In some strategic games, thinking ahead about other players reasoning can lead to better predictions about what they will do. In other games, infinitely iterated reasoning ultimately prescribes random play. In an online experiment of strategic thinking in groups, we tested participants in a game with the formal structure of a random game, but the superficial structure of a game that rewards iterated reasoning. We found that participants conformed to the superficial structure of the game, and earned more than they would have by playing randomly. We estimated how many steps participants thought ahead in the game and matched it to previous findings in iterated reasoning. We also discovered implicit coordination at the group level. Participants unexpectedly matched their degree of iterated thinking to each other.