This paper reports on how two different flexible student grouping strategies in a mobile-assisted Chinese character learning game affect the players' collaborative patterns. The game application assigns each student a Chinese character component on their smartphones. The students are required to form groups to assemble eligible Chinese characters using the components that the group members possess. Fifteen Primary 3 (3rd grade) students were involved in the study. The game process data and the transcriptions of focus group interviews were qualitatively analyzed in order to investigate the dynamics of student collaboration and competition during the games. The study aims to explore the patterns of social interactions during the activities, especially the varied impacts of the two different grouping rules (allowing versus not allowing each student to join more than one group at one time) on the students' game behaviors and their learning gains.