If the outcome is certain, no roll is needed
As has been discussed elsewhere, hit points (as well as armor class and other defensive features) are abstractions: a measure of how well characters (PC or NPC) can survive in mortal combat. Sometimes, they may lead to surprising outcomes, where David slays Goliath. Other times, they may allow the escape or survival or a character that appears helpless. But ultimately, they are measures of likelihood of survival: a way of tracking and simulating how someone fares in an uncertain contest.
But not all contests are uncertain. While fantasy narratives are full underdog victories, there are times when no amount of luck will help. Times when an enemy (or ally's) fate is absolutely certain. And in those times, it's helpful to remember one of the first rules given in the Player's Handbook (p. 7, bold added):
In cases where the outcome of an action is uncertain, the DUNGEONS & DRAGONS game relies on rolls of a 20-sided die, a d20, to determine success or failure.
The dice are not there to be rolled on every action (eating breakfast, opening an unlocked door), but rather they are there to determine the result of an uncertain task. If the outcome of a task is certain, a DM may declare that it simply happens without any need for rolling dice.
Ok... but what counts as "certain?"
This is an important question. In Dungeons & Dragons, the party often plays the role of underdogs: they face foes with immense power and resources, and regularly find themselves outnumbered. On the other hand, the PCs are often heroically capable: they have features which allow them to mow down lesser enemies, and stand where lesser characters would fall. Thus, any number of situations which would assure victory or defeat for a normal character might not do so for a PC.
Fortunately, the Dungeon Master's Guide gives us some guidance on this issue (DMG, p. 237, bold added):
When a player wants to do something, it’s often appropriate to let the attempt succeed without a roll or a reference to the character’s ability scores. For example, a character doesn’t normally need to make a Dexterity check to walk across an empty room or a Charisma check to order a mug of ale. Only call for a roll if there is a meaningful consequence for failure.
When deciding whether to use a roll, ask yourself two questions:
- Is a task so easy and so free of conflict and stress that there should be no chance of failure?
- Is a task so inappropriate or impossible — such as hitting the moon with an arrow — that it can’t work?
If the answer to both of these questions is no, some kind of roll is appropriate.
A particularly helpful guideline here is that an action that requires no roll should be "free of conflict and stress." If an enemy is fighting for his life, even while bound and gagged, it is likely not "free of conflict." And if the enemy's allies are on their way to rescue them, and the PCs must finish them quickly, it is not "free of stress." But this is not always the case. Sometimes, a PC has unlimited attempts to dispatch an enemy: no one is coming to save them, and the enemy is incapable of fighting back. In these situations, where even such a significant action as killing someone could be seen as "free of conflict and stress," the rules support the idea that you may not need to roll at all.
Probably the best rule of thumb is the first bolded statement in the above quote: as a DM, I try not to call for rolls if there is no "meaningful consequence for failure." If an achievable task could be attempted unlimited times, and failure on previous attempts do not make the next attempt less likely to succeed, then I see it as reasonable to simply declare that a task is successful.
Beware of the message this sends
Keep in mind that your players will learn the kind of game they are playing as they go along. If you are strict with the rules as it applies to them, they will probably expect you to be strict with rules that apply to NPCs as well: and vice-versa. In other words (to quote a helpful comment by NautArch):
Mechanics available to a PC are known and available to NPCs. What a player considers fair game for an NPC, they may not think is reasonable when their character is under the same circumstances and dies.
Thus, if you sometimes declare that a PC is successful at killing an enemy without requiring a roll, players may become concerned that you will similarly harm or even kill their characters without allowing any dice rolls to prevent it. This may seem an unreasonable conclusion (after all, we all know that the rules favor the heroes, and the game is designed to allow good [or at least protagonists] to triumph in the end), but it's surprising how much people can extrapolate from experiences without even realizing it.
If you plan to kill characters (PC or NPC) without any rolling of dice, I highly recommend you explain your reasoning first. Saying something like "Ok, we could roll dice ten times until you got another hit, but there's no need: you have as many tries as you need to kill him, and no one is coming to help," can let your players know that you will only remove the dice in certain circumstances, and that at other times they can rely on the rules to protect them.
And keep in mind... sometimes it's worth rolling
The above statements are meant to give you ways to justify and judge when to allow characters to be killed without rolling dice. But keep in mind, sometimes even in those situations it might be worth rolling. Killing a person is complicated: the body wants to survive, and will do what it can to do so. Even an unconscious enemy will tense and flinch when wounded, and armor (not to mention magical protection) are designed to help a person survive wounds that would otherwise be fatal.
There can be narrative value to an execution that, while eventually successful, is harder than expected. If a PC swings their sword and doesn't get through the enemy's AC, they may look momentarily foolish; they may lose face in front of their companions; and they are forced to face the decision, not just spur-of-the-moment but one that they need to commit to, to take a life. All of these things can add "stress" or "conflict" to a scene, and could be seen as "consequences of failure."
It's worth deciding, as a DM, whether or not such experiences will make a scene better. It also could be a way to show character growth: a botched execution could encourage a character to improve their prowess, and the next time they need to dispatch an enemy they may do so cleanly, showing their improvement.
But sometimes it's just time to move on. Sometimes a task is so simple, and outcome so certain, that you don't need to rely on the rules designed to dramatically track a character's chances of success. Sometimes, you'd rather just let the inevitable unfold. Consider the consequences, and consider the message, but sometimes... it's just time for an enemy to die.
