Social interactions are the most important part of a human’s life. Cooperation and competition interactions are required more cognitive engagement between participants. In this study, an EEG hyperscanning study was conducted while nine pairs of recruited participants performed a card game, slapjack. The experiment was divided into three kinds of playing modes, single-player, cooperative, and competitive modes. In addition to behavioral performance estimation, the inter-brain synchrony between subjects was quantified by Phase Locking Value (PLV). Results showed that subjects' reaction time in response to targets was the longest in the single-player mode and the shortest in the competitive mode. Additionally, the inter-brain EEG synchrony changed as the playing mode changed. Stronger inter-brain coupling between subjects has been found in cooperative and competitive modes compared to a single-player mode. The inter-brain synchrony reduced as the roles of subjects switched from a partner to a competitor.