How to handle degrees of success in roll under systems

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).

• Yes, NPCs also roll for their actions opposed rolls happen PC vs NPC, PC vs PC etc. – Johannes Dec 14 '20 at 20:44
• The Fantasy Trip had a combat system where if A wanted to hit B, A first had to roll under their target number, and then B had to fail to roll under theirs. (This was different from the earlier version of the system in Melee, which lacked the second step.) – Ben Crowell Dec 15 '20 at 1:55
• @BenCrowell That sounds pretty smart and like it would work well. The only problem I see is with this approach is that character who are worse (smaller Target Number) will always be harder to beat, because if they succeed, their roll is naturally low. – Johannes Dec 15 '20 at 7:29
• What is this system intended to do? You want it to be a 2d6 roll-under system, but with degrees of success (which for some reason can't simply be the margin of success), and automatic success and failure, and 1's and 6's having special meaning, and you need opposed rolls... For what purpose? – Mark Wells Dec 16 '20 at 3:09

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).

• Pendragon also uses this (D20 vs. skill, higher wins contested rolls). Plus if your skill is over 20 (often an older knight's lance) the amount over adds to your roll. It works fine. Low-skill has a decent, almost too good, chance. – Owen Reynolds Dec 14 '20 at 20:21

Is there some specific reason why a "blackjack resolution" (i.e. try to roll as high as possible, but no higher than your skill threshold) scheme, with double 1s always succeeding and double 6s always failing, wouldn't work for you?

This scheme would have the following properties:

• It needs no math other than adding up the dice and comparing them to a threshold (and possibly checking for two simple special rolls).

• If the degree of success is determined by the raw dice roll, the character's skill threshold acts as a cap on the degree of success they can achieve. High-skill characters can succeed with flair, while low-skill characters will barely scrape by even if they do succeed.

• The automatic success / failure on double 1s and 6s, assuming no other special effects on these rolls, is equivalent to simply restricting skill thresholds to the range from 2 to 11.

• If you do want double 1s and double 6s to have special effects, the probabilities of these effects won't depend on the character's skill.

Having double 1s and 6s trigger special effects does complicate the system a little, insofar as the "worst possible successful roll" may now actually be the best due to the special handling, and vice versa. But in my opinion this extra complication isn't all that bad, and quite likely tolerable if not harmless.

The only argument I see you giving against this system psychological: you say that it would be "iffy" because it complicates the ranking of rolls, which is certainly true to some extent: in such a system, a roll of 2 (double 1s, critical success) may be better than one summing to 3 (which is merely a marginal success), which can be worse than a sum of 4 (slightly less marginal success), which might again be better than a sum of 5 (if the player's skill threshold happens to be 4).

That said, I don't think the system is particularly complex or unintuitive, if presented clearly. I'd probably describe it something like this:

"Determine your skill level (ranging from 2 to 11) for the task you are attempting and roll 2d6. If the sum of the roll is less than or equal to your skill, the attempt succeeds.

The sum of the roll also determines your degree of success [add explanation of what this means]. Thus, you generally want to roll as high as possible, while not exceeding your skill level. Characters with higher skills can achieve higher successful rolls, and thus higher degrees of success.

As a special case, rolling a sum of 2 (i.e. a pair of ones) counts as a critical success [again, add explanation] and is even better than an 11 (which is the highest possible normal success). On the other hand, a roll of 12 (i.e. a pair of sixes) can never succeed, since skill levels only go up to 11, and is treated as a critical failure."

In particular, lots of dice-rolling and/or card games already have similar mechanics, where an otherwise exceptionally bad roll or hand may actually get special treatment that makes it really good, or vice versa, and players of such games don't seem to mind it. In fact, such exceptions to an otherwise simple result ranking system can make the game psychologically more interesting by giving the players a chance to "seize victory from the jaws of defeat".

Ps. You might also want to consider inventing names for the two special rolls — or perhaps borrowing e.g. "snake eyes" for 2 and "midnight" for 12 from craps — to make the concepts easier to remember and to refer to. Humans tend to like having names for things, especially if the things are somehow exceptional.

• The "blackjack resolution" is probably the easiest way of resolution. The problem I have with it though is that a single 1 and a single 6 also have a special meaning. Hence, rolling a 1 has a positive effect, but especially in a contest you'd want to avoid them, because they lower your degree of success. (see my Clarification for single ones and sixes) – Johannes Dec 15 '20 at 12:47

If I remember correctly, the original Alternity system used a roll under mechanic where the roll was d20+Modifiers vs the skill target number, with precalculated success thresholds of 1/2 and 1/4 of the skill target (rounded down). So with a skill target of 15, a basic success would be 15-, a good success would be 7-, and an exceptional success would be 3-. With the lower values of your system and smaller range of a 2d6 roll, targets of 2/3 and 1/3 (or 3/4 and 1/2) may be a better fit.

• Just to add to this, Alternity's character sheet "expected" you to precalculate the various thresholds for each skill. So if we go with the example above you would write 15 / 7 / 3 on the character sheet. I mention this only because OP is concerned about "mental math fatigue" (fair enough), but from experience playing Alternity it wasn't mentally taxing to compare your roll to these set numbers. – Nichevo Dec 15 '20 at 8:17

Paul's mention of Alternity is absolutely correct in degrees of success and it makes for an easy system with low player and GM workload. Roll your dice and look at the number(s) written on your character sheet.

He missed a bit though, which I think is important to the problem you are grappling with. You are talking about opposed rolls, which I don't think need to happen. You talk about character A and B both rolling for resolving a single action.

Character A shoots at character B. Guns skill for character A. What is character B rolling? Also guns? Dodge? What happens when there isn't an obvious counter-skill in your system?

Alternity handles this by marrying each skill to one of the primary stats. Shooting a gun is (ususally) DEXterity. The player shooting the gun rolls against their gun skill, with any situational modifiers provided by the GM. Situational modifiers are things like range, cover, darkness, fog, etc.

The player rolling then adds the target's res mod - their resistance modifier - to the overall modifier on the roll. The res mod is derived directly from their main stats.

If the target is especially dexterous, this might apply as a +2 modifier (plus modifiers are bad, negative ones are good in a roll-under system) or if the target is a slow beefcake, this might be a -1 modifier. This way every skill has a 'counter' modifier based on the raw stat of the target and only the person taking the action needs to roll.

Update: BBeast brought up in a comment things that I would actually apply opposed rolls for; things like arm wrestling or running a race. Alternity has a tool for this in the form of a complex skill check. The GM would set a threshold needed, in the case of arm wrestling I would probably set it at 10 successes. Each party would roll together until one hits the target. An ordinary would be 1 success, a good would be 2 and an amazing would be 3. In the case of arm wrestling I would apply the opponent's res mod to the rolls, in the case of running a race I wouldn't. Any other situation modifiers would still apply.

PS: you would do well to look into how Alternity does its modifiers too, they are non-linear. In the +2 example above, the player taking the shot would roll a d20 base die and add the result of a d6 to it, then compare that to their skill level.

• What you describe sounds like it works for asymmetric contests. But what happens if two people are trying to beat each other at doing the exact same thing (e.g. arm wrestling, a race, getting a patron to choose you over the other person)? It's possible to arrange a system such that you can declare one entity to be the main actor, but that's a fundamental design choice. Or you could have both parties roll repeatedly until someone fails while the other succeeds, although that has a cost of needing multiple rolls. – BBeast Dec 15 '20 at 11:30
• Those sort of things happen rarely. Alternity would handle it with multiple rolls. The GM would set a target for a complex skill check. Arm wrestling in a bar might have a target of 10 successes. Each party would roll together until one hits the target. An ordinary would be 1 success, a good would be 2 and an amazing would be 3. – Skrrp Dec 15 '20 at 15:43
• @Skrrp Thank you for the clarification, I own Alternity but never got a chance to play it, and it is currently packed away because of a move. Your clarifications just reinforce that I'd really like to get it to the table some time, the mechanics were distinctive from other games of the era, and the settings were very evocative. – Paul Pearce Dec 15 '20 at 16:02
• @Skrrp I think adding that comment to the answer would improve the answer. – BBeast Dec 16 '20 at 5:57
• @BBeast - done, thanks. Paul Pearce - I would strongly recommend you dig it out. I think you'll find a lot of answers to your design questions in there. It's a remarkably simple and flexible system. Aside from standard future-space campaigns I've run wild west scenarios (no change to rules), 40k with homebrew psyker rules (that was fun) and fantasy homebew (Ankh Morpork). There is also the semi-official fantasy ruleset hanging around. – Skrrp Dec 16 '20 at 10:57

Your systems seems really fun! For me it seems that you are worried about doing math and the speed of plays. But that you find it nice to have the difference of skill an impact. One note thought You have a system that encourage to roll under a value but want to give more weight to heavy roll. I found it a bit non-consistent. I am not aware of others system but I have an alternative that you may or not consider.

IMO a way to do it would be to do use threshold and quick math before the role. It would for sure be less quick than others answer but may still give you the feeling of better skill should matter.

The threshold you could use:

• A/ If the opponent skill difference is less than 2 no effect.
• B/ If the opponent difference is between 2 and 5.
• C/ If the difference is over 5.

If you want to stick to the higher role the better: compute the threshold (A, B, C) Make the rolls.

If contested success. The character with the higher skill receive a bonus based on the threshold (case B means +1, case C means + 2 (or +3 adjust to your feeling)). It is not as strong as previously but can change an outcome.

Sure you still have to compute the corresponding threshold. But you do not need to have the exact results just to know if it passes a threshold or not. Which may proves easier.

If you are ok at being consistent. Lower role better, The character with higher skill remove instead of adding value to his/her role.

To go simplify even further because I know this answer is a compromise between speed and accuracy. Let go even further into the simplification. You can use a single threshold like a plus 5 differences. Allow the player with higher skill over this threshold to launch a third die. Then he/she pick the two dies he/she wants from the three dies.

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.

Your "naive" solution is as good as any. With curve-inducing rolls (i.e., summed dice like 2d6 or 3d6 rather than 1d12 or 1d20), every number straying from the median (either above or below) is less likely than the next closer one, so tying in degree of success with what you roll makes sense. In contrast, in most, e.g., d20 systems, if your target number is 15, it doesn't matter if you roll 15, 16, or higher (although most arbitrarily give special meaning to the "natural" 20). But then you have to roll another die (i.e., damage dice in combat) to determine the level of success. Either method gives you opportunities for interesting outcomes.

Nonetheless, the mental effort of subtracting one small number from another is likely to be very small in a group of average minds from the age of, say, 10 on up. Most of the time, you're subtracting single digit numbers from single digit numbers, something most of us learn around the age of six or so. And we add and subtract small one- and two-digit numbers in games all the time, so don't be afraid that elementary school arithmetic will somehow limit the fun of your games.

This sounds fairly similar to GURPS except that GURPS uses 3d6 and the critical system is different.

In GURPS margin is just subtracting your roll from the target number. This works just fine in play. One thing about GURPS is that it has other mechanics besides comparing margins for handling common "opposed roll" situations though so they aren't as common as they might otherwise have been.

Comparing margins is in GURPS a "Quick Contest" used in opposed events that happen once and are over immediately (Stealth vs Perception) Repeated rolls until one side succeeds and the other fails is a "Regular Contest" and are meant to give an opportunity to add roleplaying though the course of a longer contest like a tug-of-war.

Finally, one place you might expect a lot of opposed roles would be attack/defend in combat, but GURPS uses two unopposed rolls with a successful defence roll negating a successful attack roll. By itself this would be boring but mechanics for working around this bias toward defence are where a lot of the tactical fun of the combat system comes from such as making a 'deceptive attack'.

You don't necessarily want to copy all of that (Otherwise you might as well just play GURPS) but it does provide an example of roll under margins working just fine in play in a well known and long lived system and some examples of ways to have more variety in contests than just comparing margins.

• You make an excellent point, that opposed rolls (Quick Contests and Regular Contests) are rare enough that calculating Margins of Success/Failure don't slow down the game, especially if combat implements different mechanics on handling opposed rolls. – Johannes Dec 16 '20 at 10:16

You want two different results from one roll:

1. Whether you succeed: 2d6 under the target number
2. The degree of success REGARDLESS of the target number
3. Example: A double-one can EITHER be a low OR high degree of success
4. Example: A double-six can EITHER be a low OR high degree of failure

The problem is that you can't solve for both results at once with one roll! The decreasing target number range conflicts with the need to have multiple degrees of success that can happen regardless of that target number.

So... what can you do? My suggestion is to instead add a third, differently colored (or numbered) die. This third die would only be used to tell you the degree of success.

This meets the goal of making the degree of success independent from the target number. The downside is that it may be TOO independent! No matter the skill level, you now have identical odds of degree of success.

If you want to mitigate that, there are multiple mechanisms that I've seen used. The best known example is probably PowerAttack from D&D. The player can choose to make the target number worse, but with a better effect if they succeed.