For me they usually pick the same card twice in a row. For example they'll ask me to play to win a shirt and the answer ends up being heart, then when we play to get them to move in the answer is heart again. But I've noticed if I get the answer right then they change it. Don't know if this is actually a thing but its worked with the 6 campsite villagers I got. Also if you lose a few times sometimes they say something like I felt bad for rejecting you last time and move in without playing a game