explosion is obtained or not, is little affected by the stochasticity of the explosion geometry.

In fact, the right panel of Figure \[fig2\] shows the evolution of the average shock radius for our 1D (blue line), 2D (green lines), and 3D (red lines) models, respectively. Before the onset of shock revival (before 100 ms after bounce), the evolution of the shock is all similar to that of the 1D model (blue line). After that, our results show that the shock expansion is systematically more energetic in 2D (green lines) than in 3D (red lines). This feature is qualitatively consistent with @takiwaki12, and also with @hanke13 who recently reported 2D vs. 3D comparison based on a single 3D model but employing more detailed neutrino transport than ours. Due to our lack of necessary computational resources, our 3D models should be terminated typically before $t_{\rm end} \lesssim 300$ ms postbounce (e.g., in Table 1), but we expect them to produce explosions subsequently, seeing a continuous shock expansion out to a radius of 500 km in 3D (and 700 km in 2D). Given the same numerical resolution (e.g., model series 3D-L in Table 1), the average shock radii in this study is smaller 