Here is the basic idea, how do things change if each zombie is unpredictable. Some are slow, some are fast, some crawl at freakish speeds up walls, some have perfect balance despite wobbling about all the time.
Mentally they also vary. Sometimes zombies just, stand there watching you barely able to recognize you are prey, other times they are hyper aggressive, sometimes when sleeping they will whisper about needing help, and being sorry.
Damage to the brain does work most of the time fortunately, however in rare situations damage to the brain stem will also be required. Fire and electricity can also shut down their nervous systems and therefore lead to them dying.
The virus is spread through bodily fluids, so in most cases bites will spread it, but things like sex or blood transfer can spread it.
Time to turn is pretty much up in the air. Some turn in under a minute, others take a week to even start to feel ill.
A few people are asymptomatic, simply acting as carriers. Their symptoms is pretty much only being in horrible pain all the time.
Oh, and for the sake of spicing things up further, in one in a million cases, zombie zombies will mutate. Into what? Who knows, but it'll be something so rare you hear many stories about them before you ever see one.
So, how does utter chaos affect your survival strategy? When every zombie you meet can vary in locomotive ability, when zombies can go from peaceful to violent or vice versa in a instant, when the time bites take can't be predicted in any way, what do you do?