Figure A1.

The larger the difference between the means the better the performance. $\mathbb{E}\left(\left[A_1|\mathbf{s}\right]\right)$ is computed for an increasing value ${({\mu }_1-{\mu }_2)}^2$. Every point corresponds to the average value from 10,000 simulations and red lines correspond to the analytic solutions. From the darkest to the lightest gray, triplets $\{{\mu }_1,{\mu }_2,\sigma \}$ are as follows: $\{0,0.1,1\}$, $\{0,0.25,1\}$, $\{0,0.5,1\}$, $\{0,1,1\}$ and $\{0,1,0.5\}$.