While I think the classic "standard first combat" for D&D tends to be against goblins, or sometimes kobolds, for whatever reason, I tend to prefer using undead creatures. Maybe it's just because I loved Wrath of the Lich King (World of Warcraft's second expansion,) but there's something really satisfying about fighting the undead. I guess in part it's pretty guilt-free (hell, you might be doing them a favor) and also because I think that they make for cool monsters that imply some larger, supernatural threat to deal with later.
There are lots of undead monsters at all challenge ratings, but I think two of the most versatile and ubiquitous are skeletons and zombies. I'll leave the former for another day (even though I think I actually like them more as monsters) so we can focus on these Romero-esque shamblers.
Let's break the zombie down: How do we use this thing?
Well, let's talk about the various important elements of the zombie, and how it relates to 1st level adventurers.
Something you'll learn from DMing a 1st level adventure, especially if you've been running a lot of mid-to-high-level stuff, is that you need to be very careful not to kill your players. If you're the kind of DM who really takes an adversarial role with your players, the lower their level, the easier they are to kill. But there's nothing preventing you from just stomping them with three krakens at a time, and there's little fun in that. I think a good DM is always trying to hit a sweet spot in which the players are challenged but are also probably going to win the day.
At the highest levels, players are so powerful that you can throw pretty much whatever you want at them. But the inverse is also correct: PCs will go down very, very easily at low levels.
Let's talk about a zombie's offensive capabilities.
First off, and importantly, a zombie has a movement speed of 20. That's slower than any playable race's speed, which means that a player character will always be able to run away from a zombie. That being said, a zombie can dash, like any other creature, and can close that distance at the expense of their attack, but could get an opportunity attack if the player tries to run away. Still, a zombie is slow, and that means that players have a good chance to get in a hit or two before the zombie becomes a real threat.
They have a single attack that has a +3 to hit and deals 1d6+1 bludgeoning damage on a hit.
Characters wearing medium or heavy armor will typically have an AC of 16, or maybe 15 if they're in scale mail with only a +1 to Dexterity. If they have a shield, bump that up to 17 or 18. Dex-based characters in light armor might have an AC of 13 or 14. A creature with no armor and 10 Dexterity only has an AC of 10. But let's assume that the targets the zombies are more likely to go after, because they have to wade into melee range as well, will have an AC of about 16 on average. That means the zombie will have to roll an 13 or higher to hit, which is only roughly 1/3 of the time. Against a true tank - like a fighter or paladin in chain mail with a shield - they're only going to hit on a 15 or higher, which means they're only hitting just over 1/4 of the time.
That's actually great for a monster that 1st level characters fight - you want them to miss more often than they hit, because a hit looks really bad at 1st level.
Even if you have a Barbarian who rolled insanely high stats and has a +5 Con at level 1, and maybe is a variant human who took the tough feat, they're still only going to have 19 health at level 1.
Most characters won't have nearly that much. A Monk might have a +2 to Con, and starts with just 10 HP.
The zombie's slam attack will do 2-7 damage, with an average of 4.5. That means that a single hit will often take about half a target's health. If it hits a wizard or sorcerer, who might have a +1 to Con, they could take them down in a single unlucky hit.
Still, they're unlikely to, and characters with lower AC and health should generally try to stay away.
With only a +3 to hit and not a huge amount of damage output, one might wonder how a zombie gets a CR of 1/4, rather than being 1/8 or even 0.
That's why we need to look at their defensive capabilities.
First, an argument for a lower CR: their AC is only 8, which is far lower than most things in the game. A level 1 player will generally have a +5 or +4 to hit with their primary attacks, and that means that you only need to roll a 3 (or 4) or higher on the d20 to hit these guys. We can reasonably assume that in most fights with zombies, every attack against a zombie will land.
How can this be allowed? Because a zombie has 22 hit points. For comparison, most other CR 1/4 monsters have under 20 hit points, with a lot of them hovering around 10, maybe a bit more.
An attack with the heaviest (non-firearm) weapon you can muster (a lance, greataxes, maul, or greatsword) will do 12 damage on a hit, plus a modifier, so a maximum of 17. That means that, without a crit, the best roll a level 1 player can land will still not actually take a zombie down in a single strike.
In fact, I think that there are only a couple 1st level spells that can do 22 damage or more on a non-critical hit.
The point is: a zombie isn't going to go down immediately, and with the action economy so sparse at low levels, that means that a party up against an evenly-matched number of zombies won't be able to take them all out before they get a turn, even if their initiative is terrible.
Beyond that, though, zombies also have Undead Fortitude. This is a trait that prevents them from dying when they get hit with a killing blow. If they're reduced to 0 hit points, they can make a Con save with a DC equal to 5 + the damage they've just taken, and if they succeed, they drop to 1 instead. There's no limit on how many times they can do this, so a zombie could actually take far more than just two or three hits to go down.
There are two exceptions to this, though: if the damage is from a critical hit, the zombie automatically fails (this I think generally represents the Romero zombie convention of zombies requiring a head shot.) The other exception is radiant damage.
At level 1, I think that only Clerics (and I guess Divine Soul Sorcerers) have access to radiant damage (paladins get it at level 2,) so this will, once again, encourage the party to pack a cleric. Their Guiding Bolt, which does 4d6, could actually take out a zombie in one hit, though only if you roll very high (two 5s and two 6s minimum.)
Now, the DC of undead fortitude will often make the save fail, so it's not as if this will make theme extremely resilient. But it will sometimes extend their longevity.
If we sum this all up: we have a monster that is slow and very easy to hit, and does not a terribly huge amount of damage, though enough to be a real threat to a low-level character. What does that mean?
It means a single zombie is very rarely going to be much of a threat. But in hordes, the amount of damage needed to take them down will be fairly high. The party will thus want to make use of their slow speed to keep them at a distance.
In fact, I think that a tactically exciting zombie fight, and one you could do at low levels, is actually basically just Night of the Living Dead. The party can have a big building with barred doors that can keep the zombies away or at least bottlenecked into narrow entrances. Melee characters can then man those entrances and swing at the zombies that come in, while ranged can shoot down at them from above.
Given those advantages, you could use a lot more zombies than would typically be recommended, so long as you don't have too many of them in a position to attack at a time. Large numbers will tax resources and force players to be strategic, but as long as it's not like every player character is surrounded on all sides by them (unless they've really messed up) you should have a winnable scenario.
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