Social relationships are known to shape human behavior, yet when and how social ties influence strategic cognition remains unclear. We adopt a dual-measure approach that combines observed gameplay behavior with elicitation of partner-specific beliefs at each decision point, allowing us to examine how social ties shape both decisions and predictions across interaction structures. Dyads classified as having no ties, weak ties, or strong ties played three canonical economic games: the Dictator Game, Ultimatum Game, and Centipede Game, while also making predictions about their partner's actions. Using a mixed design that held partners constant across games while varying social distance between dyads, we examined how relational proximity affected the alignment between behavior and partner-specific beliefs. Across two norm-saturated games (Dictator and Ultimatum), neither offers nor belief calibration differed reliably by social distance. In contrast, in the sequential Centipede Game, where outcomes depend on anticipating a specific partner's future actions, strong-tie dyads both cooperated longer and expected later termination than no-tie dyads, with beliefs and behavior shifting in parallel. These results indicate that social ties become strategically relevant when the interaction structure makes partner-specific accountability cognitively necessary, but not when behavior is governed primarily by shared norms or institutional constraints. The findings provide a structural account of when relational knowledge enters strategic cognition and help reconcile mixed results in prior work on social distance in economic games.