Last time I wrote about my homebrew ASU I gave the overly story game, narrative version of the combat system. While I'm still a fan of it I also have come to appreciate numerical systems of combat more, and can understand why many would want a more structured game. For both myself and others, I have an alternate set of rules for my basic rule system that works a little better for a tabletop game.
Every round, each character must roll their class HD as their initiative dice. Higher numbers go first. If they roll a 6 or higher, they get advantage on their attack roll. If they roll a 10 or higher, they can either choose to deal double damage on their attack if they hit OR attack two separate enemies. Sages use d6, Rogues use d8, and Fighters use d10 for their combat dice.
To hit, roll 1d20 vs target's AC. Enemies have a base AC of 10 + modifiers from the creature itself, environmental elements like darkness, and fear or morale penalties. AC above 16 is meant to be very rare to avoid fights taking too long. On a hit, you roll your class die for damage. Sages deal 1d6 damage with all weapons, Rogues 1d8, and Fighters 1d10. You can only roll damage like this if you are armed with a real, functional weapon. Broken or improvised weapons may deal reduced damage, and unarmed attacks may deal only 1 damage or no damage at all. Weapons can be differentiated by weapon training, or by using the fiction. Skeletons still can't be hurt by arrows and such. Two handed weapons get to roll your damage die twice and taking the bigger result.
Hit Dice Rules
Characters roll their class HD at 1st level and once every level after. Your minimum starting HP is 2, so if you roll a 1 you count it as a 2 instead for first level only. For every point of Constitution modifier, you roll additional hit dice each level and take the highest for positive or lowest for negative. This incentives players to consider playing as a Fighter if they roll high constitution as opposed to a Wizard in traditional D&D, as they will get much more out of that swingy d10 and take highest then much smaller range of the Sage's d6.
Monsters also use HD. Creatures with 10 HD are considered the most powerful, as the players cap at level 10. Monsters also use their number of HD as their initiative, meaning a highly powerful monster gets to go first more often. Some monsters break this rule, very fast creatures may be able to always go first or very slow creatures may always go last regardless of their HD. If a player exploits a monster's weakness or uses a hex to lower its HD temporarily, this would also lower its initiative and other tacked-on features of high HD, such as resistance to spells and so on.
Each class has a maximum AC. Sages have 12, Rogues 14, and Fighters 16. Each piece of armor, dexterity bonus, weapon specialization bonus, and magical bonuses count towards but cannot exceed this limit. This means a very dexterous Fighter highly trained with parrying swords could wear no armor but yet have maximum AC, and a Sage could reach their maximum AC by just putting on gloves and a helmet.
There is also no class based armor restrictions; Sages can wear heavy metal plates if they choose, but their AC is still capped at 12 and each point of AC gained from heavy armor gives -1 to combat saves, so they will opt for something like a gambeson instead. This system does allow more freedom for characters overall; as an MU can now totally wear the metal skullcap that lets him see invisible creatures and, if it gives him maximum AC, can just wear robes for the rest of his outfit.
Magic weapons can seemingly have a mind of their own. They demand to be wielded by powerful warriors, and those without the skill or power to use them will be betrayed. Magic weapons have an Ego score which is the minimum point total the user must have to avoid being negatively impacted by the weapon or to avoid waking up one morning with the weapon vanished to find a worthy master.
Ego points are calculated by the user's class and charisma modifier. Each level as a Fighter class get +1 ego point, half fighters get +½ point per level, and non-fighting classes get no points. Each positive point of charisma modifier counts as +1 Ego point. If you meet the weapon's Ego score, you will not receive the negative impacts of the weapon or be betrayed by it when you need it most. If you have double the weapon's Ego score it may be imprinted on you and attempt to return to your if stolen, or cause its negative effect to happen on your aggressive if they try to turn it upon you.