Often battles in D&D (all editions) get to a grind of many units battling each other. A group of 4-6 players against a dozen goblins is not that uncommon to see. Or sometimes monsters just make a bunch of attacks. Dragons with their claws plus bite plus tail, and many beasts with double claw plus bite.
What this means is that you will be rolling a lot of dice for attacks which takes a lot of game time. So, the idea is taking the example of wargames, which commonly have many units fighting each other, and try to optimize rolling.
For that, attack rolls are made with 1d6. If you are proficient with the weapon, you roll 2d6. If you are inept, you roll 1d6. You have to roll equal or higher than the target’s AC, which is: No armor (2), Leather (3), Mail (4), Plate (5) and shield gives +1 AC.
Each die that is equal or higher deals 1 damage. Hit points are calculated differently. Each HD gives 2 hp, and then you add the extra points. A 1 st level warrior with 1+1 HD would start with 3 hp. High constitution bonus or penalties apply every 2 levels.
Instead of a bonus to attack rolls (or THAC0), fighters get +1 attack die every 3 levels. For monsters, each damage die give them 1 attack die. For spells, each damage die equals to 1 hp damage, with the target entitled to a saving throw for half damage (round down).
For saving throws, you just divide by 3 and round up. A 13 to 16 would be a 5+, a 10 to 12 is 4+, a 7 to 9 is 3+ and a 1 to 6 is 2+.
That’s the basic premise of what I’m calling ol’d6. In practice, it makes rolling faster. If you have a dozen goblins, roll a dozen d6s and compare to the target’s armor. Each success is one damage. Just like that.
There are a lot of possibilities for customization here with ideas for burden, different equipment and stuff like that.
I might elaborate more on a later date and try writing a more cohesive post, but ol’d6 have been playing well in the games I’ve tried it. Would like to hear what you folks think.