In the early days of Dungeons & Dragons, the XP tables were designed so that characters went from 1st to 9th level relatively quickly, and then slowed down.
Gygax suggested that it take 40-60 sessions (a year of play) to reach level 9, then a gain of 2-3 levels a year after that
Meanwhile, Hit Point acquisition slowed down significantly after "name" level. Magic-Users gained a solitary hit point per level thereafter!
However, the power of magic-users (number of spells, etc.) kept increasing significantly.
I think it's fair to say that the various designers of D&D during the early days weren't sure WHAT to do with the higher levels. There was a structure there, but most of the game was aimed at levels 1-9.
The first time that someone really sat down and looked at the progression of D&D is likely for the BECMI books edited by Frank Mentzer.
I don't think 2E did that much at looking at the structure (though there's a little fiddling with it, it is pretty beholden to 1E).
3E took a much better look at it. Though it squibbed on the mathematics, so characters diverged too much.
4E is probably - to my mind - the edition that most looked at the progression from level 1 to 30. Though even then, the options for levels 21-30 (Epic tier) aren't as exciting as those for levels 11-20 (Paragon tier). Paragon tier is a masterpiece of design.
5E doesn't actually do a bad job of the higher levels (it's playable and fun), but it isn't a great job. The limitation on high level spell slots is significant, but available spells vs. monsters still cause problems.
The big shift of 3E is making it that characters progress from level 1-20(+) in a mostly linear fashion, rather than the sudden slow-down of AD&D 1E and 2E. That's something later editions kept.
I haven't really looked at the Mentzer Companion rules enough to determine how fast advancement should be - though I seem to remember the advice on XP does make it a faster progression than AD&D. So, in some ways, 3E may inherit the progression from Companion.
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I delight in running all levels of Dungeons & Dragons. There are always interesting challenges you can throw at the party, and they can always surprise you with their solutions.
I find nothing better than setting a challenge without knowing how to overcome it, and watch the players invent something in front of my eyes.
As the DM, you are the interpreter of the adventure environment. You should have a good idea where the key elements are, and then be able to extrapolate where additional elements are.
I've just been reminded that one of the most significant changes in 3E from what came before was to make it much harder for high-level monsters and characters to resist spells.
We're still living with those effects.
In AD&D, a very high-level fighter needed a 6 to save vs a fireball. There was nothing the caster could do to change that number (as I recall).
Add in magic (cloaks of resistance, rings of protection) and the fighter was only failing to save on a natural 1.
Trap silliness: in one of my dungeons, a group of kobolds lived in a room where they’d set up a swinging log to hit anyone entering the chamber. I think it was possible to detect, but my players didn’t, and so triggered it before being swarmed by kobolds.
The players survived the experience, and then, because players, painted a smiley face on the end of the log and reset the trap. Then left.
Several months later, they returned to the dungeon, some new players, some experienced, and looked down at their map upon which one room was marked with a smiley face. “Let’s go there, they said!”
Some traps are designed just for amusement value, though often of the DM not the players. (Though, given the right group, players can find them awesome as well).
One of my “favourites” is found in Castle of the Mad Archmage. It’s a stuck door that is actually made of balsa wood, so anyone trying to force it open hurtles through and is impaled on the spikes beyond.
It’s completely ridiculous and made explicitly to punish a common manoeuvre in D&D: opening a stuck door. That ridiculousness is why I’m so amused by it, and so have been more than a few players.