Social presence, or the subjective experience of being present with another existing person, varies with the interaction medium. In general, social presence research has mainly focused on uni-directional aspects of each exchanged message, not on bidirectional interactions. Our primary purpose is to introduce such bidirectional evaluation by quantifying the degree of social presence with a few statistical measures. To this end, we developed a software called “TypeTrace” that records all keystrokes of online chat interactants and reenacts their typing actions and analyzed the results from different chat conditions, mainly focusing on the characterization of bi-directional interactions. We also compared the chat interaction patterns with the patterns from phone call datasets to investigate the difference of live communication in different media. The hypothesis of the experiment was that either richness or concurrency of communication is important for organizing social presence. Richness is defined by the variety of information at a time in communication and the concurrency is the number of temporal thread being processed at the same time. Our results show that when we merely increase the richness of information by presenting the typing process, the cognition of others' presence does not significantly increase. However, when the information concurrency is augmented by introducing the transmission of realtime text, we found that the transfer entropy between the interactants becomes considerably higher, and the social presence and emotional arousal, intimacy increased. High transfer entropy was also observed in the phone call dataset. This result shows that the mere augmentation of information richness does not necessarily lead to increased social presence, and concurrent communication is another critical factor for fostering vivid conversation in digital environments.