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Behold the Dread Horse, whose hooves shatter good times!
D&D attribute scores are cool. As a concept, I like them and think they're neat. Additionally, the system they provide is sleek and elegant- if you need to do something, consult the most relevant attribute, roll 1d20 and add your modifier. If you roll well enough, you succeed. If you don't, you fail.
That being said, there is a problem with these six numbers. They were never designed to do that.
As smarter people than I have pointed out, the problem with D&D's ability scores are not all-encompassing, even though they are all used that way. That's why you sometimes get strange things like Perception being under Wisdom, Charisma being treated as a blank check for rascally or mischievous behavior, or Intelligence being a glorified Hint or Lore dump button.
As such, I've been thinking long and hard over, based on what other people have said and changes that others have made.
For example, the Angry GM removed Intelligence on the basis of it is impossible to role-play as someone more intelligent than yourself without the Referee just giving you the answers or letting you make die rolls to come up with ingenious plans. That's not interesting or satisfying, nor does it give the players more interesting choices.
And while removing something like Intelligence is a good step, as it neatly side-steps the old "Intelligence or Wisdom" debate that has plagued this system nearly as long as Alignment debates have, it is a bandage on a gaping wound. So I decided to operate and see if I could come up with a better solution.
There are now five ability scores: Strength, Dexterity, Constitution, Cognition and Charisma.
Strength (STR) governs exactly what you think it does. Climbing, lifting, doing pull-ups and etc. If your class doesn't give you an automatic damage bonus, add your STR modifier to melee attacks.
Dexterity (DEX) governs agility, precise movements, reaction time, hand-eye coordination and etc.
Constitution (CON) governs pain tolerance, health, resistance to poison and disease, general hardiness and etc. Determines your total HP as well.
Cognition (COG) governs instinct, perception, memory, bodily and mental awareness, resisting Charm or Fear effects, willpower and etc. It also determines the number of Memory slots your Character has.
Charisma (CHA) governs how charming or personable you are. When making a Reaction roll in a social situation, if the Referee determines one is required, he should add the player's CHA modifier to the roll.
It is my humble opinion that you should not have social skills, such as Diplomacy, Intimidation or etc in your game. It is boring and uninteresting. Instead, have the players just role-play their characters while you role-play the NPC. If they manage to convince you, acting as that NPC, then they pass. But if you're not sure or if the player(s) is/are not that good at speaking, but you think the NPC could potentially be swayed by that, make a Reaction Roll.
Here's a Reaction table from First Edition, modified by me, in case you don't want to make your own.
NPC Reaction Table
2d6 + CHA modifier
2-3: NPC has a very unfavorable response to what was just said. He is likely done talking. Make sure to justify it in context.
4-6: NPC has an unfavorable response to what was just said. He is unlikely to listen further.
7-9: NPC is on the fence and could easily be swayed to one side or the other, depending on what else is said.
10-11: NPC has a favorable response to what was just said. He might be willing to help now, but even if not, he will definitely keep talking to you.
12: NPC has an extremely favorable response to what was just said. Listening further is the least of what he might do for you.
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