The Riddle of Steal: HD, Attrition, and Black Sheep
We all have an understanding of HD. Bigger amounts are better, heartier, can likely do more damage. Lesser amounts are weaker, chaff, the yet-to-be-bleeding meat to be cleaved! It's become such a main stay of RPG conventions, specially those that revolve around D&D to include them or some analogous form of them. Two pillars of the most agreed upon idea of attritional play rest upon them though, Cleave Rules and ever increasing HP totals. These two ideas work in tandem to allow higher level PCs cut through the lesser fodder with little fear as to their safety. The big focus of this kind of attritional play is watching your ever shrinking pile of hit points dwindle closer and closer to zero and trying to find the perfect time to reap the benefit while avoiding the danger. Cleave also remedies the large encounter sizes the 1974 version of the game has. Fighters can break ranks of weaker foes with ease! HD surely has a place in all of our games for how easy it makes this kind of play.
Extremely large caveat emptor that YES, your setting can tweak or change these assumptions and that I am approaching each game as if it was being run out of the box until otherwise stated.
Well there is a style of game that some prefer that doesn't have anything similar to HD. Games like Traveller, Delta Green, and Openquest have no instant measure of character strength like that. It's no secret I prefer these kinds of games. Troika! and Classic Traveller have been recent fixations for me and I know BRP is there for me when i need that d100 fix. And so being in communities that almost entirely focus on the conventions of D&D it can feel a bit bewildering to try and imagine how these D&D fixtures can exist in these games that don't share some of the core DNA. It's mostly due to the fact that so much of what blogs do is train us to see that gameplay in the structures of D&D and similar games do not have such a dedicated amount of ink spilled about them.
Troika! and its kin have the double track of Stamina and Luck to consider when delving. During the Troika! mega dungeon game I ran I was pleasantly surprised by how much the provisions recouping Stamina led to players pressing on deeper rather than retreating when they would normally in D&D. Especially after I added rules to regain Luck from drinking and other sources that familiar pattern of get beaten down, weigh options, push on or retreat filled our sessions. And if you're willing to go outside the world of RULES AS WRITTEN there has been numerous attempts to use the Troika! initiative stack to focus more on attritional play. Franc's work on expanding the the stack to include the Dungeon and Gourd Dwarf's work on Star Marauders which takes the similar structure of Troika! and puts an even bigger focus on the gritty details of raiding and spending the loot.
Traveller's "three strikes" approach to losing your physical stats, which are your HP in Traveller, creates tension as people can keep pushing after being knocked out the first time. A few times in sessions players that have only gone to 0 once are picked up and able to make a daring escape or push on with the mission. Though if you're playing in a campaign with a ship the referee has even more levers to attrition you by! Money, supplies, information, connections, jobs... the list goes on for what an enterprising Traveller might desperately need
And my beloved Mythras/Runequest solves this by making minor healing magic common among all characters, not just clerics and wizards. HP is a smaller pool to attrit in this game, but the focus can be applied to the reserve of spell points and other items that prolong the crawl.
The differences in these games for how attrition plays out is usually a game of inches or beholden to white room imaginings of how things will play out. I've run the Troika! Dungeon, I've run the BRP Dungeon, I've run the high level DCC Dungeon, I've run the Wolves Dungeon: asides from the very specific flavors those games brought the core skeleton of play remained the same. Though the fantasy of that very specific type of 1974 play can be appealing even so.
The vision of attritional play in Dungeons and Dragons is a very specific type of attritional play. It's the fantasy of cleaving through dozens of lesser foes and going to the bottom of those dark labyrinths with various nicks and scrapes before finding the next big horde. Those big pools of HP and growing piles of spells are easily identified as targets to whittle away at. Having identified what other game's attritional play looks like, let's get ready to do away with the idea of HD and Leveled Spell Slots for a moment and peruse Chaoclypse's adjusted rules for damage in Chaos Reigns which proposes that creatures/men get as many actions as they do HD! This is a splendid way to begin to strip away the assumptions of HD in attrition based play. Maybe we introduce a little Cottonmouth to give reasons for why some foes attack more than once! Or tie it to how much wealth they have upon them like the alternative Wolves rule. HD is not as crucial to that feeling as is assumed. Though this is all stripping away HD away from D&D, what if we wanted to add back to those other games?
For Troika! I think there's very little you need to do as strong characters will be consistently winning melee roll offs against hordes of foes. It could be fun to add a Cleave! skill and let its level be how many foes a hero can strike and kill each time their token is brought out.
Traveller I could see adding Cleave as a perk to a certain level of Blade Combat. Say at Level 3 a combatant can strike a group of enemies all at once so long as their weapon skill isn't higher than theirs.
And finally BRP. I think this is one of the easiest to change make better use of rabble and underlings and add a combat trait that allows them to cleave such fodder!
All this said, I don't hate D&D or ever feel annoyed playing it. I just prefer skill based systems that usually eschew towards fixed HP amounts for a character's entire life with little to no room for them to ever increase. I also have seen this type of play bandied about as something that D&D does better at the expense of everything else but think that's just more system as a cop crap.
Go forth and attrition thy players.