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One problem. Two characters with the same Skill. How do they combine abilities to make the problem easier to solve? Or are two heads no better than one? This is the Dual Competence rules problem.

Another problem. One character has the Skill needed to solve it, another who doesn’t – but who has to actually do the work, acting as the eyes and ears of the first. Is the second character a help or a hindrance? To what extent? This is the Two Places At Once rules problem.

A third problem. Two characters, one with the relevant skill, one with a related skill. Both need to work together to succeed.
This is the Combined Competence rules problem.

A fourth problem. There’s a large weight to be lifted, or a heavy door to break down. It’s going to take the efforts of more than one character to achieve the desired result. How do you correlate their attempts into a straightforward success or failure? This is the Universal Shoulder-To-The-Grindstone rules problem.

A fifth problem. It would normally need two or more characters acting in a coordinated fashion to solve it – but the only character in the vicinity is on his or her own. How much more difficult is it to find and apply a solution? This is the Two-Is-Less-Than-Many-Hands problem.

Most game systems ignore these questions entirely, putting them into the too-hard basket, especially when you realize that the one set of procedures/rules (ideally) have to handle all five problems. Is that even possible?

I have to admit that this article has sat around unfinished – practically un-started, to be honest – for the best part of a year because I found the subject matter so daunting. Well, it’s not going to get any easier just sitting there, and if it’s a daunting subject for me, how much more problematic must it be for a GM with less experience? So I’m biting the bullet…

These are all instances of the correlation of two skills or abilities possessed by different characters combining in some way to achieve outcomes that are more difficult, or even outright impossible, for one alone. They are the sort of problems that crop up with great regularity in real-world play – from two characters combining to research something in a library, to multiple characters searching a room, to a craftsman and an apprentice working together to make something (the latter presumably under the direction of the former), to a team trying to move a football from one end of the playing field to the other.

Typically, the only aspect of rules which is in any way similar that is addressed by rules systems are the existence of Flanking rules for Combat, and these often feel tacked on or superficial, mostly concentrating on the question of whether or not the rules apply in a given case. Little or no profound thought is spent on exactly what the impact of achieving flanking actually is – if for no other reason than anything other than outrageous oversimplification quickly bloats out with variables that distinguish one situation from another.

Not exactly a template to be considered analogous to a solution to these other problems, then.

Potential Solutions

Most GMs will quickly come up with five possible solutions. Those with any knowledge of probability and a little time on their hands will usually think of a sixth. I’m going to add a seventh to that list that would only occur to anyone with some familiarity with D&D 5e (actually, I’m dropping it into the list at a point where that seems appropriate).

These are the building blocks of solutions to the problems posed at the start of the article. Which one provides the best solution to a specific problem, and whether or not a common one-size-fits-all solution can be identified, will need to be determined after I’ve taken a hard look at these potential solutions. It’s even possible that none of these solutions will be ideal, or even workable.

The possible solutions are:

1. Add skills/ranks/stats/stat modifiers together, one player rolls for both characters?
2. Add a fixed bonus/penalty if second character makes their roll.
3. Add a scaled variable bonus/penalty if the second character makes their roll.
4. Add a capped bonus/penalty if the second character makes their roll.
5. Second character success confers advantage to the first; both must succeed.
6. Multiply chances of success?
7. Multiply chances of failure?

Add skills/ranks/stats/stat modifiers together, one player rolls for both characters?

This is an obvious technique when it comes to stats, such as multiple characters combining their strengths. Many GMs then extrapolate the same approach to the other questions by combining other numeric variables. And yet, while on the surface, this seems like a sound approach, it is easily demonstrated that it is incomplete and inadequate as it stands.

Contemplate a tug-of-war. If simply adding the strengths of the different individuals on each side together and comparing the totals were all that was involved, the same team would win every time – or, if evenly matched, neither would ever win. Clearly, this doesn’t happen in real life – so there clearly needs to be some kind of die roll involved, and that propels us into the realm of one of the other answers.

Nevertheless, the concept that some numeric value associated with a character may be applied to another character, perhaps in scaled or modified or capped form, may be a vital one and is worth noting for future reference.

A second problem stems from the perfection of the act of totaling values in this way. There’s no loss for redundancy of effort, no wastage from overlapping efforts. Again, it seems unlikely that this matches real-world experience, though it does suggest a possible nature for the required variability – that when numeric values accumulate through mutual effort, the total contribution of an individual represents a theoretical maximum, with reality being a fraction (large or small) of that theoretical total. Another principle that might be important!

Add a fixed bonus/penalty if second character makes their roll.

This seems to answer most of the skill-related problems raised, at least at first glance, and for a long time, this was the approach that I took. I even extrapolated backwards, applying this principle to attempts to combine stats.

Without bogging too deeply down in mechanics, lets look at how it functions: Character 1 has the greatest expertise or greatest contributing stat. He has, say, a 60% chance of success. Character 2 has a considerably small contribution to make – 40%, say. The concept would be that if character 2 succeed in his low-probability attempt, he confers a bonus to character 1’s attempt, and if character 1 also succeeds, then the group effort as a whole succeeds. The bonus could be as little as 5% or 10%, or as much as 35% or 40%. Assuming a d20 roll, those are the equivalent of +1 through to +8, the latter being as much as the character has to give.

How to decide what the bonus should be? Well, in this case – assuming we’re talking D&D/Pathfinder – I would fall back on a principle that I have noted previously in the scale of bonuses from magic items and feats. As a general rule, these confer +2 to a stat (i.e. +1 to a stat bonus) or 2 lots of +2 to separate skills, or one lot of +4 to a single skill. This works because it implies a focusing of the effects – +1 to all abilities deriving from a particular stat, or +2 to a narrowly-defined subset of related abilities, or +4 to a single specific capability. I’ve even inferred from these relationships that it should be theoretically possible to confer +1 to four specific, related, skills in the same way – something that’s proved useful as a theoretical model from time to time – or even +2 to one and +1 to two others, all more or less equivalent.

Well, this is clearly one specific application of the principle of combining abilities, so I would argue in favor of +4, or +20%, being the fixed contribution.

So far, then, so good. But the whole structure is about to come crashing down. Why? The bonus conferred is all-or-nothing. It doesn’t matter if the second character’s chance of success is 10% or 55% (having defined it as less than that of the first character) – if the character is successful, the first character gets +X to his chances. In the abstract, this seems reasonable, but it trivializes the contribution of the second character in a way that might not sit well with players over the long term. What’s more, there’s no capacity in this system for incompetence to get in the way. If a character with a chance of success of only 10% tries to help out, there should be at least some risk of them being more hindrance than help.

Part of the problem is that there’s a limited window for improvement to the first character’s chances – in the example cited, that’s only 40%. If the first character’s chances were 80%, there would only be 20%. Less, if the system defined a given natural result as an “always fails”, which some do.

So, for these reasons, the results seem inadequate to reasonable needs. We may need to look further.

But there is a variation to consider before we abandon this line of thought altogether. The second character’s attempted assistance could simply provide a fixed bonus to the first character with no need for the second character to roll at all. This interprets the assistance rendered purely in terms of its effect on the capabilities of the first character, and is a far simpler solution in real-world play.

It doesn’t take much thought to discover the flaw in this arrangement, however. Taking our example of 60% again, character 1 is 40% away from certain success (or 35% away from near-certain success if that’s as close as he can get). If each character assisting is worth +1 on d20, then he simply recruits 8 (or 7) of them. If they contribute +2, he needs 4 assistants to succeed every time (or almost every time). And it doesn’t matter how incompetent those assistants are, how ham-fisted or feeble-thumbed. Even a total incompetent only needs 20 assistants to be perfectly capable. I’m sorry, that just won’t cut it.

But this does extract a valuable principle – each participant in a shared activity needs to make a roll of some sort to determine their contribution to the group’s success. And, ideally, they should contribute a greater risk as well as a greater potential for success.

Add a scaled variable bonus/penalty if the second character makes their roll.

One solution to these needs is to measure the amount by which the second character succeeds, then apply that amount – perhaps scaled – as a bonus or penalty to the chances of the first, who is then rolling for the ultimate success or failure of the group activity.

This certainly answers all the objections raised about the preceding solution, which is why this is the model that I eventually settled on for both my 3.x house rules and the official rules of my home-brew superhero campaign. But it might not be the final word on the subject; it’s simply a workable solution.

A key question must be what scaling to apply. First, should any scaling be linear, or non-linear in nature? Linear involves simple mathematics, non-linear makes extremes far less likely and seems more realistic as a result.

If the 2nd character only succeeds or fails by a small amount, something close to a 1-to-1 scale seems appropriate – succeed by 1, add +1; succeed by 2, add +2; and so on. But from the +3 point onwards, that seems to grow too large, too quickly. That argues against the use of a simple scale.

My instinct would be to double intervals. So, succeed at all, and you get +1. The interval between no success and some contribution is 1. Double that to get to the next threshold and you can see that success by 2 or 3 yields +2. Double again, and success by 4, 5, 6, or 7 yields +3. Double once more, and success by 8, 9, 10, 11, 12, 13, 14, or 15 gives you +4. And success by more (on a d20) might give you +5. Similarly, failure could yield -1 all the way down to -5.

Suddenly, the competence of an assistant matters, but is not all-important. When you bring in multiple assistants, however, even this starts to look a little extreme. So how about tripling the intervals instead? Succeed by 1 or 2 and you contribute +1. Succeed by 3-5 and you contribute +2. Succeed by 6-14 and it’s +3. Succeed by 15-20, and it’s +4. And you have to allow for the possibility that another of the multiple assistants will fail by a similar amount.

There are other options. My aforementioned superhero campaign rules double the number of assistants needed for a potential bonus. The number who succeed in their checks is the number who contribute. At one point, I looked at using the total margin of success by all of them as a percentage of the accumulated potential margin to determine the fraction of the potential contribution actually passed on. Practical considerations – a team of 100 researchers under the direction of a chief scientist would have required 100 skill checks – put the kibosh on that notion. Instead, I chose the option of differential thresholds of skill, which is a little more complicated to explain. In a nutshell, it divides the “assistants” into ever-growing “bands” of competence, and doubles the number of each more-incompetent band required to equal a single member of the next less-incompetent band, while placing a cap on the number who could occupy a given band (which also doubles).

You could have 1 Grade-1 Assistant, 2 Grade-2 Assistants are the equivalent of a second Grade-1 assistant, 4 Grade-3 makes a single additional Grade-2, 8 Grade-4’s make a single additional Grade-3, and so on. Maximums are 1, 4, 16, 64, 256, 1024, and so on. Each band is 25% wide in skills (the system is d%-based). So, if the lead researcher has a 60% skill, Grade-1 assistants are those with skill between 35-59%, Grade-2 are 10-34%, Grade-3 are -15%-9%, and so on (the system sets 0% as the minimum skill needed to employ a skill to a professional standard, and the total skill range is -140% to +140%), so Grade-3 are university students and new graduates, and Grade-4’s are secretaries and janitors and the like.

Your first grade-1 assistant can add 20%, each successive equivalent to a grade-1 assistant – or, more accurately, given the maximum populations stated, each grade-2 assistant or equivalent can add +10% (up to a maximum of +10Î4=+40%). Each grade-3 assistant or equivalent not already contributing can add +5% (up to a maximum of +5Î16=+80%). In theory, each grade-4 assistant or equivalent not already contributing can add +1% (up to a maximum of +1Î64=+64%), but there is a maximum modifier permitted within the system of plus-or-minus-150%, and assistant grades 1 to 3 (or equivalents) already account for +140% out of the +150% cap.

Of course, there’s nothing to prevent you having more grade-4’s than can contribute – or even splitting your forces (i.e. making your grade-1 a researcher looking into some separate problem). You can have assistants that are almost as competent as you are, or a lot more assistants that are barely fit to wash your beakers out, or any combination in between.

Something like this is necessary when institutional research becomes possible and relevant, i.e. in Sci-Fi and Superhero campaigns (but even there, I have it apply only when absolutely necessary; the rest of the time, I’d use a modified form of the first system). In a Pulp campaign, discoveries are made at the speed of plot, and maverick lunatics are just as likely to come up with impossible-to-replicate results as a world-class university professor. In anything more primitive than the pulp era, the number of assistants you can have is so restricted by economics and politico-social structures that simpler models are adequate.

The takeaway of greatest significance is that any hope of a “universal solution” should be regarded as pie-in-the-sky.

Getting back to it, then, we seem to have an adequate answer for D&D/Pathfinder and other similar Fantasy Games, and for Pulp games for that matter. There may be better answers, but at least we have a fallback position.

Add a capped bonus/penalty if the second character makes their roll.

Rather than a non-linear scale, perhaps the idea of a linear scale can be salvaged by adding in a cap to the advantage or penalty. At least, that’s the question that quickly occurs. But capped to what? +2? +3? Anything more, and you might as well not have the cap. Frankly, this doesn’t really add anything, and enthusiasm for it as a solution is likely to quickly fade.

Second character success confers advantage to the first; both must succeed.

This is an interesting idea drawn straight from D&D 5e. If the assisting character succeeds in his roll, he gives the second character a mulligan that he can exercise in the event of failure, and perhaps a small bonus if he succeeds by a relatively substantial amount – say, +1 if the assistant succeeds by 6 or more.

What’s immediately missing from this formulation is the question of incompetence. But we can modify the notion to provide it: If the assistant fails by a certain amount or more, he confers an anti-advantage upon the main character attempting whatever it is. Balance suggests that it should match the threshold to the added bonus – so this might require a failure by 6.

What’s an anti-advantage? Well, “advantage” lets you re-roll – once – if you fail. So an anti-advantage forces you to re-roll – once – if you don’t fail. Or, you could phrase them, respectively, as rolling 2 dice and choosing the best result or the worst – they mean the same thing.

This solution even scales to accommodate multiple assistants, if you’re lucky enough to have them. Two assistants, say: the following combinations are possible: 1) Bonus+Advantage from both; 2) Bonus+Advantage from one, Advantage from the other; 3) Bonus+Advantage from one, Anti-Advantage from the other; 4) Advantage from one, Advantage from the other; 5) Advantage from one, Anti-Advantage from the other; or 6) Anti-advantage from both.

The two options available are clearly either “advantage stacks” or “advantage doesn’t”; the first scales more genuinely, the second is more consistent with normal 5e practice.

The option 1 outcomes for the 6 combinations listed would be: 1) Double Bonus+2 re-rolls if needed; 2) Bonus+2 re-rolls if necessary; 3) Bonus, no re-rolls; 4) 2 re-rolls if necessary; 5) you’re on your own!; and 6) 2 re-rolls must succeed before overall success can be achieved. Overall, there is a substantial benefit to having multiple assistants, but it comes mostly from evening out the risk of one of them failing.

The option 2 outcomes for the 6 combinations listed would be: 1) Double bonus +1 re-roll if needed; 2) Bonus +1 re-roll if needed; 3) Bonus only; 4) re-roll once if needed; 5) you’re on your own; 6) must re-roll once if you don’t fail the 1st time. That’s three of the possible outcomes that give a re-roll, and two of the remainder that confer no penalty.

Personally, I would choose to simplify the mechanics by choosing option 2.

The flaws in this proposal are those that are inherent in the Advantage-re-roll mechanic, which I analyzed back in 2012 in On The Edge: Implications of the D&DNext Advantage mechanic. In a nutshell, the lower your chance of success, the less benefit you get out of a re-roll because you are still likely to fail the second time around; the higher your chance of success, the less benefit you get from a re-roll because you are less likely to need one, and the maximum benefit (worth +25%) comes at an 11-or-less chance, but so does the maximum penalty from the other side being advantaged. In other words, the game system both rewards and punishes mediocrity disproportionately. If you are highly skilled, you have less need of advantage and are less concerned with the other side having advantage, and if you are very poorly skilled, neither will have much of an impact.

This makes it very hard to work out exactly what a character should need to succeed in any attempt to do anything, at least in comparison to a simpler mechanism. Presumably, if you’re playing 5e already, you’re used to doing so, in which case this might be your ideal solution by virtue of the consistency with the rest of the game system.

For anyone else – interesting idea, but no. The downsides are too great, and the fact that it would bear no resemblance to the game mechanics used elsewhere in the game system are a distinct negative.

Multiply chances of success?

When I was very much younger, an even younger player who knew just enough to get himself into trouble suggested that this was the way to go. I didn’t buy it then, and I don’t buy it now, and some simple examples will show why. Let’s look at the effects for three different main characters (50%, 60%, and 80% chance of success) with (a) no assistance; (b) a 10% assistant; and (c) a 50% assistant.

Assumption: attempting to do a 2-person job single-handed is worth +2 to the target number, i.e. -10% chance of success. (Note, however, that I would normally use a +5 value – this will be shown to significant later).

Aa: 50%-10%=40% chance of success.
Ab: 50%x10%=5% chance of success. Red flag #1.
Ac: 50%x50%=25% chance of success. Red flag #1.
Red flag #1: The main character is better off with no assistant.

Ba: 60%-10%=50% chance of success.
Bb: 60%x10%=6% chance of success. Red flag #2.
Bc: 60%x50%=30% chance of success. Red flag #2.
Red Flag#2: Having an assistant minimizes the benefit of greater skill.

Ca: 80%-10%=70% chance of success. Red flag #3.
Cb: 80%x10%=8% chance of success. Red flag #1. Again.
Cc: 80%x50%=40% chance of success. Red flag #1. Again & Again.
Red flag #3: the higher your skill, the more relatively insignificant the penalty for not having enough hands becomes, so the less you need an assistant – not that you ever DO get any positive benefit out of an assistant.

It’s simple mathematics, really: if you need to succeed with both rolls, the fewer the rolls you have to make, the more likely you are to succeed. To determine the chance of succeeding on all rolls when that is what’s needed, multiply the individual chances of success together.

Unfortunately, this kind of throws some cold water over every suggested solution, even the standby one – because they are ALL of the “both rolls need to succeed” variety other than the already-rejected simple-modifier-for-assistance model. I’ll come back to that in a moment.

Multiply chances of failure?

No, the correct mathematical approach to any set of rolls in which only one of them needs to succeed is to multiply the chances of failure together to determine the net chance of failure.

Let’s run those same series of calculations from the previous section over again, and you’ll see what I mean.

Aa: 50%-10%=40% chance of success.
Ab: 50%x90%=45% chance of failure = 55% chance of success.
Ac: 50%x50%=25% chance of failure = 75% chance of success.
There is a definite benefit to having an assistant and it is proportionate to the skill of the assistant.

Ba: 60%-10%=50% chance of success.
Bb: 40%x90%=36% chance of failure = 64% chance of success.
Bc: 40%x50%=20% chance of failure = 80% chance of success.
With increasing skill, the benefits of having an assistant diminish…

Ca: 80%-10%=70% chance of success. Red flag #3.
Cb: 20%x90%=18% chance of failure = 82% chance of success.
Cc: 20%x50%=10% chance of failure = 90% chance of success.
….but never vanish entirely.

There’s a lot more work, because first you have to convert chances of success into chances of failure, then do the multiplication to get the net chance of failure, then convert that into the net chance of success. But it gives the right answers.

So it’s impractical as a solution, but provides an appropriate answer in principle.

The question now is, is either the above or the discredited “multiply chances of success” relevant to that default answer, or to the “industrial scale” answer that I placed in the sidebar?

At first glance, the answer may appear to be ‘yes’ with respect to the “chances of success”. However, closer examination shows that the question is mis-phrased. It’s only ‘yes’ if the question is to maximize the likelihood of success AND capitalize on it. The fact that the assistant can fail and the overall task still be successful means that the two rolls are decoupled, and so neither of the models of coupling rolls – multiplying chances of success, or of failure – are relevant.

The Partial problem perspective

Part of the reason why I (and probably you) feel like we’re groping our way towards a solution is because we haven’t actually defined exactly what “assistance” means. Does it mean making it easier for the main character to solve the whole thing? Does it mean solving (or attempting to solve) a smaller part of the whole, one that is commensurate with his relative skill?

There was a time when the latter set of possibilities would not even have occurred to me; GMing TORG expanded my horizons enormously. In particular, as I have stated before, TORG divides tasks into simple and complex. Simple tasks can be performed by a single character executing a single die roll, or even by simply stating their intent if the GM is feeling generously-disposed. Complex tasks are things like evading pursuit in a car-chase, or defusing a bomb. The key distinction is usually the tension that can result from only achieving a partial success with a single successful roll – if the tension doesn’t ramp up, it’s not worth making it a complex task.

Complex tasks are divided into four stages. These can all be the same difficulty, or the difficulty can vary – a lot depends on the GM’s ability to divide the overall task into four processes or procedures in his own mind, then assess them individually. Nor do all these tasks have to be completed by the same character – genuine team efforts assume new dimensions when assessed in this light.

So, under most circumstances, I would lean towards the “Partial Problem” perspective, with the Assistant or Assistants solving only one of them – and, should they fail to do so, with the main protagonist of the situation having the opportunity to salvage the situation.

A related thought presents itself, however: Can the protagonist improve his chances of success by dealing with the remaining three processes or procedures individually? How can you decide what the right difficulty levels should be?

Well, depending on the circumstances, the protagonist may or may not be able to recover from a failure by the assistant. if he can, then the die rolls are still decoupled; if not, we’re back at a situation in which both phases need to be successful, a coupled roll in which each of the sub-rolls must succeed.

In the latter circumstance, the probability of success overall is equal to the product of the chances of success of each of the stages. If you want the PCs to have a 50% chance of success, or think that that’s appropriate to what they are trying to achieve, then the formula is a% x b% = 50Î100. If b% is, say, 20 – defined as the % chance of the assistant helping to solve the problem – then a% = 250%. But a% is, under the TORG model, comprised of 3 more rolls – call them a1%, a2%, and a3% – and those also have to be factored in. Let’s say that a1% is 75%, and a2% is 60%, then a3 x100 = 250Î100/75/60, or 20/36 – roughly 56%.

But a better approach is to work with target numbers. If the entire task has a target number (a DC) of, say, 40, then you can say that “a1 x a2 x a3 x b = 40Î20Î20Î20”. And, as soon as you see it laid out in that way, you can see that anything over DC 20 in a2, a3, and b reduces the twice-as-high DC of a1. So setting two of them to DC 25 gives DC 40Î16/25 = DC 25.6 – you could call it DC 25, or DC 26 if less charitable. So, to get an overall DC 40, the assistant has to make one DC 20 check and the protagonist three DC 25 checks.

Multiplication of four numbers is difficult to do in your head, though, and if you throw in some division as well… it would be far more preferable to find some approximation that used addition and subtraction, even if it were less accurate.

Fortunately, there is something that will do the job: Overall DC = the sum of all (individual check DCs minus 10). So, if there are to be four checks, and the target is DC 40, the calculation is a1+a2+a3+b-40=40. So any combination that adds up to DC 80 would be satisfactory – something like 25, 25, 20 and 10, for example.

This is superior because these are absolute targets, and the chance of success then incorporates individual skill levels. You can even leave it up to the protagonist how much responsibility he is going to allocate to the assistant, or can define the targets yourself.

The upshot is that we now have multiple viable solutions to the problem, and we can pick and choose between depending on the circumstance and needs.

Reassessing the Five Questions

So, let’s take another look at those five questions and see where we end up.

The Dual Competence problem

Two characters with the same Skill. How do they combine abilities to make the problem easier to solve? Or are two heads no better than one?

Okay, the two may have the same skill, but they won’t necessarily have it to the same degree. Mathematically, if the second character’s skill or stat roll is less than half that of the more proficient character, the latter is better proceeding alone unless he needs help – in which case, this is really a Universal Shoulder-To-The-Grindstone problem.

All of our potential solutions apply.

• Second character success gives a scaled bonus to the overall task:

  The critical decisions that the GM needs to make is what the relative Difficulty targets are going to be, because his roll is assessed in terms of degree of success or failure, which then provides a modifier to the protagonist’s roll.

  • Setting the assistant’s roll low means he is more likely to confer a bonus to the protagonist. However, it probably means that the protagonist’s roll is going to be against a harder target. Setting the roll high means that it’s extremely unlikely that his contribution will be helpful; that might be appropriate for an extremely technical task, but most of the time, it will be counterproductive in terms of game-play. In either case, this is still dividing the overall target DC into two rolls of unequal size.
  • If the assistant’s target is 12, and the overall target is 15, the assistant is accounting for just 2 of that overall total (12-10=2).
  • That leaves 13 for the protagonist to contribute, which sets his DC to 23. However, if the assistant does well, he could potentially give the protagonist a +5 bonus, effectively dropping the DC target to 18. If the protagonist already has stat bonuses of +4 and another 4 in relevant skill ranks, that would give him a better than 50-50 chance – he needs 10 or better on his die roll.
  • Compare that to the no-assistant alternative: DC 15, less 8, is 7. So the protagonist would succeed on a 7 or better – IF the GM didn’t penalize the DC because the character is attempting to do solo what should be the work of two people. A penalty of +2 to the DC leaves him slightly better off solo than using an assistant; a penalty of +3 leaves things evenly balanced; a penalty of more than +3 makes the assistant a better bet.

• Second character success confers Advantage to the protagonist (with a bonus if success is great enough); second character failure by a like amount confers Disadvantage to the protagonist.

  Once again, the critical decision to be made is in the form of the relative Difficulty targets. These establish whether or not the protagonist has Advantage, which can markedly impact on his chances of success (depending on his ability and the Difficulty that he has to achieve).

  • Setting the assistant’s target is more involved using this system. If you set it relatively low, you are more likely to confer advantage on the protagonist, and the commensurate increase in his target number makes that more beneficial. If you set it relatively high, you are more likely to confer disadvantage on the protagonist, but the commensurate reduction in his target number may make that less significant. On this occasion, it’s the “low assistant target” that is more appropriate to a highly-technical situation, and – unless some such consideration was in play – I would do my best to achieve a balanced outcome, i.e. one in which the assistant had a 50/50 chance of success.
  • If the assistant has +2 in stat bonuses, and +1 in skill ranks, a target of 14 would require a roll of 11 or better – which is 50/50 by definition. Once again, we need to split the overall DC of 15; 15=(a-10)+(14-10)=a-6 So a=21, and that’s the DC for the protagonist.
  • Half the time, the assistant will confer advantage on the protagonist. He has +4 from stats and +4 from skills, so his first roll has a target of 21-8=13 (or better). If he fails, (60% chance), he needs to hope that his re-roll salvages the situation; 60% of the time, it won’t. 60% of 60% is 36%, so his overall chance of success is 64%. If the assistant did well enough to also confer a +1 or +2 bonus, those numbers become 55% of 55% (=30%, 70% success) or 50% of 50% (75% overall success chance), respectively.
  • Less than 25% of the time, the assistant will confer a disadvantage. His target remains a DC of 21. There’s a 60% chance that he will fail immediately; if he doesn’t, there’s a 60% chance of a 40% chance that he will fail on the second roll, or 24% So there’s a total of 84% of ways that he can fail, leaving only a 16% chance of success. The success or failure of the assistant is close to make-or-break.
  • Without the assistant, the protagonist faces a +5 DC for attempting the task solo on the overall target of DC 15. So he needs 12 or better on the die roll, and has no second chances. The character is slightly better off not having an assistant. However, if the assistant gains just one or two more skill ranks, the increased likelihood of having advantage – or, more likely, the reduction in the DC target of the protagonist – more than compensates.

The Two Places At Once problem

One character with the Skill to solve a problem, another without – but who has to actually do the work, acting as the eyes and ears of the first character. Is the second character a help or a hindrance, and to what extent?

This throws a number of complications into the mix. The “protagonist” is now the lower-skilled member of the pair, possibly even having no skill at all (relying on native stat rolls). I have the vague memory that this automatically confers Disadvantage in 5e. On top of that, the character with the skill has visualize the situation from the protagonist’s description without being able to see what’s going on for himself, which has to be worth at least +2 and possibly more to the difficulty, and then has to issue clear, concise, and timely instructions to the protagonist (another +2 or more), who needs to comprehend them (+2 or more to the protagonist’s roll). The rest is the protagonist devising the correct solution and the antagonist correctly implementing it, which is to say the normal rolls.

Frankly, if the party gets out of this with the protagonist only getting +2 difficulty and the adviser only getting +4, they should count their lucky stars. Once again, the technicality of the task is a major consideration – if the task is extremely technical, +5 and +10 might be more appropriate, if it’s not, the +2 and +4 beckon. In between yields in-between numbers.

So let’s assume +3 and +7, respectively. Which means that we can disregard those complications until the last minute, and simply treat the task as a normal one.

• Second character success gives a scaled bonus to the overall task:

  This works exactly the same as it did above, assuming the same overall and relative DC base targets – but the roles of protagonist and “assistant” are reversed.

  • So we have a protagonist with +2 and +1; and an “assistant” with +4 and +4, who is taking the bulk of the base difficulty. If the overall DC is to be 15 (ignoring all those complications), that gives base DCs of 12 and 23 respectively, just as last time.
  • Once those numbers are known, we can apply the additional complications (DCs of 12+3=15 and 23+6=29, respectively), and then start to contemplate the outcomes.
  • A DC of 29 means that the assistant needs to roll 21 or better to succeed. So a foul-up somewhere along the line is inevitable. The vast likelihood is that the assistant will confer a -2 to -4 penalty to the protagonist, on top of everything else.
  • A DC of 15 would normally require a roll of 12 or better. If the penalty from the assistant is -2, that goes up to 14; if -4, it goes to 16. So the scale of the problem is such that it is possible to succeed – but difficult.

  But, if I was running a PC in this situation, I would anticipate the difficulties and do whatever I could to ameliorate the situation. If I could take extra time and double-check everything, I would make a point of it. If I could simplify the complexity of the overall task, perhaps being less ambitious, I would. In fact, I would probably overcompensate. This holds the potential of eliminating or even reversing those penalties, increasing the likelihood of success.

  And, as a GM, if I were to put characters into this sort of situation, I would ensure that I had provided the opportunity for characters to react in this way. I would rather the characters attempt something moderately difficult and succeed than attempt something more ambitious and die trying when it wasn’t necessary.

  It’s also worth pointing out that this all postulates a situation in which the expertise of the “adviser” is critical to success. If it’s as simple as draining the sump and filling the gas tank with sand, the degree of expertise required goes way down, and the overall difficulty should plummet accordingly.

• Using Advantage/Disadvantage

  Once again, and with the concluding caveats still in mind, this is also exactly the same as last time up to the point where we start resolving outcomes.

  • Base DCs are 21 and 14. With modifiers, they become 27 and 17. Looks like the GM didn’t buy the amelioration arguments, assuming that you’d be doing that sort of thing as much as possible anyway.
  • DC 27 means that the more-skilled “remote assistant” needs a 19 or 20 to succeed. So there is a slim chance of conferring Advantage. However, there’s a much greater chance of putting the protagonist at a Disadvantage.
  • DC 14 means the protagonist needs 11 or more to succeed. If he has Advantage, his net chance of success is 75%; if he is not at Disadvantage, it’s 50%; and it’s 25% if he is. The “value” of the assistance is critical.

The Combined Competence problem

Two characters, one with the relevant skill, one with a related skill, have a problem to solve. Both need to work together to solve the problem.

Once again, we have a similar basic situation, but with a different penalty to ascribe. What’s the penalty for only having a “related” skill?

With the basic system, it’s just another modifier to be applied to the “assistant’s” roll.

This might be handled differently according to the option chosen – depending on whether or not unskilled use automatically confers disadvantage and whether that precludes the possibility of also having Advantage.

Normally, Disadvantage would simply cancel out Advantage. But I would contemplate making an exception in this limited case, because if you don’t, employing an assistant cannot possibly confer a benefit to the character. Preserving the utility of having assistance demands thinking outside the box, and crawling out the bottom is the easiest way to go.

So, assuming that we do that, we now have to work out how to handle double Disadvantage (one outcome) or both Advantage and Disadvantage (another outcome).

The first is simple – add another d20 and you still have to take the worst, which is the same (in probability terms) of meaning that you need a third roll to be successful before you succeed.

The second is a little more complicated. There are two approaches: advantage first, or disadvantage first. I suspect that these will have a marked impact on the overall outcome. (I went ahead and calculated it, and found a huge difference – advantage first gives about 4.3% chance of success, Advantage second gives about a 24% chance of success.

So the question that you have to ask yourself is which one is more in keeping with the spirit of what’s going on? Given that the chance of success is about 20% with neither advantage nor disadvantage, and that it’s good to be generous as a GM when it doesn’t cost you anything much, I would go with the Advantage Second model. But that’s up to you.

The Universal Shoulder-To-The-Grindstone problem

There’s a large weight to be lifted, or a heavy door to break down. It’s going to take the efforts of more than one character to achieve the desired result. How do you correlate their attempts into a straightforward success or failure?

This introduces yet another class of issue. Most of the time when Strengths need to be combined, it’s to achieve some third-tier effect – like lifting something, or everyone joining forces to use a battering ram. And those effects are usually non-linear and only related to the other numeric variables by implication.

The Hero system fairs better than most in this respect – every +5 to a stat doubles all the derivatives of that stat, so if STR 10 can lift 100kg, STR 15 can lift 200kg, and STR 20, 400kg. That makes an increase predictable – if, eventually, too large to be plausible. But that’s easily fixed: you simply specify that having the assistance of a second character who successfully makes a STR check adds bonuses to the collective strength index as though it were a bonus to a skill roll or their total personal lift value, whichever is greater.

And, if it works that simply with one game system, why not with others? Well, it’s not quite that simple.

For a change, I’ll pull out the Pathfinder rule-book for this example. Let’s say that we have a character with a stat bonus of +2 helping a character with a stat bonus of +4 – which keeps our examples consistent. Those are the equivalent of STR 14-15 and STR 18-19 – call them 14 and 19, respectively. Let’s further assume that the lower STR character is starting with a light load and the higher STR character with a medium load. That means that the assistant is carrying 58 lbs or less (45 sounds reasonable), while the stronger character is carrying between 117 and 233 lbs (200lbs will do). More importantly, the maximum load that the STR 19 character can bear is 350lbs, so he has 150lbs of capacity left, while the maximum for the weaker character is 175lbs, leaving a capacity of 130lbs.

If the pair are confronted with a 200lb boulder that they have to relocate out of their way, it’s too heavy for either one alone. They might attempt to split it in two, but it stubbornly refuses to cooperate. The only solution is for them to work together. 200lbs is well within the combined carrying capacity of the pair, so you would expect this to represent little difficulty.

Work out the maximum result that the character can get, Divide the maximum heavy encumbrance of the character by the result. You only have to do this once for a character; the results won’t change unless the character changes his STR. What it gives you is a number of lbs per STR DC of +1, starting at zero. So, work out the DC (rounding up) for what the character is currently carrying – this won’t change unless the character’s load or STR changes, either. That gives you the DC for them to make a Stat check. As usual, the results then convey a bonus or penalty. Now do the same DC calculation (if you haven’t already) for the other character. Determine their STR DC. They get to make a check, with the bonus from the assisting character(s). Multiply the weight per DC by however much the stronger character succeeded by. Adding that to the amount they are already carrying gives you exactly how much the pair or group can lift.

So, STR 14, 45 lbs out of a maximum of 175. The character has +2 modifier, so the maximum he can get on a STR roll is 22. Divide 175 by 22 – roughly, it doesn’t have to be exact – 175/22 is roughly 88/11, so 8 lbs per +1. Which gives his current load of 45 lbs a DC of 6 (with a few pounds reserve before the next increase). The character makes a STR roll and probably succeeds – quite probably by a reasonable margin, though with any particular roll, who knows? Let’s say that he gives +3 to the stronger character on this particular roll.

Our stronger character: STR 19, 200lbs out of a maximum of 350. The character has +4 modifier, so the maximum he can get on a STR check is 24. Divide 350 by 24 (roughly) and you get 350/24 = 175/12 = 88/6 = 44/3 = 16 1/3 lbs per +1. Call it 16 lbs. This gives the current load of the character a DC of 200/16 = 100/8 = 50/4 = 25/2 = 13. He makes his STR check and succeeds by 6, plus the +3 from the weaker character, for a total of 9 – which, between them on this attempt lets them handle 9×16 = 135 lbs. Not enough to lift the boulder, but certainly enough to move it a little, perhaps rolling it to one side. Note that the problem isn’t really the assisting character; it’s the size of the load the stronger character is working with. If he sheds his armor and pack, dropping the carrying capacity that he’s using, he also reduces the DC he has to achieve, which in turn increases the amount by which he succeeds.

Or perhaps you think that the final calculation should be based on double the margin of success, and/or the contribution by the assisting character should be doubled. These are your House Rules, you can rearrange them as you see fit. You could even decide to forego the whole notion of a STR roll and simply add the unused carrying capacities of the two characters together in such cases – but there’s still that darned tug of war….

The Two-Is-Less-Than-Many-Hands problem

A problem would normally need two or more characters acting in a coordinated fashion to solve it – but the only character in the vicinity is on his or her own. How much more difficult is it to find and apply a solution?

Well, this is a question that we’ve answered a couple of times already in the course of the discussion, albeit by applying one of two arbitrary values – +2 difficulty, or my personal recommendation, +5 difficulty. Per “pair of hands” that should be used, but aren’t.

The Standard Tests

There are five standard tests that I use whenever I think deeply about this sort of thing (and turn those thoughts into House Rules). Between them, they make sure that I’ve got the practicalities nailed down pretty well. This post is already extraordinarily long, so I’m just going to hit the high points of each.

The Sneak Test

Five PCs, all trying to sneak across the room at the same time. If one fails, they all fail. Having them roll individually is the obvious approach – but it presumes that none of them can help any of the others. What if character #1 dislodges something that would fall to the ground with a loud clatter (a failure) – but character #2 is in a position that lets him or her attempt to grab it and set it down quietly? Interpret that into game mechanics using your chosen game system and apply to a couple of randomly-chosen typical characters. Make a note of any additional House Rules you come up with – for example, characters who succeed might pay their resulting “bonuses” into a pool that can be used to offset failure by another character, so that a sufficiently catastrophic noise can’t be prevented, but anything less might. The choices are yours.

The Lift Test

I’ve already shown you this one – a boulder too big for two characters to handle, given the load they’re carrying. You might like to look at an even larger boulder with three or four characters instead, because this is the sort of thing that’s likely to be a group activity..

The Man Those Oars Test

Another group activity, but this has a double-sting to it. You don’t need great strength to man an oar; it’s more important to get the timing right, matching your counterpart on the other side of the vessel. You also don’t want to get out of sync with those in front and behind. So it’s rather more complicated and comprehensive than it first appears.

The Football-Pass Test

This is another whole-of-party test. Each member in succession is to receive an object (the football) and carry it a specified distance forward past 2-6 characters trying to intercept them, then “hand it off” to the next PC – who will have to have read the plans and motion of the character with the football well enough to be in position to receive it. The more poorly they have done so, the more difficult the roll needed to take possession. The goal is to get the football the whole length of the ground.

The Crossword Puzzle

Two characters are attempting to solve a crossword puzzle. They’ve gotten all the easy words, between them – and are now trying to figure out the more complicated ones. Use a real crossword for added realism. Bonus: work out a way in which the roll determines how long you can research the subject on Google.

The very ordinariness of these potential applications go to showing how universal this problem is. You don’t have to adopt my solutions; you just need to find a satisfactory answer. Finding your own techniques and mastering them is therefore something that should be a priority for every GM. Because the one thing that you can state for certain is that before too long, these rules will be needed – and probably in relation to a problem that you’ve never even thought of. That’s just the way these things work.

Even with the considerations described at the start, I almost didn’t write this article today. You see, last night I thought of a new category for the Blogdex, one that to the best of my recollection would have absolutely no articles to populate it, even though it is a very common occurrence. I was tempted to write that article, instead…

Updates Björn Arnold, in the comments, has quite astutely pointed out a couple of omissions. Some hasty research later, here they are. Aid Another Rather than the 3.5 rules, I looked at the Pathfinder version on the basis that it was more likely to be current and in use. “You can help someone [succeed] by making the same kind of skill check … If you roll a 10 or higher, the character you’re helping gets a +2 on their check.” There are a number of restrictions, the most significant of which is that the character aiding another has to be capable of solving the problem or challenge on their own (presumably with a successful skill check at an improbable DC, or why don’t they just solve the problem in the first place). This is typical of the limited attention devoted to cooperative actions in RPGs, an inadequate gesture in the right direction. It’s full of holes. The the DC is high enough, a character can work miracles on a successful roll – “I run across the sunbeam until I’m on top of the thief then jump on top of him” stuff. So either the restriction is totally irrelevant, or the GM is required to enforce a double-standard and hope that no-one notices that high-DC successes only only count as successes when he “wants” them to. It’s too restrictive. “The same kind of skill check”? Please, as though there were only one way to skin a cat. If that were rephrased to “Only abilities that the GM deems appropriate can be used in an attempt to aid another. A skill check of the same kind is always considered appropriate,” then the situation would be much improved. Consider: Character #1 is attempting to burst through a gathered crowd of Undead to place a holy symbol on the altar. Character #2 attempts to Aid Another by using his Turn Undead to make the gathered crowd hesitate and rear back, even though he is not capable of Turning them all.” That sounds utterly reasonable to me, and reasonably clever, to boot. It’s inflexible. One size of difficulty fits all, and the benefit is always +2 if you succeed, no matter how much or how little ability you have to contribute. It could be seen to punish competence – “If you roll a 10 or higher” is vague. If that’s a straight die roll and not a fixed DC target, then the rules make the DC for Aiding Another effectively equal to 10 + your skill level and stat bonus. I don’t think so. In the alternative, it’s too easy. A DC of 10 means that even with a single skill level and no stat bonus, a character needs only to roll a 9 or better to succeed, which they will do more than half the time. A character with +8 in skill and stat bonuses only needs to roll 2 or better, and will come as close as you can get to automatic success. Frankly, that’s why the benefit has to be so trivial. All right, to be fair, at low levels – up to level 4, say – +2 can be a significant boost. But to your 16th-level whatever? This is a symptom of a lot of games that comes from insufficient variety in playtesting. Most playtesters will play a game the way it’s supposed to be played, i.e. characters start at 1st level and have to work their way up. That means that by the time the playtest concludes, either the characters have advanced way too fast, or higher levels have hardly been tested at all. Most game companies don’t even realize this is a problem, so they don’t do anything about it. Another question arises: Stacking limits. “Aid Another” bonuses either stack, or they don’t. If they don’t, only one character can ever aid another, denying the conceptual existence of the 3-man job. If they do, it’s far too easy to just keep throwing warm bodies at an impossible check until enough of them succeed to give you +20 or +40 or whatever. Both answers are irretrievably flawed. Conclusion: Aid Another is not a good prototype for rules on Collaborative Efforts.

“Skill Challenges” from D&D 4e Caveat: I’m not a 4e expert, I’ve never played the system, so the following is strictly from a theoretical appraisal of the mechanics as described on the WOTC website. The GM defines a problem or situation as an encounter requiring a certain number of successful skill checks before the encounter is resolved in the PCs favor. If they accumulate a certain number of failures before achieving that target, it ends in a PC failure. The GM also nominates which skills are most applicable to the situation (the Primary List) and a number of lesser skills that may be able to contribute to a solution (the Secondary List). Skills on the Secondary List must achieve a “Hard DC” while those on the Primary List must achieve an “Easy DC”. Anything the players want to try that’s not on the Primary List are automatically considered to be on the Secondary List unless it is utterly brilliant (which some interpret as being ‘capable of solving the situation with a single die roll’, i.e. aborting the entire Skill Challenge). The GM is entitled to consider any roleplayed action or ability use other than a skill as an automatic success or an automatic failure towards the respective totals. On the face of it, an interesting concept, with a lot of things to like about it. It took a little while to digest it, but then the flaws began to make themselves apparent. It’s inflexible. Some solutions may be far more viable than others and should count for more than one success. The rules as stated break a problem down into N equal steps, of which N-F must succeed (where N is the number of successes needed to “win” and F is the number of failures needed to “lose”). It then insists that each of these stages must be resolved separately – you can be 5/6ths of the way to success but that doesn’t make the final step any easier. It’s anarchic. There’s no need for a rational and coherent plan; a character can do anything he wants, even something that would arguably make matters worse, and it still counts as a success if he makes his skill check. At the same time, no matter how “right” a character’s intended action is, if they don’t have the skill to perform it on their own, it doesn’t count as a success. It’s easily abused and encourages cliche behavior instead of roleplaying. Once again: as a character, you have a choice: go with what the GM wants you to use to resolve the situation (easy DC), even if that’s not your character’s style, and no matter how bad you are at it, or you can go with your strengths, no matter how irrelevant or harmful they might be to the situation (hard DC), because you are more confident of making a hard DC in an area of competence. At low levels, this might work; at mid-to-high levels – as soon as you have 10 skill ranks in something – the whole system starts to break down. It’s inflexible in other ways, as well. It locks the GM into one of two black-and-white outcomes, success or failure. You might as well be using a Choose Your Own Adventure book. Real life isn’t like that, and neither is a well-run RPG – there are all sorts of halfway houses in between. Perhaps you get offered everything you’ve been trying to bargain for – but at a much higher price than you really want to pay, for example. It’s an overbearing solution. The system imposes the adventure author’s preferred solutions onto the players and penalizes them for thinking outside those channels. On the positive side, however, the players are free to contribute anything they think might help the situation (assuming they are playing it straight and not trying to exploit the mechanical failures described) and they will be assessed even-handedly – even if the system is prejudiced against them. That’s more than most game systems manage – just take a look back at “Aid Another”. But, last – and the worst failing of all – this system turns what should be a roleplaying situation into a die rolling situation. Despite the interesting elements – which take a more holistic view of the party as a whole than most game systems, which are focused exclusively on the individual – this is an abysmal solution to the problem with some minor saving graces.