Adult, healthy, and well fed survivors roll 2d6. If they're weaker, only 1d6
Add +1d6 if the survivor is wielding a proper zombie killing weapon, like an axe or baseball bat.
Add +1d8 if the survivor is wielding a badass zombie killing weapon, like a sawn-off or chainsaw.
Every zombie in the group rolls 1d6. Special infected, like acid blood or Tanks from L4D, roll 1d8.
Roll all dice simultaneously. Highest number on a single dice wins. In the event of a tie, the highest number of dice rolled total wins. If the survivor wins, they get away. If the zombies win, they get in a bite or you take one wound or lose a life or whatever.
If you can't find enough dice to roll for the zombie's dice pool or if its statistically ludicrous for the survivor to win, they just die. Huge groups of zombies just rip you apart.
Note: Yes, it's intentional that you can't be bitten by a group of zombies if you get a lucky roll of 7 or 8 on your big weapon die. This is to represent your guy running through a crowd of zombies blasting and sawing them all to pieces without getting bitten. Yes, it's also intentional that most rolls will end in ties of 6, meaning that the zombies will always succeed if there is more then three of them at once.
Example: Rodney gets cornered by a group of undead, who press at him from all sides against a wall. There are 5 zombies. They roll 5, 5, 4, 3, and 2. Rodney swings his bat and gets a 6, 3, and 2. He gets away. That was a very lucky escape, Rodney.
Also if the survivor has a really shitty weapon like a knife or rifle in close range they roll a 1d4 for their weapon instead. Same for really shitty zombies like crawlers or weak ass skeletal zombies, they just add +1d4 to the hoard's dice; still adds to the hoard's deadliness but they're much easier to escape from in small numbers. Also this combat system has nothing to do with actually running around and shooting zombies or fighting zombies in a big army against a shield wall of survivors or anything cool like that, it's just a little grapple rule.