This study utilized unplugged computational thinking learning material named Robot City as the instructional material. The board game corresponds to structural programming, including sequential structure, conditional structure, repetitive structure, and the modeling concept of calling a procedure in programming languages. According to the different task assignment methods, the aim of playing the board game is to help instruct the seventh-grade students in computational thinking, and to explore its impact on students' learning achievements of computational thinking and the behavioral patterns of computational participation. The results revealed that the learning achievements of the students who worked together to solve the clear-ended task objectives were significantly higher than those of the students who cooperated within their groups to solve the open-ended competitive tasks. When the target task is not gained in advance, the students had to compete with other groups and vie for their target task, resulting in students' logical thinking constantly changing and being interrupted. From the behavioral pattern analysis, it was found that the students continued to discuss the problems during the game. The pattern of collaborative analysis was iterative itself, indicating that the board game can deepen students' interaction and enhance their higher level thinking. The results also showed that collaborative creation was observed (RO) by others, proving that the game can increase students' desire to learn, and thus improve their learning achievement.