According to the diversity-beats-ability theorem, groups of diverse problem solvers can outperform groups of high-ability problem solvers (Hong and Page 2004). This striking claim about the power of cognitive diversity is highly influential within and outside academia, from democratic theory to management of teams in professional organizations. Our replication and analysis of the models used by Hong and Page suggests, however, that both the binary string model and its one-dimensional variant are inadequate for exploring the trade-off between cognitive diversity and ability. Diversity may sometimes beat ability, but the models fail to provide reliable evidence of if and when it does so. We suggest ways in which these important model templates can be improved.