[RPG] How to handle degrees of success in roll under systems

game-designstatistics

I'm working on an RPG system that uses 2d6 roll under Skill for resolutions. On paper this system looks really good so
far, but I have one major issue: Degrees of Success, especially when it comes to Contest (Skill vs Skill) resolutions.

Status Quo

Your character's Attribute + Skill (e.g. Charisma + Persuasion) form a Target Number that's between 2 and 12. You roll 2d6,
sum them, and the sum has to be equal to or lower than the Target Number. Rolling a 1 has a special positive meaning,
rolling a 6 has a special negative meaning. Additionally, 2 ones are always a success, 2 sixes are always a failure,
regardless of Skill.

The problem

Imagine 2 parties contesting each other:

Character A has a Target Number of 5 (pretty bad), and character B has a Target Number of 10 (pretty good).
Character A rolls a 5 and succeeds. Character B and rolls a 6 and succeeds.
Character B has the better Degree of Success, as the margin between the player's roll and the character's Skill is
bigger than for Character A.

If you say that lower is better, a character with Target Number 2 (very, very bad), who rolled a 2, will always have
a better Degree of Success over a character with a Target Number 12 (very, very good), who rolled a 3.

Skill contests mainly occur in combat scenarios, or when two characters are competing against each other. This involves both PCs and NPCs in any combination.

Additionally, the degree of success can be used for any skill check a character attempts. Especially, when the skill check includes a time component, the degree of success is a measurement of how much time did it take?

Clarification for single ones and sixes

A 1 in the current iteration creates what I call an Opportunity, which is a positive side-effect (whether or not the roll was successful). Same goes for 6 what I call a Threat, which is a negative side-effect. So on a double 1 you automatically succeed, and get 2 Opportunities and vice versa for double 6.

This mechanic makes it hard for me to opt for the Blackjack/higher is better variant, as it would seriously flip around meanings of lower is better vs higher is better. If there is a better way of adding additional mechanics to the game to make a roll <= Target Number-system more elaborate, then I might just go with the higher is better variant.

Possible Solutions

Naive solution

My approach was to subtract the rolled number from the character's Skill. You have a Target Number of 6 and rolled a 4?
6-4=2. You have a Target Number of 11 and rolled a 3? 11-3=8. It works, but I'm worried that this resolution will be
too slow for actual play – we all know these sessions that last for hours and nobody is able to count straight anymore.

The best solution would allow a player to determine the Degree of Success/Failure in the same step to see if the
character succeeded or not.

Blackjack

Roll under, but as high as possible. This works best, if there are no special faces/digits you can roll. Unknown Armies
works great, as the only thing special is rolling doubles, and the chance of rolling doubles increases the higher your
Skill is.

In my case, where a 1 has a special effect, Blackjack resolution imposes a problem, as you want to roll as high as
possible.

Is there a system, that has roll under but as high as possible, including special effects on special faces?

Idea – inverted Contests

When you roll a contest, instead of trying to roll under your Target Number, you have to roll over the opponents Target Number. This way, you are more prone to failing against an opponent who's better than you, and a better chance of success against an opponent who's worse than you. Additionally, rolling higher is better. Ties result in a stalemate – this is also nice, as the bell curve of 2d6 means, that average characters will more likely stalemate each other, which I think is not unrealistic. It also enforces the aspect of you're trying to be better than somebody else, not better than everybody else or a specific task.

The issue is that the special meaning of 1s and 6s (Opportunities and Threats) would either have to switch sides, meaning that a 6 you roll would cause a Threat for the opponent, or switch meaning, i.e. a 6 in a contest is suddenly an Opportunity, not a Threat anymore.

On paper I think this idea is pretty good, but they major flaw is the flipping/inverting the whole aspect of the whole roll mechanism when rolling conflicts.

Also it doesn't allow for degree of success for normal checks per se, because normal checks are still roll under.

Are there already systems that do this or something similar? Or do you think this would be too complicated to resolve?

Other systems

Other systems that handle Degrees of Success for rolling under mechanics:

Call of Cthulhu: You have certain threesholds (half your skill, 1/5 your skill) at which you score an increased Degree of Success. – very coarse when you only have 2d6 instead of a 1d100 (but could work)
Unknown Armies: Basically like Blackjack–you roll under your Skill threshold, but as high as possible. Doubles (11, 22, 33) are criticals. – sadly doesn't work, as ones and sixes have a special meaning. Flipping the meaning (6 is good, 1 is bad) also is iffy, as it's flipping the understanding, that you have to roll under a threshold.
???

What other systems or resolution systems are there, that tackle this problem?

Question

I'm looking for feasible solutions on how to implement degree of success in a roll under system. Especially-but not necessarily limited to-in regards of my special rules for single ones and sixes, including the automatic success/failure on double ones and sixes.

Ideally, existing RPG systems already implement these mechanics and proved to be practical in analog play (not computer aided).

Best Answer

Make higher rolls better, assign absolute thresholds for levels of success

This was a solution used by (among others I’m sure) Fading Suns. In their Victory Point system, a player rolled a d20, trying to roll as high as possible while still rolling under the total of their applicable attribute plus applicable skill plus/minus any difficulty modifiers. The higher the roll, the more “victory points” awarded (per a little table on the character sheet), and getting more than an opponent matters.

This system also has some special effects for certain faces, though they differ from yours. If you roll exactly the target, that’s a critical success, doubling your victory points. In addition, a 1 always succeeds, a 19 always fails, and a 20 is a critical fail. (which spoils the otherwise elegant basic idea of “higher is better, up to the limit of your ability”, but still...)

A simpler version of this could work in your case, adjusting for the 2d6’s different probability curve (results in the middle of the range are significantly more likely). But it has the benefit of modelling that someone who is more skilled has a definite edge, as they are not only more likely to succeed but to succeed better.

Another example would be the Resistance Engine used in Spire and Heart; while the basic mechanic is very different (skill equivalents grant you extra dice to roll, and you use your highest single result), the result is directly compared to a table which describes the degree of success, from critical fail, to success at a cost, to complete success and critical success. You could assign absolute thresholds for those sorts of outcomes here, which I suppose is also a bit like Powered by the Apocalypse (with a 7-9 being a hit, and 10+ bestowing bonuses, and 12+ extra bonuses for advanced basic moves).

Does the "Degree of Success" Approach Require More Arithmetic?

Not inherently.

In particular, if you use roll-and-count dice pools rather than roll-and-add math, then players can find the degree of success just by sorting dice side-by-side. This still takes time but isn't as sensitive to players' math skills or level of fatigue.

Does Using "Degrees of Success" Over "Hit, Then Damage" Restrict Tactical Options or Character Variety?

Not inherently.

For instance, if you want to create a niche for a big-damage weapon, it's as easy as "If you win the attack, +2s to damage." This weapon has a very different feel from a more "balanced" weapon with "+1d to attack and defense rolls." Ditto you can create a niche for a big-damage character by just writing something like "Add your Strength to damage when you hit." (Or how about "Margin of success add damage to your hit, up to your Strength number?")

One notable way that "degrees of success" changes back-and-forth damage math is that defense still benefits you even if it falls short of stopping the attack. Consider a system where we roll attack vs. parry — I roll 5 on my attack, you get 4 on your defense: in a "to hit, then damage" system, that's a straight-up failure for you and I get to roll my damage just as if we had 5 vs. 1; in a "degrees of success" system, you've turned a potential killing blow into a glancing one.

The "Realism" Question

Defining what's "realistic" is incredibly tricky here.

Smaller weapons aren't inherently more "agile," because you don't fight with a longsword by just sweeping it back and forth in wide arcs.

Real armor both deflects blows and dissipates some of the their energy. Weapons designed to defeat armor act very differently than those which aren't.

Realistically, a cunning thief with a dagger isn't going to be able to hurt an enemy in gothic plate with "fast" or even "precise" attacks. She needs to straight-up wrestle him into a position where that blade can actually do its job.

If you've chosen to use abstract hit points, your system is already privileging gameplay or genre considerations over "realism." Embrace that! Figure out how you want combat to feel and that'll drive whether you use separate or combined damage, static defense or opposed checks, &c. Just remember that a lot of what seems "realistic" based on other media is just a set of narrative conventions.

I Want Fast Resolution, What Should I Do?

I don't think there's a major difference between separate damage rolls or degree of success, at least compared to other factors like how many modifiers are involved or the size of a dice pool.

Really, though, if you want the fastest resolution of combat, decrease the number of actions involved overall (one opposed die roll with ten situational modifiers is still going to be faster than an entire combat encounter in D&D3/D&D4), and reduce decision points that are exceedingly opaque or offer only trivial benefits.

[RPG] How to model Burning Wheel probabilities in AnyDice

AnyDice handles exploding dice in a peculiar fashion that's poorly-suited for roll-and-count dice pools. I have cobbled together a somewhat inelegant solution, but it appears to work correctly.

Here's the link to the program.

Instead of using dice in the usual manner, I've created several functions that, given parameters of a die, return its output, i.e. the number of successes it has produced.

function: roll ROLL:n threshold T {
  if ROLL >=T {result: 1}
  result: 0
}

function: rollexploding ROLL:n threshold T{
  if ROLL =6 {result: 1+[rollexploding 1d6 threshold T]}
  result: [roll ROLL threshold T]
}

function: rerollfailures ROLL:n threshold T{
  if ROLL < T {result: [roll 1d6 threshold T]}
  result: [roll ROLL threshold T]
}

function: rerollthenexplode ROLL: n threshold T {
  if ROLL < T {result: [rollexploding 1d6 threshold T]}
  result: [rollexploding ROLL threshold T]
}

Then I made a wrapper function that would figure out which of these functions to call, and handle requests for multiple dice being rolled:

function: wrapper DICE:n threshold T explode E reroll R{
  RES:0
  loop N over {1..DICE} {
    if E & R {RES: RES+[rerollthenexplode 1d6 threshold T]}
    else {if E {RES:RES+[rollexploding 1d6 threshold T]}
      else {if R {RES:RES+[rerollfailures 1d6 threshold T]}
        else {RES:RES+[roll 1d6 threshold T]}
      }
    }
  }
  result:RES
}

Finally, I made a bunch of functions that simplify input by providing pre-determined combinations of parameters. I'll provide only 3 of them here:

function: b DICE:n{
  result:[wrapper DICE threshold 4 explode 0 reroll 0]
}

function: be DICE:n{
  result:[wrapper DICE threshold 4 explode 1 reroll 0]
}

function: gr DICE:n{
  result:[wrapper DICE threshold 3 explode 0 reroll 1]
}

To use it, type things like output [b 4]