Could cooperation among strangers be facilitated by adaptations that use sparse information to accurately predict cooperative behaviour? We hypothesise that predictions are influenced by beliefs, descriptions, appearance and behavioural history available for first and second impressions. We also hypothesise that predictions improve when more information is available. We conducted a two-part study. First, we recorded thin-slice videos of university students just before their choices in a repeated Prisoner's Dilemma with matched partners. Second, a worldwide sample of raters evaluated each player using videos, photos, only gender labels or neither images nor labels. Raters guessed players’ first-round Prisoner's Dilemma choices and then their second-round choices after reviewing first-round behavioural histories. Our design allows us to investigate incremental effects of gender, appearance and behavioural history gleaned during first and second impressions. Predictions become more accurate and better-than-chance when gender, appearance or behavioural history is added. However, these effects are not incrementally cumulative. Predictions from treatments showing player appearance were no more accurate than those from treatments revealing gender labels and predictions from videos were no more accurate than those from photos. These results demonstrate how people accurately predict cooperation under sparse information conditions, helping explain why conditional cooperation is common among strangers.