I don't think you're correct that the hare can skip past the tortoise indefinitely. Certainly, I cannot find such a loop.<p>On the question of whether it is a constant factor optimization, though, it rather depends on the relative costs of following a link versus the bookkeeping accounting for steps taken. Empirically tested in a simple program, teleporting turtle (TT) is slower than tortoise and hare (TH) when simply following linked lists in adjacently laid out in memory. When retrieving a link is made more costly, TT pulls ahead. I cannot find any scenario where TT follows more links than TH, only less or equal.<p>So it seems that following links is the thing that is being optimized for, which makes sense for finding loops in PRNGs and similar problems: you want to optimize to reduce the number of links taken. As I explain in a different message, because each iteration of TH is so much more costly than TT, TT can't really lose.