Left of L* you leave growth on the table. Right of the red line the quadratic drag has eaten the whole linear edge, and you lose money with the edge still in your favour. The curve drops the −¼E[x⁴] term, so it flatters high L — realised growth sits below it once levered volatility gets large.

A strict upper bound on geometric growth over all constant-leverage rules. Sizing moves you along the curve; only a higher Sharpe moves you up it.

With auto-reset on, each run plays to the horizon or to ruin and then restarts, accumulating the distribution above. Red bars ended below the starting stake.