Flexible requirements
Right now, all weapons have minimum requirements to use, which are treated as absolute. I suggest these are treated as relative requirements to use these weapons efficiently instead. Not meeting the minimum requirements doesn't mean you can't use them, just not as well.
What does that mean? That means the base damage of weapons is adjusted by
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(character's current stat - minimum required stat)/minimum required stat
Strength
Weapons are physical objects, so wielding weapons requires moving them around by strength. Therefore, each and every weapon should have a minimum strength requirement for lifting and moving it. Furthermore, physical damage is incurred by smacking a foe with a weapon. The more powerful the smack, the greater the physical damage. Therefore, damage done by a weapon should be primarily proportional to the strength of the character brandishing it.
Dexterity
Dexterity doesn't directly increase physical damage dealt by weapons, but the more dextrous you are the better you will be at pointing the business end of weapons at foes. So a higher dex should entail greater accuracy and greater critical chances. Which is the way it is, I think.
Cunning
Cunning doesn't directly increase physical damage either, but allows you to notice weak spots and vital areas of foes. Cunning, then, also increase critical chances and probably critical multipliers.
Using one-handed weapons with two hands
Allow characters who are not strong enough to use one-handed weapons with two hands give the game more flexibility and characters more options to consider. Assuming the off hand is 60% as strong as the main hand, this gives a lower strength bound of 62.5%. So to use a one-handed weapon with a minimum strength requirement of 35, the lowest strength a character needs to have is 35*0.625=21.875, or 22 (rounded up to the nearest integer).
Using two-handed weapons with one hand
If weak characters can use one-handed weapons with two hands, why can't brutally strong characters use two handed weapons with just one hand? Requiring a character to have double the minimum strength seems like a good place to start.