I don't think that any single one of them is bad, really, but I generally do see a TPK as a bad thing. Sure, there may be examples that folks can provide where a TPK was fun and rewarding, and perhaps even furthered the story. This is why I'm not saying that a TPK should absolutely never happen. I question it as advice given to a DM who asks how to handle a situation where his players have foolishly gone up against an encounter that is too tough for them.
Who made the list that you rolled from? Who placed the area that list pertains to?
Setting aside the whole "neutral DM" aspect of the discussion, the DM has still made several choices in regards to this. So even if ultimately, a die is used to randomize the encounter....the die is randomizing from details chosen by the DM.
Even if it's a list in a published game book, the DM has chosen that list. And this is fine....I am not saying this is a bad thing, or a bad way to handle it....but the DM has made choices about these things. He is not absolved of responsibility for them.
This is not about keeping the PCs safe. It's about letting them know that the danger may be too great. For example, naming the hills the Giant Hills and having the PCs hear of giant attacks, and maybe speaking to a veteran NPC missing an arm who tells them if they ever see a giant, they should run. Those are the kinds of things I am talking about. Now, those seem to be reasonable warning signs. However, since this is a game, the players may actually see things like that as a dare. This is why I say that the DM is responsible to make sure things are clear....because different players may pick up on different cues, and what's an "obvious warning" to one player is seen differently by another.
So I have to disagree that this is not your job. The DM has to try and portray the world to the players so that they can make informed decisions. It's not about keeping them safe....it's about letting them make as informed a decision as possible.
Glad we agree here!
In this case, I mean more about the decisions of monsters/enemy NPCs. When the tide of the combat seems to turn against the PCs, the DM is able to ease off a bit....there's no reason that he has to continue to run the bad guys as perfectly efficient killing machines who will not take a moment to gloat, or waste an action in some other way. There can be plenty of story related reasons for this. Yes, a lot of this depends on the reason for the combat and the creatures involved, but my point is that this is another decision point where the DM has the ability to influence the likelihood of a TPK.
What about when PCs flee? That's what I was taking about. Again, I think it depends on the context of the fight, and the enemy motivation for the combat, but in most instances it would be pretty easy to justify letting PCs run away. Or if it's not, then the pursuit can be resolved with skills rather than continuing the combat, or the chase mechanics in teh DMG (weak as they may be) can be used to mitigate the results.
"Far too many factors" is what I am talking about. Any of those factors may allow the DM an opportunity to mitigate the deadliness of the encounter. The Bullette drags off the downed PC to eat rather than chase the other fleeing PCs, etc.
Even once all PCs are down....unless they've all failed 3 death saves, I don't see this as a TPK. Once the last goes down, I'd stop combat and then narrate what happens. They could be taken prisoner or wake up with their gear stolen or any other option we can come up with.
People also like stories where there is definitely no chance that the main character will die. And such stories are not inherently weaker.
(Also, Robb Stark was clearly an NPC, so no the RW was not a TPK

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Having said that, I agree, I prefer that my game has the risk of PC death. There have been two from our current group. Stuff happens and sometimes there are bad results. But I don't think that's the same as going for a full on TPK. They don't happen by accident, despite the examples provided. A TPK has to have DM approval.
And that's fine if that's the game you're playing and that your players expect.....but as general advice? I think it's probably not a good idea.