The traditional D&D combat system is sometimes criticized as being “whiffy,” which means that missed attacks are frequent and frustrating. The idea is that, especially when there are a large number of players, it kind of sucks when your turn comes around, you finally make your attack roll… and miss. Nothing happens and then you need to wait for the next round before you can do anything.
Now, I do not believe this is a major problem with old school D&D, particularly where combat is often something to be avoided or stacked in your favor prior to engagement, and where HP totals are relatively low, even for powerful creatures, leading to quick resolution. The occasional miss, miss, charm spell… save made (nothing happens), miss, etc sort of combat happens, but is rare. This is obviously a bigger issue in a game like Third or Fourth Edition, where combat is more of the focus, but in a game focused on exploration and creative problem solving, it is less important. With that caveat out of the way, might there be a way to make old school combat even faster and more interesting by taking this complaint seriously? Here is one method.
When the players decide to engage an enemy in combat, an attack rolls is made as normal. If it hits, damage is dealt (or an effect happens, depending on the circumstances). If the attack misses, however, the enemy succeeds in damaging the PC. “Automatically.” Automatically is in scare quotes there because of course it was not actually automatic. The player first needed to engage the enemy, which put the PC in danger, and then the roll went badly. Either the enemy takes damage or the PC takes damage, driving the eventual conclusion in one direction or the other on every action. HP being abstract, this of course does not mean that someone is physically being wounded (though it could), but instead that one side is getting the best of it for that particular combat turn.
Since what we really care about here when making at attack using this system is the threat level of the enemy, not the enemy’s armor or defensive skill specifically, the target number should probably be based on enemy HD or level rather than using a traditional armor-based AC number (though the actual fictional meaning of AC has always been a bit ambiguous). 10 + HD seems like the natural, intuitive value. This means that when a first level fighter (assume no attack bonus, for simplicity) attacks another first level fighter, the target number is going to be around 11, leading to a roughly even chance of the either combatant taking damage (5% in one direction or the other is irrelevant, and in any case the numbers can be adjust to make this work in any mathematically desired way). Armor is probably best represented as damage reduction (light = DR 1, medium = DR 2, heavy = DR 3), given that monsters never make attack rolls directly. At most, an enemy forces a PC into a position where they must defend themselves.
And how exactly might that work, given that monsters don’t make attack rolls per se? The simplest answer is that each combatant takes an action and resolution happens as necessary. If this results in a PC attacking and then defending themselves from other enemies as well, it seems like that would work, though combat rolls could also be limited (perhaps to one per round, or something based on level). This could make being surrounded particularly dangerous, if you can only defend against one attack (the others would presumably just deal damage minus armor). The benefit to a proactive versus reactive combat roll is of course that you get to choose your target, rather than having your hand forced by a particular enemy.
How to handle some other common cases using this system might not be immediately obvious, but are not too difficult to figure out with a bit of thought regarding the underlying dynamics. What about missile weapons, for example? If it is possible for foes to engage each other with missile attacks, the player makes a combat roll. On success, the enemy takes some damage, assuming that makes sense in terms of what the PC is doing (the PC would need to be armed with a missile weapon to actually deal damage over distance). On failure, the PC takes a shot to face (or whatever).
This is partially inspired by Dungeon World and Numenera. However, this is not just a port of either of those systems. Dungeon world involves more mechanical choices depending on move details rather than using a separate mechanic to represent combat abstractly. Numenera uses a system for lowering the target number rather than stacking bonuses, which requires understanding how various powers and situational actions can be used to do this. Neither of those approaches are bad, of course, and though their player-focused design has informed this system, the end results are a bit different.
There are a few other details that would probably need to be nailed down to make this fully functional. There are also a few additional features that I think would work well as added tactical options, but I am going to leave it here for the sake of comprehensibility.
Edit: I wrote up an example of a potential monologic combat.