I like 24XX. A lot. It's very adorable, and adaptable, and here I've adapted it to tell Homeric stories by adjusting how the dice are rolled.

In Dory+Apsis, each hero has a nature, a virtue, and a value (maybe more than one). Conforming to these grants additional dice, which bias results toward success. But still and always, the gods may spite your hero. That's how they are.