Do anthropic arguments really work?

The anthropic explanation for the peculiarly small observed value of the cosmological constant $\Lambda_{\rm obs}$ argues that this value promotes the formation of stars, planets, and ultimately of observers such as ourselves. I show that a recent analytic model of cosmic star formation predicts that although $\Lambda_{\rm obs}$ maximises the overall efficiency of star formation in the universe, the probability of generating observers peaks at $\sim400-500 \, \Lambda_{\rm obs}$. These preliminary results suggest that an immediate connection between star formation efficiency and observers' generation is not straightforward, and highlight the subtleties involved with the application of anthropic reasoning.