## 3 Experimental Studies and Results
### Experiment 2: The Robot Helps Humans in a Game  
To further evaluate the influence of social gaze, we tested the model in a situation where the robot was helping a human solve a tangram puzzle. The goal of the experiment was to evaluate the influence of oriented gestures with directed gaze on a human (\(n=31\), \(12\) females, mean age of \(27.4\)). The task of the participants was to arrange the elements within a given contour on a white sheet. During the experiment, the participant was to complete several figures, including a parallelogram, a fish, a triangle, and a ship. For each task, the game elements were placed in front of the participant on the left and right sides of the playing field. Two paired elements (two large triangles and two small triangles) were always placed on different sides of the playing field. The robot helped the human, indicating in speech which game element to take and where to place it (Figure 4). In half of the tasks, the robot used oriented communicative actions (pointing hand gestures, head movements, and gaze) to indicate the required game element, and then the correct position to place it (Condition 1). For the paired elements, the left or right element was chosen randomly. In the other half of the tasks, the robot used non-oriented, symmetric gestures while providing the same speech instruction (Condition 2). In the first condition, the direction of the robot's gaze was considered an indication. In its speech instructions, the robot always referred to an element by its shape and size, not by color. So, when the robot named paired elements, the reference was ambiguous and could indicate the element on either the right or the left side of the playing field.  
Figure 4: Robot refers to the game element with speech (with ambiguous reference) or with speech and gesture.  
Results and a Preliminary Discussion  
According to the results of the experiment, most of the participants (64.5%) significantly (\(p<0.01\), Mann-Whitney U-test) preferred the robot pointing to the tangram elements and their locations with eyes and hands. At the same time, the difference between both experimental conditions was not obvious to the players; only half of them (15 people; 48.4% of the total group) noticed the difference between the robot's performance with and without the pointing gestures and gaze. Therefore, the evaluation of the robot can again be implicit because the participants did not distinguish between the two experimental conditions verbally, but simultaneously preferred the robot that indicated the necessary element and its location in the contour with the help of its head, eyes, and hand movements. This experiment is described in more detail elsewhere [37].  
The results clearly show the importance of directional gaze for communication between a robot and a user. Directional gaze is perceived as a reflection of the robot's internal state. In the speech instructions, the robot prompts the user, and gaze is used to provide the reference for this prompt. It is this correspondence of mimicked expression to the robot's internal intention that is positively perceived by the subjects; however, it occurs at the implicit level.