First, I'm not dismissive about your claim that you have a problem. I believe you! I'm saying the problem is actually not with the rules that cover exploration in D&D 5e. Based on your comments, I think it's in your understanding of those rules, your preparation, presentation, and implementation. This doesn't make you or anyone else a "crap" DM, no more than it makes me a "crap" linguist that my Spanish isn't as good as it could be. It's just something to work on. Nobody's born with the ability to run D&D 5e exploration challenges well!
Many of your comments have come across as incredibly dismissive. Even here, you are insisting that it must be my understanding of the rules that is at fault. My presentation of the game. My preparations of the game. My implementation of the rules of the game. It must be me that is the problem, because that is the only thing that makes sense to you.
And when I go, as I'm about to do, and point out how this really doesn't apply... you will say I am dismissing your advice and how that makes it even more my fault, after all, what was it you said?
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But obviously, if something doesn't work perfectly right away, you should give up immediately. It's like the old saying goes, "If at first you don't succeed, give up and blame everyone and everything but yourself." "
Yeah, that wasn't rudely disimissive of someone who has spent years struggling with this, to imply they did it once then when it wasn't perfect gave up and blamed everyone and everything around them like a child.
Overland travel rules include forced marching which can cause exhaustion. It happened to my character tonight, in fact, when we pressed on further than we can normally in order to find a safe place to long rest. We didn't, as it turned out, and I didn't want to risk another level of exhaustion pushing further. So we didn't regain any hit points or hit dice that night which was not great.
Yes, a forced march can cause exhaustion. First, this requires your characters actually travel 9 or more hours. If you are on foot that is 27 miles, if you are horseback it could be much further, same if you are in a wagon. Which offers a few different questions. But, let us stick with 9 hours of marching.
Secondly, after 9 hours they all make a DC 11 con save. This is not a terrible hard save, most people will make it. If they happen to fail though they get a single level of exhaustion. A single level of exhaustion is removed by a single long rest, per the rules, so this is a non-consequence. If you march enough to get a single level of exhaustion, then camp, you have suffered no penalties.
So, you probably need to march 30 miles, for 10 hours, to make a second check at DC 12 which is slightly more likely that at least one person will fail, maybe two, to have exhaustion be an actual factor from forced marching.
But, now let us turn back and look at why the forced march. Because, in general, the players could stop and rest after 6 or 7 hours of travel, with no penalty. So, firstly, there has to be some sort of pressure to make you want to get as far as possible as quickly as possible. Because if your group just decided to travel from one city to another just to see the city (you know, exploring for the sake of exploring) then there is no reason to push and no reason to risk exhaustion. But also, you said "there was no safe place to long rest"
So, what do you mean by that? What are the situations that make it a safe place to long rest? Because generally, our group long rests by making a camp on the side of the road and posting a watch. There are also ritual spells like alarm or Leomund's Tiny Hut to increase the security of the camp. Per some pretty contentious rules, being attacked in the middle of the night may not even break the long rest. So, how does this work? How did the group determine that there was no safe place to rest, and therefore skip a long rest? Why did they not find a place to rest somewhere between hours 6 and 9, a distance of 12 miles of terrain, nearly half the journey?
As for diseases and simple wilderness obstacles, I'm not responsible for other people's arguments, only my own. But I think you really need to be less dismissive of time as a limited resource in the game. It matters and it makes everything work better and gives meaningful choices and teeth to challenges of all sorts. I think you would also benefit from discontinuing this thing you have with separating the pillars to no good result. They work together to their mutual benefit. Leverage that.
I'm not dismissive of using time occasionally. It can be a great spice to add into an adventure. However, it is incredibly difficult to realistically have it for every single aspect of the adventure. You can't have every journey to a distant location be a clock, followed by every exploration of that location being a clock, with then every confrontation being a race against time to turn around and have a journey to a new location against the clock. That sort of rapid pacing doesn't always work.
And, you seem to misunderstand why I'm seperating the pillars. I'm not doing it because they don't work well together. I'm doing it to highlight the tools we have. If the greatest tool for the exploration pillar is combat, to the near exclusion of any other tool, then I see that as a problem, and constantly using the threat of combat to scourge your players and prevent them from using their tools and resources doesn't mean that those tools and resources don't cause issues when actually allowed to be used.
No, I didn't say it's only you that may have an issue, just that you can only speak for yourself.
Heavy precipitation and strong wind is punishing. Penalties to Perception and disadvantage to ranged weapon attacks is not great. It means stealthy monsters like yetis can more easily get the drop on us and the ranger and my rogue scout have to switch from ranged attacks to melee which isn't always ideal. On days with particularly bad weather, we could just not travel, but then there's this ticking clock. We have to weigh if it's worth sitting around when bad things are happening. Sometimes it's worth it, sometimes it's not. As an example, in my forest/swamp hexcrawl, the players stayed in town for a full month doing downtime activities because the weather was continually terrible. The players decided they'd let whatever events would unfold do so rather than risk it. Things are now worse and they're dealing with the repercussions.
So, the only threat the weather gave was making combat more difficult. It was no challenge in and of itself. Also, ticking clock meant that you couldn't simply wait out the weather, and had to journey into it and risk combat.
Remove the combat, no challenge.
Avoiding wandering monsters by sneaking past them is by definition an exploration challenge. So is following their tracks back to their lair, if they have one. Or being tailed by some and picking up your pace from slow to fast, say, to keep ahead of them while risking a penalty to passive Perception and not being able to move stealthily. If you're only thinking about wandering monsters or random encounters as fights, then you are limiting yourself to no good end. And again, that's still just you separating the pillars in the game to no benefit. Use them all, more than one at a time perhaps to reinforce each other and your game is more dynamic as a result.
Again, this isn't about the fact that my peas can't touch my potatoes, this is looking at the tools we have.
Is sneaking past the monster an exploration challenge? Maybe. What's the consequence of failing that challenge? Combat. What challenge does it provide if there is no combat... none. It doesn't work. The entire threat of the monster is combat but removing combat from the equation highlights that and makes me question "what other than combat can I do?" or to phrase another way "is combat the only viable challenge for the party?"
Following tracks can be a challenge, I'll give you that, but in the context of the story it might be just as effective to stake a location out, because the goal is to engage in combat.
Why is moving at a fast pace and losing stealth and passive perception a problem if you are being pursued? Because you might be ambushed and pulled into combat. What happens if we remove combat as the threat though? Nothing. There is no longer a threat and a reason that increasing your pace is risky. It becomes all benefits.
You are correct, combat and monsters can add to the challenge, mixing your peas and potatoes can be good. My issue is the more I look and the more I ask... the only thing making the potatoes palatable is the fact that everyone is stuffing peas into them, and without the peas, you don't have something good.
As to your question about finding the alternate entrance, we had been in this dungeon before, but went through the fortified front gate, having been let in by the monsters guarding it. We explored only a small part of it at the time before wearing out our welcome and decided to return this session. Figuring they'd not be best pleased to see us at the front gate this time (which would put us at a distinct disadvantage tactically), we declared we would explore the mountains around it to see if we could find a chimney, sewer pipe, or some other means of entry. After some searching, climbing, and balancing our way on narrow icy paths, we found ourselves on the top of the structure where we could lower ourselves down using ropes into an upper window. We had to use over 100 feet of our rope which we were not able to collect on the way out. I also nearly fell off a path while traversing it, taking some damage while being rescued, which was embarrassing because my rogue, Icewind Dale, is actually really good at balancing given he's a legendary ice skater.
So, you needed to find an alternative entry to avoid combat. If there was no risk of combat, there would have been no need for that exploration at all.
It sounds like the main "challenge" was the icy paths and potentially falling, during which you took some damage, that would likely be easily healed. But spell slots had to be saved... because you were breaking into a monster's lair and expecting combat. Which made your hp damage actually meaningful.