Identifying the evolutionary mechanisms responsible for one-shot cooperation among humans remains a highly contentious puzzle. Repeated interactions provide a canonical, if paradoxical, explanation (Haley and Fessler, 2005; Hagen and Hammerstein, 2006) for one-shot settings, with the key mechanism centred on ancestral uncertainty about whether a game is one-shot or repeated (Jagau and van Veelen, 2017). Group competition (e.g. Choi and Bowles, 2007) provides a different explanation with exactly the opposite status, heterodox but intuitively appealing. We show that neither mechanism in isolation reliably supports cooperation when actions vary continuously. Ambiguous reciprocity is a strategy, generally ruled out in models of reciprocal altruism, that completely undermines cooperation in repeated interactions and by extension one-shot settings. Group competition is a feeble mechanism because of cancellation effects at the group level (Akdeniz and van Veelen, 2020), and because groups tend to be similar under relevant conditions. Although repeated interactions and group competition do not support cooperation by themselves, combining them frequently triggers powerful synergies because group competition stabilises cooperative strategies against the corrosive effect of ambiguous reciprocity. With both mechanisms at work, evolved strategies often consist of cooperative reciprocity with ingroup partners and uncooperative reciprocity with outgroup partners. Results from a one-shot behavioural experiment we conducted in Papua New Guinea fit exactly this pattern. They thus indicate neither an evolutionary history of repeated interactions without group competition nor a history of group competition without repeated interactions. Instead, our results are only consistent with social motives that evolved under the combined influence of the two mechanisms acting together.