You are right. To be more precise, we use the van Oorschot and Weiner Method of kangaroos.
I imagined if you use Gaudry Schost method (re-place a kangaroo as soon as you hit a distinguished point) that you could have an advantage.
Especially when using tame points in the range target bit range and wild points where one or many might not be in the target bit-range (e.g. when experimenting division)