Fig. 3.

Sharp transitions at relatively low-capacity values and close to square root sampling behavior for large capacity are observed for a broad range of parameters of the prior distribution. (A) Critical capacity decreases very steeply to low values (∼10) as a function of the prior mean probability $\alpha /\left(\alpha +\beta \right)$. (B) Exponents decrease as a function of the prior mean probability and cluster around 1/2. The exponents are obtained from log-log linear regression fits of the optimal number of alternatives samples vs. capacity $\left(M\propto C^{exponent}\right)$ for $C$ values ranging from 1,000 to 2,000 in steps of 1. Shaded areas correspond to 95% CIs. In both panels, points are obtained by theoretical predictions from SI Appendix, Eq. 9. For prior mean probabilities smaller than or equal to 1/2, we fix $\alpha =1$ while $\beta$ varies from 1 to 20 in steps of 1, and for values larger than 1/2, we fix $\beta =1$ while $\alpha$ varies from 1 to 20.