Much less than half the time. Remember, if Harry1 uses his time turner, he creates Universe2 with Harry2=Harry1_6_hours_ago. But in 6 hours, Harry2 will use his time turner, creating Universe3 with Harry3...

So IF there is a stable time loop of any kind, most universes will have that loop.

This raises the interesting prospect of stable sets of universes, with 6-hour histories A, B, and C. If a Harry that experiences A uses his time turner and does B, and a Harry experiencing B does C, and Harry experiencing C does A, then most copies of Harry will experience an inconsistent time loop, and it will seem like he actually went back and changed time.

If time loops are generally observed to be consistent, then this is evidence that single-state equilibria are much more probable than multiple-state equilibria.