Cooperative communications using the Alamouti space-time block code (STBC) has been mentioned intensively. However, to our knowledge, an in-depth error performance analysis for a space-time coded cooperative communications system, where each node acts as both a source node and a relay node for its partner, has not been reported. Intuitively, cooperative communications would not always be better than direct transmission, but only under certain conditions. This paper first derives an exact performance analysis of the Alamouti STBC cooperative communications for a Binary Phase Shift Keying (BPSK) constellation, which could be extended to a higher density modulation scheme. This mathematical analysis facilitates the source nodes to decide pro-actively whether cooperative communications or direct transmission should be used, depending on the channel conditions between the sources themselves and the channel conditions between the sources and the destination. The anterior knowledge of which transmission mode should be used before nodes actually engage in cooperation is useful to keep system operations as simple as possible, while assuring that cooperative communications is definitely beneficial once it is in place. The analytical error performances are then verified by simulations and in-depth discussions on the simulation results are presented.