I'm going to need a statistics nerd to help me out here; I'm wondering if these traits are mathmatically balanced or not. In particular if Strong is balanced against Fast, and if the Agile and Tough traits need to be buffed up due to their defensive natures.

This is a very basic combat system which owes a lot to d20. It can be applied to other kinds of task resolution too, but right now I want to make sure the basics of character creation are balanced when it comes to combat statistics:

When attacking, you roll 1d6. If the result equals or exceeds the target's Defense (usually 5 or 6) you deal 10 damage. You have 100 HP and a Defense of 5. These are the general rules for combat.

Characters are a little tougher than NPCs, though;
When creating your character, pick three of the following traits:

AGILE = You have a Defense of 6 instead of 5.

FAST = When making an attack, roll an extra attack. This attack gets a +0 bonus and deals 10 damage, even if you have Precise or Strong.

PRECISE = You add +2 to your attack rolls.

STRONG = A successful roll of 5 or 6 deals 20 damage instead of 10.

TOUGH = You have 200 HP instead of 100.

Right now I'm assuming opponents will do 10 damage per attack, get one attack with +0 bonus per turn, have 100 HP, and a Defense of 5. I'm using d6s because I believe in easy-to-obtain game materials; if I want to implement ability score modifiers or something similar obviously I'll have to scale the system up to more graduated die sizes.

Thanks!

I did the number-crunching but rather then confusing myself, I just stepped back and realized that I had an answer.

The one extra offensive power will overpower characters on a whole vs the defensive ones.  Fast is the most complex mathematically and the hardest to handle mechanically; you may wish to pare that down to leave you with only Strong and Precise as attack powers.  That would leave the system mechanically balanced. 

Just my 2 cents.

So you're saying if I remove "Fast" the system works fine?

That's a shame; I place a big priority on making the different options "feel" different, and rolling twice really does feel different, you see.

A hit causes 10 damage.  You have a 1 in 3 chance of hitting a 5 defense and a 1 in 6 chance of hitting a 6 defense.

It will take on average 30 rolls to kill a character without considering attribute modifiers. 15 rolls if you're strong and 15 turns if you're fast.
It will take on average 60 rolls to kill a tough character.  If you're strong it takes 30 rolls.  30 turns if you're fast.
It will take 60 rolls on average to kill an agile character.  30 if you're strong.  30 turns if you're fast.

Your math seems fine.  However, the amount of time and rolls it takes for a character to die is absurd.  

In the interest of keeping Fast:

It appears to me that Fast on average will give you a 33% chance for 10 more damage. Strictly speaking, that's weaker than Strong, but it also gives you a chance to hit twice, meaning you are 50% (?) more likely to hit for normal damage, which makes it better than either Strong or Precise. If I were to cut the damage from this extra attack down to 5, would that make it balanced or gimp it too much?

@ Ar Kayon: I am aware of the absurdity, but cutting the HP in like half or fourth for everybody can fix that, right? I just wanted nice, clean numbers to work with (as I'm slow at math) and 100 is a good value for that.

Fast is equivalent to Strong.  It still takes the same amount of turns to kill something whether you are fast or strong.

So that means all these options are perfectly balanced anyway? Sweet.

Let's say instead of 100 HP everyone has 25 HP, and instead of 200 Tough characters have 50. Sounds good?

Ah shit I forgot about precise.   If you're precise, it takes you 20 rolls to kill an agile character.

So Precise needs to be nerfed to +1? 1.5 and then scale everything to d12s?

I did some math by myself and came up with the following version. Still needs to be double-checked -- I'm also still wondering if Agile and Tough are viable choices compared to the three offensive options:

When attacking, you roll 1d6. If the result equals or exceeds the target's Defense (always either 5 or 6) you deal 10 damage. You have 25 HP and a Defense of 5. These are the general rules for combat.

When creating your character, pick three of the following traits:

AGILE = You have a Defense of 6 instead of 5.

FAST = When making an attack, roll an extra attack. This attack gets a +0 bonus and always deals 10 damage, even if you have Precise or Strong.

PRECISE = You add +2 to your attack rolls against opponents with a Defense of 5. You only add +1 to your attack rolls when facing opponents with a Defense of 6.

STRONG = A natural roll of 5 or 6 deals 20 damage instead of 10 if you hit.

TOUGH = You have 50 HP instead of 25.

Why do you state that Fast only deals standard damage, even if you have Precise?  Precise only adds to the chance to hit? 

It might be worthwhile giving another defensive power, perhaps the defender could roll a die and use the greater of the two numbers (Defense or die roll)?  That would approximately match the Fast ability and stack well enough.

if a character has 100 HP and damage is 10...  then why not make the HP 10 and damage be 1?

Also fast could be better if it did 5 damage.  Though I haven't run the math to determine this.

Hmmm... check this out; I added a new defensive option to parallel Fast, and split up the traits into Offensive and Defensive, forcing the player to choose two offensive traits and one defensive trait during character creation (thus removing any concerns I may have had about balancing defensive options with offensive ones). I also scaled the HP from 25 to 30 (and 50 to 60) then divided by 10 to create a nice, simple and almost gritty-feeling wound point system.

---

When attacking, you roll 1d6. If the result equals or exceeds the target's Defense (always either 5 or 6) you deal 1 wound. You have 3 Wound Points and a Defense of 5. These are the general rules for combat.

<< When creating your character, pick two of the following offensive traits >>

- FAST = When making an attack, roll an extra attack. This attack gets a +0 bonus (even if you have Precise), and always deals 1 wound (even if you have Strong).

- PRECISE = You add +2 to your attack rolls when targeting Tough opponents. You only add +1 to your rolls when attacking Agile or Unpredictable opponents.

- STRONG = A natural roll of 5 or 6 deals 2 wounds of damage instead of 1 if you hit.

<< Now pick one of the following defensive traits >>

- AGILE = You have a Defense of 6 instead of 5.

- TOUGH = You have 6 Wound Points instead of 3.

- UNPREDICTABLE = Roll 2d6-1 every time you are subject to an attack roll and use the result as your Defense against that attack.

Randomness favors the underdog, so perhaps Unpredictable is inferior to Agile? They both have an expected value of 6, but I wonder if Unpredictable wouldn't screw you more often than it would help. Maybe an unmodified 2d6 would be better?

Latest version, fixes Unpredictable and adds a critical hit/miss system to increase the HSQ.

When attacking, you roll 1d6. If the result equals or exceeds the target's Defense (always either 5 or 6) you deal 1 point of damage. You have 4 Hit Points and a Defense of 5. On a natural roll of 1, you take 1 damage as you left yourself open and the opponent was able to counterattack. On a natural roll of 6 you deal 2 points of damage because your attack was a critical success. When your Hit Points equal 0, you're out for the count. These are the general rules for combat.

<<When creating your character, pick two of the following offensive traits>>

- FAST = When making an attack, roll an extra attack. This attack gets a +0 bonus (even if you have Precise), and always deals 1 point of damage (even if you have Strong or you rolled a natural 6). You do not suffer damage if you roll a natural 1 on this extra attack.

- PRECISE = You add +2 to your attack rolls when targeting Tough or Unpredictable opponents. You only add +1 to your rolls when attacking Agile opponents.

- STRONG = A natural roll of 5 deals 2 points of damage instead of 1 if you hit. A natural roll of 6 deals 3 damage instead of 2.

<< Now pick one of the following defensive traits >>

- AGILE = You have a Defense of 6 instead of 5. If the attacker rolled a natural 6, you reduce the damage by 1/2 of a point (i.e. criticals give only half bonus to your attackers). You do not reduce the damage if the attacker rolled a natural 6 on the bonus attack granted by the Fast trait.

- TOUGH = You have 8 Hit Points instead of 4.

- UNPREDICTABLE = Every time you are subject to an attack, roll 1d6. On a result of 4, 5, or 6, the attack deals no damage.

Are there certain weapons or strategies that favor particular attributes?

For example, in one of my systems, a quick attack gave you a + to attack but a - to damage.  A strong attack gave you + to damage but - to attack.  Mathematically, these techniques were equivalent, but their natures called for them to be used at different times.  It was difficult to land on an opponent at a normal fighting distance, so opening strategy favored a quick attack.  However, quick attacks didn't tend to cause any actual harm to the opponent, but they would cause stunning.  So once you stunned him and got within closer range, where it's more difficult to see attacks coming, it was advantageous to finish him off with the slower strong attack.

To further illustrate, I double-layered the concept and based each type of attack on a different attribute.  So now you had speedy fighters that liked to soften you up with quick attacks, agile fighters that liked to grapple with you, strong fighters that absorbed punishment in order to close in on you, and dextrous fighters that liked to parry and use your own strength against you. 

Thus, with no mathematic superiority given to any of the system's objects, each one can still have a unique application that makes them conditionally advantageous in one situation but would be inferior to another object for another situation.  As a result, you have a fair system of tactics that manifests different play strategies based upon a character's makeup.

Of course, I don't expect you to apply so much complexity to your own system, I'm just trying to give you ideas on how to manipulate zero-difference objects in order to make them genuinely different from one another, rather than cosmetically.

Frankly, I'm not confident in my ability to design systems that are both functionally different and perfectly balanced. I'm not sure I even want to add a strategic element to this game; my original objective was to have each character be both mathematically balanced enough to be fair and cosmetically diverse enough for each combination to legitimately feel different in play -- as the characters feeling very "samey" is one of the big complaints I have with rules-lite systems.

I could be persuaded to do something along those lines, but if I did that I would likely be better off playing in your game system (which is very impressive by the way).

I've tried my best to tweak things to ensure the balance of this game is as absurdly tight as humanly possible.

Over a period of 6 turns, six rolls will be made on either side. For average's sake, it's assumed that the die will roll a different result in every turn, and furthermore both combatants are rolling the same natural results on each side. Therefore, note that the first entry (assuming a roll of one) for both sides includes a point of damage from the counterattack rule, and the last entry (assuming a roll of 6) includes a point of damage from the critical rule.

FAST vs AGILE

1 - 1
2 -
3 -
4 -
5 -
6 - 1

1 -
2 -
3 -
4 -
5 -
6 - 1

Net Power: 3

FAST vs TOUGH

1 - 1
2 -
3 -
4 -
5 - 1
6 - 2

1 -
2 -
3 -
4 -
5 - 1
6 - 1

6
*0.5 for double HP

Net Power: 3

FAST vs UNPREDICTABLE

1 -
2 -
3 -
4 -
5 - 0.5
6 - 1.5

1 -
2 -
3 -
4 -
5 - 0.5
6 - 0.5

Net Power: 3

PRECISE vs AGILE

2 - 1
3 -
4 -
5 -
6 - 1
7 - 1

Net Power: 3

PRECISE vs TOUGH

3 - 1
4 -
5 - 1
6 - 1
7 - 1
8 - 2

6
*0.5 for double HP

Net Power: 3

PRECISE vs UNPREDICTABLE

3 -
4 -
5 - 0.5
6 - 0.5
7 - 0.5
8 - 1.5

Net Power: 3

STRONG vs AGILE

1 - 1
2 -
3 -
4 -
5 -
6 - 2

Net Power: 3

STRONG vs TOUGH

1 - 1
2 -
3 -
4 -
5 - 2
6 - 3

6
*0.5 for double HP

Net Power: 3

STRONG vs UNPREDICTABLE

1 -
2 -
3 -
4 -
5 - 1
6 - 2

Net Power: 3

When attacking, you roll 1d6. If the result equals or exceeds the target's Defense (always either 5 or 6) you deal 1 point of damage. You have 3 Hit Points and a Defense of 5. On a natural roll of 1, you take 1 damage as you left yourself open and the opponent was able to counterattack. On a natural roll of 6 you deal 2 points of damage because your attack was a critical success. When your Hit Points equal 0, you're down for the count. These are the general rules for combat.

<< When creating your character, pick one of the following offensive traits >>

- FAST = When making an attack, roll an extra attack. This extra attack always deals 1 point of damage (even if you rolled a natural 6). You do not suffer damage if you roll a natural 1 on this extra attack. Both attacks must have the same target.

- PRECISE = You add +2 to your attack rolls when targeting Tough or Unpredictable opponents. You only add +1 to your rolls when attacking Agile opponents.

- STRONG = A natural roll of 5 deals 2 points of damage instead of 1 if you hit. A natural roll of 6 deals 3 damage instead of 2.

<< Now pick one of the following defensive traits >>

- AGILE = You have a Defense of 6 instead of 5. If the attacker rolled a natural 6, you reduce the damage by 1 point (i.e. you are immune to criticals). You do not reduce the damage if the attacker rolled a natural 6 on the bonus attack granted by the Fast trait.

- TOUGH = You have 6 Hit Points instead of 3.

- UNPREDICTABLE = Every time you are subject to an attack, roll 1d6. On a result of 4, 5, or 6, the attack deals no damage. The only exception is if the opponent's attack roll is a natural 6; in this case you take 1 damage (unless the natural six was on the bonus attack granted by the Fast trait). You never leave yourself open to counterattack so you do not take damage when you roll a natural 1.