<p>Threshold public good games with binary contributions and without rebates or refunds embody both the incentive to free-ride and the risks of non-provision and wasted contributions. We investigate the implications of heterogeneity in strategic sophistication in this context, focusing on the cognitive hierarchy model. We find that the contribution of the initial strategic level (i.e., level-1) is crucial for the provision of the public good. We furthermore demonstrate that a higher average sophistication among a group of players does not necessarily lead to a higher probability of provision. Finally, we find that it would be easier to provide the public good for larger groups if the average sophistication is lower.</p>