We consider a service robot that offers chocolate treats to people passing in its proximity: it has the capability of predicting in advance a person's intention to interact, and to actuate an "offering" gesture, subtly extending the tray of chocolates towards a given target. We run the system for more than 5 hours across 3 days and two different crowded public locations; the system implements three possible behaviors that are randomly toggled every few minutes: passive (e.g. never performing the offering gesture); or active, triggered by either a naive distance-based rule, or a smart approach that relies on various behavioral cues of the user. We collect a real-world dataset that includes information on 1777 users with several spontaneous human-robot interactions and study the influence of robot actions on people's behavior. Our comprehensive analysis suggests that users are more prone to engage with the robot when it proactively starts the interaction. We release the dataset and provide insights to make our work reproducible for the community. Also, we report qualitative observations collected during the acquisition campaign and identify future challenges and research directions in the domain of social human-robot interaction.