In case when three balls are in the rest after the collision, their initial energy is transfer to the top one. The height of the throw must be (is) greater then before - (when we have constant mass ratio=2 and balls are in multicollisions). It can be shown by the applet.

Now, I would like to see if my calculation gives the same height as applet.

This state is for k=1. But which mass ratio is necessary for the same state in case of k<1.

I prepare mathematical solution for mass ratio dependence on coefficient of restitution.

It can be next step in this applet.