Yeah, I'd guess there's only one ray trace bounce used in the render settings there...?

You'd probably need at least three bounces, to get a half decent result there... i.e. the reflection of the ball in the floor, reflected in the ball, reflected in the floor again... if I've said it right ;)

How many bounces you'd get away with will depend how big / how much resolution your render has...

i.e. is a reflection of a reflection, of a reflection, of a refection going to be visible, at the resolution you're rendering to? In which case, I count four bounces would be needed?

Three bounces is usually enough for most situations, I find... unless you're rendering a closeup, or at high resolution / image size (and expect people to zoom).