We report the results of a game-theoretic experiment with human players who solve problems of increasing complexity by cooperating in groups of increasing size. Our experimental environment is set up to make it complicated for players to use rational calculation for making the cooperative decisions. This environment is directly translated into a computer simulation, from which we extract the collaboration strategy that leads to the maximal attainable score. Based on this, we measure the error that players make when estimating the benefits of collaboration, and find that humans massively underestimate these benefits when facing easy problems or working alone or in small groups. In contrast, when confronting hard problems or collaborating in large groups, humans accurately judge the best level of collaboration and easily achieve the maximal score. Our findings are independent on groups' composition and players' personal traits. We interpret them as varying degrees of usefulness of social heuristics, which seems to depend on the size of the involved group and the complexity of the situation.