the transition point by adding an appropriate size of contrarians. This work is also expected to be of value to some other fields ranging from management and social science to ecology and evolution. [ABSTRACT FROM AUTHOR]