I was looking at the explanation of the "three pillars" of D&D (5e PHB, p.8), and I was disappointed to find that exploration is not well-defined at all.
"Exploration includes both the adventurers' movement through the world and their interactions with objects and situations that require their attention, Exploration is the give-and-take of the players describing what they want their characters to do, and the Dungeon Master telling the players what happens as a result. On a large scale, that might involve the characters spending a day crossing a rolling plain or an hour making their way through caverns underground. On the smallest scale, it could mean one character pulling a lever in a dungeon room to see what happens."
This doesn't help very much to differentiate exploration from social interaction and combat. In particular, the bolded part is just the basic pattern of D&D play (p.6) that happens during any kind of interaction or encounter.
It looks like exploration is just a catch-all for everything that happens between social and combat encounters. And yet it seems like when people use the term here, they have something more specific in mind. I've even seen references to exploration pillar encounters (traps? navigational challenges?).
What does the exploration pillar mean to you?
I think that one of the main reasons that exploration is unclear to many people in 5e is that the game itself actually tries pretty hard to prevent it.
A dungeon-crawl is pretty much a classic example of exploration. At its most basic, it's exploring the dungeon. You aren't interacting socially with NPCs, nor are you in the midst of combat. This can include traps, puzzles, tricks, secret doors, decision making, mapping, difficult terrain, managing resources, and clues to what's going on in the dungeon. That sort of thing.
The problem is, that many players replace the PC side of exploration with skill checks (passive or otherwise), spells (while always useful) have become easier to gain or recover, and in particular the ones tied to exploration are much easier to use. For example, with
Leomund's tiny hut and
Tenser's floating disk being rituals it has eliminated a choice that would otherwise have to be made. Do I cast another
fireball in this combat to end it more quickly, or do I save that so we can get an uninterrupted long rest? It also didn't prevent attacks from entering or exiting, just obscured them.
One interesting approach that's largely lost is the placement of hidden rooms. When players regularly drew maps when exploring, you'd be able to spot locations where there is probably a hidden room, and then have an idea of where to look for secret doors. Now that people notice secret doors with a high passive Perception, that's gone away. (In my campaign, a passive Perception might key you into that hidden space instead, but you still have to go looking for the secret doors).
There's one level of difficult terrain, and when traveling overland it's entirely negated if you have a ranger with you. I have slightly different rules: terrain does slow you, but you can try to move at a normal pace and risk falling, you also have disadvantage on attacks when in difficult terrain. In addition, some creatures have advantage when attacking a creature that is at a disadvantage in difficult terrain. I also have very difficult terrain. So you might have what's obviously a shorter route, but more difficult terrain, or a longer option that isn't. It gives a meaningful choice, knowing the risks if they are attacked in the difficult terrain.
Another aspect that I think is lacking (and has for most editions) is a decent fatigue rule. Exploration is tiring. There's a park near me with a tower on a ridge. Getting up to the ridge itself is the equivalent of something like 24 flights of stairs. It's tiring. And the ridge is not level either. A couple of hours of that sort of thing in armor with packs is going to have an impact. Sure, better trained individuals less so than others.
There is almost nothing with regard to puzzles and tricks, and the published adventures pretty much avoid them altogether. In the original A-series, the designers had very specific guidelines (since they were tournament modules) and one of those was that a room needed a puzzle or challenge for the
players to solve.
It's very difficult to do that, because you don't know the types of skills the players themselves have, nor whether they like that sort of thing. Plus, you can't assign a DC, and therefore XP for it because it's not addressing the characters, it's addressing the players. So they have pretty much disappeared entirely.
Good puzzles work when they figure them out and when they don't. In a recent catacombs, which were huge and I based them off of maps of the miles of catacombs beneath Rome and Paris, I had a very large room entirely filled with a mist that prevented any sort of vision. So the natural thing is for them to go along the walls to start. So they did. They came to another hall, then wend a bit farther, and a corner. Followed that around to more of the same, until after corner number four, and came to a passage that wasn't the one where they started, and then found corner number 5. Once they came to number six, without finding their starting point, they were thoroughly confused, and decided to just pick a passage instead.
The room itself of walls that very gently curved back toward their entry point. They had opted to use a rope to follow each other, but if they had joined hands along the wall, they would have detected the slight curve. Those curves ended in a corner, which they mistook for the corner of a rectangular room. They never figured it out, but it didn't really matter, since they were able to continue anyway. They had marked the passage they had entered from, so if they returned, they would just need to continue around the walls until they found it. In the end, they found a different way out.
When I design traps, I also know how they work so I know what might be helpful in discovering them. That way, as they describe their actions, I can determine what sort of modifiers (advantage/disadvantage) are needed, and if a die roll is even necessary.
All of these issues can be addressed by play style. The problems aren't unique to 5e either, although it does make some of them worse. A rule in my campaign is that a player can't request an ability check. You tell me what you're doing, and how, and if I feel an ability check is warranted, I'll ask for it. I do make use of passive skills a lot, and I also take into account their abilities and skills so I can avoid a lot of die rolls. But mostly it's to make the players work through and engage the world rather than just ask if they can make an ability check.
Don't skip "the boring stuff." This was a direct instruction in 4e, and there's still a bit of an undercurrent in 5e with that idea. Obviously, part of the key is to not make it boring. But more importantly, as the DM you should
always be feeding them information, and preferably information with choices. But exploration also calls for relatively unimportant information. It calls for
setting information. It sets the stage. Tombs in my campaigns are lots of atmosphere and little activity. A trap here or there, and as you move deeper, constructs and undead guardians, but mostly just a feeling of being very alone. Those last four uneventful passages set up the trap in the fifth. You start to ignore the statues that attack you in the 17th room, because the ones in 9 other rooms didn't.
Exploration is also a good way to add dynamics to the game. It's not all combat, combat, combat. Combats with space between them become more interesting, more directed. There's more purpose to them if they are grounded in the setting - that is the dungeon - and the process of getting there. The periods of exploration are also times where the players/characters are interacting among themselves. This is far more effective if they have things to talk about. My campaigns have lots of plot hooks and threads running through them. I don't write a directed story line. So they always have things to discuss, and the exploration is also providing clues and direction to those discussions. The funny thing is, you don't even have to provide much
actual information at that stage. They start making things up on their own, anything can be a clue, and they often read much more into things that intended. And later on they figure out it wasn't that important. Every game is different, but a classic dungeon might be 50% exploration, 40% combat and 10% social interaction or something like that. Exploration is really the opportunity to set the stage, flesh out the narrative, and to add context to the other aspects of the game. I think there's a tendency to replace exploration with a "cut-scene" approach where you provide this information in short bursts rather than to let the PCs experience it themselves.
I recently picked up the 5e
Adventures in Middle Earth and they have a ruleset specifically for journeys which is interesting. I probably won't use it as written, but some good ideas. Of course, you still have the normal type of exploration once you're in a dungeon as well. But it's definitely worth checking out.