2d6 under ability score: A system sketch

Expanding from the last entry, and opposed to all the other previous entries, in this one I devise a system without levels, classes, hit dice, etc. But the weight falls over the ability scores, and uses 2d6 for resolutions. But there are no +mods involved, only the scores themselves.

A good curve seems to be to roll 2d4 at the start to generate the scores. 6s are meant to be greater than average; and anything over 7 carries implicit superheroic feats. Saves are rolled with 2d6 under relevant stats, with only super-heroic characters able to stastically save more often than not.

The basic combat rules are that you roll 2d6 to attack, everything that exceeds the monster's AC is damage dealt. Longer weapons attack first. Over this premise, I explain some uses of each attribute:

STRENGHT: 

-When you attack with a heavy weapon, and roll your strenght or less, you can re-roll the smaller die.

-When you have strenght 7 or higher, you get a save vs death when at 0 hp

-The score is also the amount of big things you can carry

DEXTERITY

-Spend a turn aiming with a bow and roll 2d6: If under this score, you add +2 when shooting after.

-If you use a light weapon and roll less than your dexterity, you can diss your roll but get +1 AC this turn.

-You roll a save to catch or flee from a monster with higher dexterity. It doesn't have to roll anything, only the one with lowest score does.

-Over 7 you can perform acrobacy feats.

WISDOM (the magical stat)

-At 6, roll under it to use magical tools, detect magic and other minor magical skills 

-At 7 you can cast level 1 spells, at 8 you can cast level 2 and so on.

INTELLIGENCE (the mundane knowledge)

-At 6, you can use one set of specialist tools (Specialized kits detailed in the inventory: doctor bag, thief's tools, artificer, etc) or know an extra language.

-At 7 you can attempt to produce something you've been working on (state what it is at the moment) related to the tools you carry (poison, chemicals, a small gadget), and maybe more times per day at 8+

CONSTITUTION (which really just says how well a fighter you are, or a measure of you will to live): 

-The score is your HP. Armor adds to your AC, but some armors also add some HP.

-At 6 you always act before your opponent in combat providing there are no other substantial differences in leverage.

-At 7 you get +1 attack per round with any favored weapon

-At 8 you get +1 AC for free

-At 9 you get an extra attack regardless of weapon

CHARISMA

-I like to conceive it as a save vs manipulation, fear or some measurement of "self-integrity"

-Also the classic hireling numbers and their morale checks.

-If you use animal companions, you also use this for complex rapport with them.

-On monsters (because with this system, numeric values from monsters are also rolled like this as there is no other math) this can represent how many allies they have in an area. For example an undine with 7+ charisma might use this to command friendly animals or entangling vines in the encounter area. This is the score that a Disney Princess would max out.

Advancement rules: 

When you level up using whatever method you prefer (as there is no need for numeric levels, I'd try to avoid using them for advancement and probably use sandbox milestones) you roll 1d6 against one ability score you want to increase.

If you roll less than it, raise it by 1, to a maximum of 9 or maybe 10

If you roll equal or over than it, raise it by 1 and raise any other stat by 1 

In this way, people who rolls bad stats at creation can increase them slightly faster than the others, and there is some risk/reward between raising "dump stats" and maybe not getting what you wanted, or raising your main ability score straight.