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Opportunistic cooperation (OC) dynamically switches between a cooperative mode (CM, using direct and relayed links) and a non-cooperative mode (NM, using only the direct link). In this letter, we consider OC in amplify-and-forward (AF) relaying systems where a best relay is selected as an active relay if CM is selected. The OC is shown to have the same full diversity order as the CM. In terms of asymptotic outage probability, we show that the power gain (sometimes also referred to coding gain) achieved from using the OC compared to the CM is -10/(K+1) log10 (1-((2R)/(2R +1))K+1) dB where R is the data rate used for outage threshold. The result says that the power gain is always positive (in dB) and it increases when the data rate increases or the number of relays decreases. Numerical results are provided to verify the analysis and to give insights on the outage performance of the OC.