This paper presents a study that analyzes the effects of robots’ gaze hints on children's performance in a card-matching game. We conducted a within-subjects study, in which children played a card game “Memory” in the presence of a robot tutor in two sessions. In one session, the robot gave hints to help the child find matching cards by looking at the correct match and, in the other session, the robot only looked at the child and did not give them any help. Our findings show that the use of gaze hints (help condition) made the matching task significantly easier and that children used a significantly fewer number of tries than without help. This study provides guidelines on how to design interactive behaviors for robots taking the role of tutors to elicit help-seeking behavior in children.