Speaking of Shadowrun...
This happened in one of the Shadowrun iterations (might have been houseruled):
In Shadowrun, if you had enough initiative boost (through cyberware or magic) you got multiple actions during the same combat turn. In this particular instance of the initiative rules, first everybody acted in initiative order, then those with two or more actions acted again in the same order, then those with three or more yet again, etc...
However your move was by combat turn, so you had to split your movement among your actions.
So, my character got chased by a particularly vicious overgrown dog.
* I had twice the movement rate of the dog.
* I had enough initiative boost to get four actions in the turn as opposed to the dog's one.
* I had a head start of a few meters.
On my first action, I started running - but since I got four actions that turn, I could only move 1/4 of my movement rate.
On its first action, the dog got to run its full movement, since it only had a single action that turn. Now, its movement was half mine, but that easily beat the quarter of a move I had gotten to use, plus my head start. Cue nasty bite and drag-down...
So, because the dog reacted much slower, it managed to catch up...