But, they are not very clear on the jumps and especially the average distance of the jumps.
As the wild are on a shorter range, may be steps have to be different than tame's one (not yet tested).
I also didn't coded a stop and retry after a certain number of jump (sqrt(n) ?), i let the algorithm continue outside the range, so it may loose the symmetry...
You cannot loose the symmetry.
Are you sure that algorithm goes outside the range so often? I don't think so, with this kind of jump (back and forth), I would use longer jumps, because you in sqrt(n) shouldn't go outside of the interval (on average) like the classic version.
I suppose the main problem is the loops (a single kangaroo with itself)