The left panel shows the case when \(p<1/2\) and the regime threshold \(\theta^*\) is monotone decreasing in the precision \(\alpha\). The right panel shows the case when \(p>1/2\) so that \(\theta^*\) is non-monotone in \(\alpha\). In both cases, for low enough precision \((\alpha<\underline{\alpha})\) the regime threshold coincides with the Morris-Shin benchmark \(\theta^*_{\text{MS}}=1-p\) while for high enough \(\alpha\) the threshold is less than \(1-p\).