Rolling under your abilities.
One of the most controversial of ruling suggestions in B/X - nested snugly into the subsection, Dungeon Mastering as a Fine Art on page B60 under the moniker that There's always a chance. This rule has become a default mechanism for some referees - it's simplicity and quickness at the table while differentiating characters more or less naturally capable luring them in - and has become anathema for others: it's emphasis on abilities defying the class-level focus of almost any other challenge in the game, it's swingy potential for a well-endowed character to fail while an incapable character succeeds (the "I loosened it up for you" hypothesis) puts them off. However - in recent vintage - I've come across a variant which may help to alleviate some of the tensions - rolling under using a d6 dice pool.
My interpretation as follows:
Pooling Under your Abilities
When presented with a task - skill, talent, or otherwise - not covered by a rule but requiring a roll to account for potential of failure, the referee should, having considered the described manner of resolution, ask the player to roll a number of d6 proportional to the difficulty of the task compared to the efficacy of the proposed resolution mechanism:
- Easy tasks, or tasks well achieved, roll 1d6.
- Normal tasks, or perhaps easy tasks the method of resolution provided being questionable, roll 2d6.
- Challenging tasks, or tasks being approached poorly, roll 3d6.
- Difficult tasks, or tasks being approached entirely wrong, roll 5d6.
- Impossible tasks, or descriptive equivalent, roll 8d6,
If the result of the pool exceeds the ability score of the character rolling, the task fails. Otherwise, the task succeeds.
Optionally, to represent the off-chance of failure even when doing
something simple (or, I Missed My Mouth With The Cup syndrome), use
single-explosion dice. Thus, an Easy task has a likely result of 1-5, but an
unlikely result of 7-12; or a Difficult task has an average result of 17 or
18, but a potential (and highly unlikely) result of as much as 60.
Credit where Credit is Due
Note, as is most of the time with house rules, I did not originate this idea. Googling it to find the page on which page the "roll under" rule in B/X was, I found several social media platforms where this or a similar system was being discussed. Credit where credit is due, I am writing this article listening to the Biggus Geekus podcast. Kudos - Randy and Joe, for the interesting topic - and credit, DM Dastardly Dad for the great suggestion!
Why write about it then, if it's already so popular, as you say? I
think it's a neat idea - but what I didn't see was a detailed breakdown
and mathematic scrutiny. Also - it's a great idea: why wouldn't I amplify
it?
How Do the Chances Look?
Without the optional exploding die rule, the average roll for each of the respective pools are as follows:
| Minimum | Average | Maximum | |
|---|---|---|---|
| 1d6 ) | 1 | 3 | 6 |
| 2d6 ) | 2 |
7 |
12 |
| 3d6 ) | 3 |
10 |
18 |
| 5d6 ) | 5 |
17 |
30 |
| 8d6 ) | 8 |
28 |
48 |
Thus, an average character (ability score 10) cannot fail an Easy task, would
only fail ~8.3% of the time for a Normal task (requiring an 11 or 12 on 2d6),
and would conversely fail ~47.2% of the time for a Challenging task. With this
system, it becomes difficult to be impossible to pass: however the
chance of failure changes rapidly as the curve becomes wider and wider. Also
of interest - a character with a maximum score will never fail for Challenging
tasks or below; where a character with a minimum score has at least a 50%
chance for an Easy, the minimum score on the standard 3d6 stat array being
3.
To expand, a character with a high or low ability has a chance to succeed on this scale as follows:
| Ability | Easy | Normal | Challenging | Difficult | Impossible |
|---|---|---|---|---|---|
| V. Low (4) |
66.7% |
16.7% | 1.9% | 0% | 0% |
| Low (7) |
100% | 58.3% | 16.2% | 0.26% | 0% |
| Avg (10) |
100% | 91.7% | 50% | 3.23% | 0.03% |
| High (13) |
100% | 100% | 83.8% | 15.2% | 0.11% |
| V. High (16) |
100% | 100% | 98.1% | 40% |
0.78% |
The numbers chosen were chosen for their relationship to the assumed 3d6 curve
of character abilities: 13 is one standard deviation above, 16 two standard
deviations above, 7 one below, and 4 two below.
Additionally, the percentiles are estimated - rounding conveniently for my brain - especially to the "Impossible" side of the scale: as rolling numbers less than 11 is almost statistically implausible: the likelihood of hitting those numbers being percentages of a percentage point. A character with an 18, for example - the nominal maximum in an OSR game - only has a 2.37% chance to succeed at an Impossible task.
Introducing the exploding mechanic makes the math substantially more difficult. So - thank you, AnyDice, for doing it for me! The likelihood of success, based on high or low ability score, with exploding d6 (depth 1: that is, if you roll a 6 on your explosion roll, that second 6 does not, itself, explode):
| Ability | Easy | Normal | Challenging | Difficult | Impossible |
|---|---|---|---|---|---|
| V. Low (4) |
66.67% |
16.67% | 1.85% | 0% | 0% |
| Low (7) |
86.11% | 58.33% | 16.2% | 0.27% | 0% |
| Avg (10) |
94.44% | 91.67% | 50% | 3.24% | 0.01% |
| High (13) |
100% | 97.22% | 83.8% | 15.2% | 0.08% |
| V. High (16) |
100% | 97.69% | 98.15% | 39.97% |
0.74% |
At first glance, the numbers seem somewhat similar in some places. And this makes sense - for example, a character with an Ability score of 4 has no impact to an Easy task: if you roll a 6, eligible to explode, it doesn't matter: the roll has already failed and no explosion is necessary - thus, the chance of success is unmodified. However, it does introduce increased failure (albeit unlikely) for any other of the ability bands calculated: a score of 7, for example, on an Easy task would, if an initial 6 is rolled, only have a 1-in-6 chance to succeed as any other roll on the explosion would push the result over the ability score and into failure territory.
Regarding the range and average of task rolls, incorporating the explosion
mechanic, consider as follows (again, courtesy
AnyDice):
| Minimum | Average | Maximum | |
|---|---|---|---|
| 1d6 ) | 1 | 4.08 | 12 |
| 2d6 ) | 2 |
7.19 |
24 |
| 3d6 ) | 3 |
10.55 |
36 |
| 5d6 ) | 5 |
17.5 |
60 |
| 8d6 ) | 8 |
28 |
96 |
At a glance, the higher dice pools seem less phased by explosions than the
lower ones, in terms of averages. That does make some sense - as the
likelihood of the higher number of explosions, and thus higher results,
becomes vanishingly small as it increases.
Curiously - looking at some of the intermediary probabilities of success
chances, it becomes impossible to have certain results. On an Easy check - 1d6
- obviously, you can never have a result of 6: because there will always be at
least a +1 from the second die rolled. AnyDice, however, claimed that a 12 was
also impossible on 2d6, or a Normal task, with exploding dice. At first, it
seems plausible - there is only one way to get 12 on 2d6: two 6s, which would
explode - but then if you think about it: you could have one 6, exploding by 2
to 8, and then roll a 4 on the other die: 8+4 is 12: so, at least one way to
get a 12 on 2d6. I wonder if that's a glitch or if I simply entered an
improper command. Similarly, I wonder if this would have impacted calculating
the means...
Conclusion
I like this. I could see myself using this rule with the explosion variant. It's less swingy than 1d20, but still makes abilities matter. Likewise, the explosion acts as an equalizer: producing a setup where you can fail - but the likelihood of that failure is largely dependent on your ability and doing the task right.
There is room for some interpretation in the "would X work?" - speaking to defining the mechanism of the task - but that's what refereeing is all about. I ... probably would not call for any Impossible checks though. Waste of dice time.
Delve on, readers!
Public domain artwork retrieved from
OldBookIllustrations.com
and adapted for thematic use. Attribution in alt text.
I'm reading through The Halls of Arden Vul right now, and they use a lot of these kinds of checks, not only with d6s, but sometimes with d8s or d10s.
ReplyDeleteThat's interesting! I haven't done the math - I'm replying with one hand while holding a toddler in the other! - but the larger die size creates a much wider curve! Generally, it follows the same pattern with the extremes being less likely - getting snake eyes on 2d6 is a 1-in-36 chance; where it's 1-in-64 on 2d8 - and the bulge increases according to the dice average (7 on 2d6 vs 9 on 2d8). It might be cool to see how HoAV implements it and see how the math adds up, encouraging or discouraging different avenues!
DeleteHmmm, interesting.
ReplyDeleteThat's a cool note subhuman. I have the Halls. Maybe it's next in my list!
ReplyDeleteThis is the perfect solution to one of the few problems I have with B/X, the clunkyness of telling a player to +/- a number to their roll to reflect difficulty. Just telling them to roll Xd6 is much simpler.
ReplyDeleteI'll be using this without exploding dice, I think.
Another adaptation might be to roll 3dX, 3d3 being easy, to 3d8 or higher being hard.
Rock on, brother! Keep me up to speed on how it goes!
DeleteVery interesting man. I'm very up to test this. One of my recurrent houserules is to have thief skills work more or less by dexterity checks; this allows me to ban thieves and give everyone the chance to perform strange things. Same with the Open Doors skill (str check)
ReplyDeleteWhat about other attributes? do you usually test them? because in the game (osr at least) they dont find uses beside their current ones that are worthy to be checked.
Numerically I am tempted to make it 2d6 / 3d6 / 4d6 / 5d6 with a twist: only one 6 can explode. So the maximum of 5d6 is 36 (6x6). Something that is meant to be easier than that is probably not worth a roll, while something higher is probably too hard to do to be feasible (the average of 5d6 is 17'5, so a 18+str fighter would succeed 50% of the time without exploding. If one die explodes, which is very likely, the average ramps to 21, with the 18str guy having a 28% of succeeding and anyone under that having exponentially less chance still).
I can see this rolls being made by the GM instead of the players, hiding even the number of the dice rolled so players dont know how hard the obstacle is. So its a point to the exploding dice: you dont have to explain the mechanic to the players unless they explicitly ask
At the table, I've done this with Str and Dex so far. For Str and Dex, it worked well - players were able to gage their chances and for, say, climbing a wall, I could say, for example, "This is a 3d6 wall" and they'd know it was doable, but not to rely on it unless they were particularly gifted.
DeleteI did try replacing Thief skills with it, but I have not come to a place where I was happy with advancement yet. Would love to hear how it handles (or how you handle it!) at your table!