This is a rather light post, mainly intended as a walk through of how to build a monster in NGR, in this case the lower forms of undead, a walking corpse out to (potentially) cause murder and mayhem.
So the first thing to do is treat it like a completely average human. All attributes are 10. You might ask yourself (you know what, no. You are a strawman in this case so you DO ask yourself) but why does a skeleton or zombie have a health score? its a corpse. True, but in this case it would be the health of its magic or other means holding it together. While it may be immune to human poisons and diseases that doesn't mean it doesn't have its own forms of maladies that follow the same molds.
Snake venom is unlikely to poison a shambling corpse, but throwing salt upon it would impact it in the same way. Its health score lets you know how much salt it can handle. Magical or fungal rots may impact it similar to a disease, destroying its form and binding magics.
But what about its intelligence you ask in a forced manner, as you are a strawman I have constructed to highlight my points. Zombies are mindless. I answer to that, they can be. If you want them to be dull, give them an intelligence of 1. They could also have any level of malignant (or even non malignant) intelligence. I was always a fan of the skeleton in the last unicorn who held conversations and had wants and goals (to remember the taste of wine). The will score of the undead (their courage in some respects) can likewise be supernatural (if they are fearless killers) or even fairly low and cowardly (like the undead in Army of Darkness who break and run at times).
How do you differentiate skeletons and zombies? I wouldn't, they are all skeletons. A zombie is just a skeleton wearing meat armour. If the skeleton is covered in desiccated withered flesh (like a mummy or bog mummy) I would count it as leather armour and a leather cap. A fresh corpse would also have its "armour" use the bulky tag, giving it extra padding against blunt weapons.
In terms of special resistances and weaknesses:
-Fire is a big one. Fire dealing double damage against undead is pretty standard, even skeletons can have their binding magic consumed in flames. As with all rules, this can be broken for effect (I am a fan of hellfire creating zombies that scream in pain and only animate while the fire burns).
-Salt poisoning undead if thrown upon them (along with any other substance that fits in your setting) is a good one.
-Sunlight is something that is a good idea to burn undead as a general rule. The base necromancy spell has it deal 1 damage per round, though divine undead do not have this limit.
- If shooting the brain/heart isn't a special way to destroy the undead, consider making all piercing weapons gain the minor tag (ie, they only deal 1 damage on non-critical hits).
Finally, for any undead summoned by a wizard rather than a priest remember than the undead can be captured and reverse engineered with the SAGE wizard ability, allowing the PC's to learn the spell that raised the dead (And craft dispell potions against it).
In terms of what do you need to think of when an unexpected encounter with a zombie turns up?
It has standard 10 for stats, takes double damage from fire and counts as wearing padded armour and a cap due to its meat. If a wizard wants to capture one it has the basic necromancy spell template.
Cthulhu Fhtagn! Cruz Edition.
5 hours ago