Interacting with other individuals to negotiate how we want distribution of resources (e.g. money, time) to be made is an important part of our social life. Considering that not all of our requests from others are always granted, the outcomes of such social interactions are, by their nature, probabilistic and therefore, risky. While risk-perception has been well studied in non-social contexts, its computational mechanisms in social interactions remains unknown. Here, we investigated value computations underlying how people make unfair, fair or hyper-fair Ultimatum offers to others who accepted or rejected these offers probabilistically in relation to how they valued them. We showed that people adjust their risk-preferences dynamically in social interactions, and these can be predicted from a weighted linear combination of ones degree of prosociality (i.e. Social Value Orientation (SVO)), inference about the opponents SVO─including ones uncertainty in it; and relative prosociality ( SVO) interacting with ones risk attitude in the value-based domain. In tandem, our results provide the first evidence to suggest that dynamic risk taking is a cardinal element of social interactions.