##### Heretic of The Seventh Circle
I need some help figuring out probabilities in practice with a dice rolling method. I’d be very grateful for any insights y’all can give.

So, my TTPRG, Quest for Chevar, is a skills based game where character creation is very specific, and then gameplay is narrative, player facing, and open-ended. Basically, imagine if instead of the DM in dnd deciding whether something works, your check directly tells you, you say what that means, and the DM smooths over any transitions, NPC reactions, etc. It's a conversational system, but one in which much of the GM responsibility is put into the hands of the group, and the acting player.

Anyway, I've realised thanks to @hawkeyefan @pemerton @AbdulAlhazred @Campbell and others that, among some other insights that will lead to some further investigation, the roll vs DC model doesn't work as well for that, and I haven’t done as much as I can to put things in the player’s hands.

This thread is mostly about the dice. It’s also a plus thread, simply because I don’t want to see it detailed with stuff like “dice pools are bad, actually” or “if you want a success ladder just make it a pbta game”.

What I’m wondering about is the numbers relative to the dice, and how the odds play out.

Right now, the game rolls 1d10 + 1d10 per skill rank. Nothing else ever adds to a skill check, and skills govern everything that is rolled for in the game.

Attributes only interact with skills when you want to spend a resource to improve a skill result.

Each skill, in case it matters, is basically a description of a competence with some very simple parameters.

For instance, the Warp Specialty under the Geomancy Skill allows you to make portals. Making a simple short distance portal between points you can see just takes an action. Doing so as a quick action, increasing distance or size, doing something complex or that requires another skill, or putting one or both portals where you can’t see, all require a skill check.

At chargen, you can have up to 4 total ranks in a skill specialty, for 5 dice, but most of your skills will be from 1-3 ranks.

So, rolling anywhere from 1 to 6 or 7 d10s, what does a pbta style success ladder need to be, for the following goals:
• Each step on the ladder is a range of results (eg 1-8, 9-12, 13-15, 15+)
• Lowest result: Total failure
• One Step Up: Mitigated Failure (you fail, but can still get something out of the action or situation, use the action to set up something else, or otherwise mitigate your failure, or you can bargain for dire consequences or spend an attribute point to get one step higher on the ladder)
• Second Step Up: Mitigated Success (you succeed, but there’s a cost, or you can bargain or pay, as with the first step)
• 3rd Step Up: Total Success.

Probability goals:
• Total Failure shouldn’t be common for trained characters under normal circumstances.
• Mitigated Failure should be all you can get if you are untrained, with no help, an no prep, ie rolling 1 die, and even it should be uncommon (like 8 on 1d10). Most novice skilled checks should fall here and the next step, and it should be fairly rare for masters.
• Mitigated Success should be the most common result for journeyman level characters, so 3-4 ranks.
• Full Success should be possible for anyone with 2 ranks (3 dice) or more (or 1 rank (2 dice) if it can be done, so 20 at most). It should only be common for Journeymen or better, and only really common for Masters.

Circumstance can add or subtract dice, to a minimum of 1 die, max of 6 or 7 (probably).

So with all that, I can input stuff into anydice, but what I have trouble with is math burnout after about 20-30 minutes of reviewing different graphs, and collating that data into a full model I can build from.

Any thoughts? I know it’s a lot of info, but I hope the discussion will be fun for dice nerds?

#### pemerton

##### Legend
Are you summing the dice, or taking the best roll? Or some combo (eg Cortex+ Heroic and Agon both, by default, sum the best two dice in the pool)?

##### Heretic of The Seventh Circle
Are you summing the dice, or taking the best roll? Or some combo (eg Cortex+ Heroic and Agon both, by default, sum the best two dice in the pool)?
Sum.

Edit: I find d10s very easy to count, but I’d also be fine tuning numbers down and using d6s. I just prefer the pool of d10’s.

#### pemerton

##### Legend
If you're generating numbers on 1 to 6 d10s, and summing them all, you're going to have wide ranges in ability - which I guess you've already worked out.

If you set Total Failure as 7 or less, that will be 70% of 1-die rolls, about 20% of 2-dice rolls, and less than 10% of 3-dice rolls.

If you set Mitigated Success at 15+, that will be about 20% of 2-dice rolls, nearly 65% of 3-dice rolls, and about 90% of 4-dice rolls

If you set Total Success at 20+, that will be 1% of 2-dice rolls, around 28% of 3-dice rolls, a bit more than 65% of 4-dice rolls, and close to 90% of 5-dice rolls.

#### Aldarc

##### Legend
I know the OP has me on ignore, but maybe my comments will nevertheless generate conversation that they would find helpful.

There are multiple ways to potentially get the desired results, and playtesting would be required to see what works best for the OP.First, there are some other systems that I could see as possible pools for inspiration:
(1) Ironsworn: a 2d10 PbtA-derived game
(2) Cortex Prime: a dice pool game with a simple mechanic of rolling a bunch of dice and adding two dice of your choice
(3) Blades in the Dark: a game that weds die pools with PbtA design principles - including failure, complicated success, success, and critical success

The benefit of (3) is that it can better account for variable die pool sizes. The OP can key the fail/success states to the sides of a d10. So if you have 1d10, you know what you need, just as well as if you had 7d10.

But if one is hypothetically summing the dice, then I would probably opt for something more akin to Cortex: roll what you have and add. But I would limit the number of dice being added together to two. One could play around with the mechanics a bit. You could tie the success ladder to a range (e.g., failure is 2-10, success is 11-20), have different effects key off die results (e.g., 1 introduces a complication), or even do things with the excess dice (e.g., criticals), etc.

##### Heretic of The Seventh Circle
If you're generating numbers on 1 to 6 d10s, and summing them all, you're going to have wide ranges in ability - which I guess you've already worked out.

If you set Total Failure as 7 or less, that will be 70% of 1-die rolls, about 20% of 2-dice rolls, and less than 10% of 3-dice rolls.

If you set Mitigated Success at 15+, that will be about 20% of 2-dice rolls, nearly 65% of 3-dice rolls, and about 90% of 4-dice rolls

If you set Total Success at 20+, that will be 1% of 2-dice rolls, around 28% of 3-dice rolls, a bit more than 65% of 4-dice rolls, and close to 90% of 5-dice rolls.
That sounds about right. This means that most checks will be a mixed result, unless you’re a Master. It might also mean it’s worthwhile to reduce the number of ranks you can start with by 1, down to 3.

7 as the baseline for non-flub means that a 5 rank character would have to roll at least 3 1s to flub. It could happen, but it won’t happen often.

#### pemerton

##### Legend
7 as the baseline for non-flub means that a 5 rank character would have to roll at least 3 1s to flub. It could happen, but it won’t happen often.
If 8 is the requirement to avoid Total Failure, it basically won't happen if someone is rolling 5 dice: about 1 in 10,000 rolls.

##### Heretic of The Seventh Circle
If 8 is the requirement to avoid Total Failure, it basically won't happen if someone is rolling 5 dice: about 1 in 10,000 rolls.
That would match the goals, actually. I’m considering a trait that you could take when you’ve reach max ranks, that makes it so you never get a total failure with that skill, and any dice pool penalty for a check with that skill is reduced by 1.

Basically, you’ll still see some mixed results sometimes with that one skill, but you’ll never flub, and your mixed results will usually be mixed success.

I imagine 6 ranks is basically “you always win” anyway, so 5 ranks might be the max.

Hmm. The original model for skills was :

Skill:
Specialty:​
Specialty:​
Specialty:​

when you make your character you get some skills from origin, some from archetype, and a few freely chosen.
For each skill rank you also get one specialty rank.

When you make a check, you usually do so with a specialty, which means you add your skill and specialty ranks together. This effectively means that a skill rank is a rank in each specialty of that skill. When I reference total rank, it is skill+spec.

Generally as you advance, you only gain specialty ranks, unless you train in a new skill, or spend significant resources and/or time on training with the skill. Also for ease of bookkeeping, if you have ranks in all 3 specialties you can convert them to 1 skill rank. Mastery is having 5 ranks in a specialty, with probably a benefit somewhere for having mastery in an entire skill.

But basically this is the only complicated thing in the game, and it’s not as complex as it sounds. PCs don’t really get more health or do more damage as they advance, they just get better at skills, gain new traits, and slowly gain more attribute points to spend on special abilities and on upgrading a check up the success ladder.

Spending all your AP in any attribute has a risk of Trauma, and you only regain a little when you rest, unless you take at least several days in a safe place.

Just in case any of that is helpful or interesting. Tbh explaining it helps me order it all in my head before writing the next draft.

#### pemerton

##### Legend
Error in the above: that should be 1 in 5,000 I think , not 1 in 10,000.

##### Heretic of The Seventh Circle
Okay I think I like;

Total Failure: 1-7
Mitigated Failure: 8-14
Mitigated Success: 15-20
Total Success: 16-20

I might drop lower mitigated success but 1 or 2, but I kinda like that mitigated failure takes up more space by itself on the ladder, while the two success states together take up more, so we will see.

max starting ranks is 3, so you can only start a Journeyman, and that only in a few skills. Max total ranks is 5. Further mastery is about mastering related specialties and skills to support what you’re best at, and earning traits that make you more able to do more with a given skill and/or more reliably roll high. For instance a Master’s Focus trait for the Sigils specialty is to be able to create a circle for complex magical workings without having to manually draw it, bypassing the need for a check, and saving time.

##### Heretic of The Seventh Circle
@pemerton Okay, I really appreciate the help, here. I know how to use anydice to get the raw data but I just go full himbo for some reason when I try to turn it into useful information. I mean I exaggerate, I built the old dice system by running numbers, but kinda like making a slick looking character sheet by beating my head against excel for hundreds of hours over the course of dozens of iterations, sometimes asking for help is really the better way!

So, one last question (I think), if you’re willing: how much smoother is the distribution with d6s? How about with a d12 and d6 rank dice?

I started with d10’s originally because it’s was d100+d10 rank dice, which is roughly the same as d20+ 1 point per rank, but curvier. So I’m not married to d10s, but they aren’t part of the game’s identity in my head. Especially since all attacks also function in d10’s, the idea being you only ever need up to 6 d10s to play the game. Obviously d6s are more common to have that many of, but we can also commission specialty dice sets with the Fir Bolg (of myth, big folk who spoke the first mortal language, and have a knack for linguistic, riddles, and throwing stuff) sigil for the game on the 10!

#### pemerton

##### Legend
So, one last question (I think), if you’re willing: how much smoother is the distribution with d6s? How about with a d12 and d6 rank dice?
Can you explain what you mean by "smoother" in this context?

My combinatorics and probability stops at an upper high school level, so I'm not doing anything very sophisticated: just calculating (with a bit of help from Anydice for the bigger numbers) the likelihoods of various results. I'm pretty sure it will be possible to set up d6-based thresholds that produce much the same spread of probabilities. But I think you already know that, and hence my question above.

##### Heretic of The Seventh Circle
Can you explain what you mean by "smoother" in this context?

My combinatorics and probability stops at an upper high school level, so I'm not doing anything very sophisticated: just calculating (with a bit of help from Anydice for the bigger numbers) the likelihoods of various results. I'm pretty sure it will be possible to set up d6-based thresholds that produce much the same spread of probabilities. But I think you already know that, and hence my question above.
My understanding is basically that bigger dice will “swing” more than smaller dice, but I’m not sure if that is true. Perhaps a “rounder” or “less steep” bell curve? I’ll try to do some anydice work tomorrow to find answers.

Basically I’m curious if the change in success chance per additional rank will be less extreme with a smaller die size? IOW, will the difference from 1 die to 2 die be less of a jump with smaller dice?

#### pemerton

##### Legend
It depends where you set your boundaries.

Using d10s (and just repeating/consolidating from above):

If you set Total Failure as 7 or less, that will be 70% of 1-die rolls, about 20% of 2-dice rolls, less than 10% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and about 1 in 5,000 5-dice rolls.

If you set Mitigated Success at 15+, that will be about 20% of 2-dice rolls, nearly 65% of 3-dice rolls, and about 90% of 4-dice rolls.

If you set Total Success at 20+, that will be 1% of 2-dice rolls, around 28% of 3-dice rolls, a bit more than 65% of 4-dice rolls, and close to 90% of 5-dice rolls.​

You can get a similar spread with d6s:

If you set Total Failure as 4 or less, that will be two-thirds of 1-die rolls, one-sixth of 2-dice rolls, and a bit less than 2% of 3-dice rolls. It's fewer than 1 in 1,000 4-dice rolls, and impossible for 5-dice rolls.

If you set it at 5 or less instead, that will be a bit over 80% of 1-die rolls, close to 30% of 2-dice rolls, less than 5% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and fewer than 1 in 8,000 5-dice rolls.

If you set Mitigated Success at 10+, that will be one-sixth of 2-dice rolls, a bit over 60% of 3-dice rolls, and about 90% of 4-dice rolls.

If you set Total Success at 13+, that will be impossible with fewer than 3 dice, around 26% of 3-dice rolls, around 66% of 4-dice rolls, and just over 90% of 5-dice rolls.​

So I think changing from d10 to d6 has the effect of making it impossible rather than just extremely unlikely to get full success with 2 dice; also pushes the rate of Mitigated Success down a little bit for 2-dice rolls; and forces a choice about whether you want Total Failure to be a bit less likely, or a bit more likely, for one or two dice.

##### Heretic of The Seventh Circle
It depends where you set your boundaries.

Using d10s (and just repeating/consolidating from above):

If you set Total Failure as 7 or less, that will be 70% of 1-die rolls, about 20% of 2-dice rolls, less than 10% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and about 1 in 5,000 5-dice rolls.​
If you set Mitigated Success at 15+, that will be about 20% of 2-dice rolls, nearly 65% of 3-dice rolls, and about 90% of 4-dice rolls.​
If you set Total Success at 20+, that will be 1% of 2-dice rolls, around 28% of 3-dice rolls, a bit more than 65% of 4-dice rolls, and close to 90% of 5-dice rolls.​

You can get a similar spread with d6s:

If you set Total Failure as 4 or less, that will be two-thirds of 1-die rolls, one-sixth of 2-dice rolls, and a bit less than 2% of 3-dice rolls. It's fewer than 1 in 1,000 4-dice rolls, and impossible for 5-dice rolls.​
If you set it at 5 or less instead, that will be a bit over 80% of 1-die rolls, close to 30% of 2-dice rolls, less than 5% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and fewer than 1 in 8,000 5-dice rolls.​
If you set Mitigated Success at 10+, that will be one-sixth of 2-dice rolls, a bit over 60% of 3-dice rolls, and about 90% of 4-dice rolls.​
If you set Total Success at 13+, that will be impossible with fewer than 3 dice, around 26% of 3-dice rolls, around 66% of 4-dice rolls, and just over 90% of 5-dice rolls.​

So I think changing from d10 to d6 has the effect of making it impossible rather than just extremely unlikely to get full success with 2 dice; also pushes the rate of Mitigated Success down a little bit for 2-dice rolls; and forces a choice about whether you want Total Failure to be a bit less likely, or a bit more likely, for one or two dice.
Huh. Thank you.

It looks like d6s require shorter "bands" of results, as well. That could be a good or bad thing, as a style choice. A very short ladder works very well for pbta games, but those games don't tend to feature much numerical/statistical improvement over time.

The spread you have there works pretty well. 1 die only happens when you are unskilled at a thing, or have 1 rank and a penalty (or more ranks and a severe penalty, but that is probably going to be rare). 2 dice is 1 rank, so the lowest that total success could be would be 12, I think. That results in 99% total success at 5 ranks.

Of course, rolling nothing but 1's and 2's happens. I've seen it happen when someone casts fireball in dnd, when rolling for stats, etc, enough to not discount it. Part of the reason I chose rank dice rather than rank bonuses is that you always have the ability to totally fail. Thing is, at 5 ranks, total failure has to be 6 or less for that to even be possible, and that would make it literally impossible when unskilled.

Okay, yeah, I think that d10's work better than d6's. Since I don't work for a few hours yet, I'm going to tinker with things like d12+d6 rank dice, just for fun. It feels pretty good in The One Ring, but the One Ring also has special pips on the d12 and the d6s that mess with probabilities.

##### Heretic of The Seventh Circle
Before I map out the percentages, now that you've helped me grok the sort of field of play, here, the reason I'm considering d12+d6 is that by making the "Action Die" and the "Rank Dice" separate types, I can more easily do stuff like say, "when you make a skill check that deals damage, mitigates damage, heals, etc, the result of your Action Die is the number used for that effect." Rather than asking for a second roll. Could even do things like, "Your damage/healing/whatever is equal to you Action Die. For each level of success you achieved, you can add 1 rank die from the roll of your choice." Doing so could allow for active defense to be a roll where your result on the success ladder reduced the dice pool of the effect you're defending against, rather than subtracting a number. It just opens up a lot of stuff I could playtest and tinker with to make the system dynamic without increasing complexity in unfun ways.

1d12

7+ is 50%
8+ is 41%
9+ is 33%
10+ is 25%

1d12+1d6
7+ is 79%
8+ is 71%
9+ is 62.5%
10+ is 54%

1d12+2d6
7+ 95%
8+ 91% (similar in feel to all d10s, so far)
9+ 87%
10+ is 81% (this puts it closer to the d6s)

1d12+3d6
7+ 99%
8+ 98.6%
9+ 97%
10+ 95%

Any difference no longer matters, in terms of getting past total failure. Anywhere from 8-10 feels good here.

1d12
11+ is 16.6%
12+ is 8.33%
13+ is impossible

1d12+1d6
11+ is 46%
12+ is 37.5%
13+ is 29%
14+ is 21%
15+ is 14%

1d12+2d6
11+ is 74%
12+ is 66%
13+ is 58%
14+ is 50%
15+ is 42%

1d12+3d6
11+ is 92%
12+ is 88%
13+ is 82.6%
14+ is 76.5%
15+ is 69.5%

1d12+4d6
11+ is 98%
12+ is 97%
13+ is 95%
14+ is 84%
15+ is 88.5%

1d12+5d6
11+ is 99.77%
12+ is 99.5%
13+ is 99%
14+ is 98%
15+ is 97%

1d12
cannot be achieved untrained or without some sort of help or bonus.

1d12+1d6
16+ is 8.3%
17+ is 4%
18+ is 1.4%
19+ is impossible
20+ is impossible

1d12+2d6
16+ is 33.5%
17+ is 26%
18+ is 19%
19+ is 13%
20+ is 8%

1d12+3d6
16+ is 62%
17+ is 54%
18+ is 46%
19+ is 38%
20+ is 31%

1d12+4d6
16+ is 84%
17+ is 78%
18+ is 72%
19+ is 65%
20+ is 57.5%

1d12+5d6
16+ is 95%
17+ is 92.5%
18+ is 89%
19+ is 85%
20+ is 80%

Okay, so...I looked at a few progressions using those numbers, had to clarify my goals a little in terms of which steps on the ladder have shorter or longer bands of numbers, decided that the 80% chance of total success (20+) is about the highest I want total success to get, and I think that the following could work.

1-9 Total Failure.

10-15 Mitigated Failure. Highest possible result without a rank die. With 1 rank you'll get this 37.5% of the time, 3 ranks goes up to 87%, and masters sit at 99.5%. This is the Master's effective floor, though technically total failures will still happen every once in awhile.

16-19 Partial Success. Rare with 1 rank, impossible with none. 3 ranks is 62%, 4 ranks 84%, 5 ranks 95%. That feels good for being the halfway mark of the ladder, splitting failures and success.

Still might increase the size of both mixed results, tbh, but for now it's good enough to playtest.

20+ can't be got without 2 ranks and it's less than 10% then. 3 ranks is still only 30.5%, then about 58%, then about 80%. I wish I could keep the rest of the spread but not jump quite as high with 5 ranks, but I just can't find a way to do it with this model, and it takes a decent amount to get there.

At CharGen, you will likely only have 2 or 3 specialties at 3 ranks, and none higher than that. You'll be rolling 1d12+1 or +2 most often, meaning you'll mixed results the vast majority of the time, though at 1 rank you'll need to angle for a bonus more often.

You also have a few skills (and can never gain more) that are "Accurate", which means you reroll 1's. Obviously it behooves you to specialise in these, which is why they come from origin and archetype.

Also, again, you can spend an Attribute Point, which you start with 12-13 of, and you regain only some of per rest, to just increase a check by one step on the ladder. You don't want to do this too much, unless you don't mind not being able to use special abilities or mitigate incoming trauma, or push the scene in the direction you want, etc.

I think this feels really good. I'll playtest and report back soon.

#### Argyle King

##### Legend
You've stated that nothing else ever adds to the rolls.

Does anything subtract from the rolls? For example, would fog make a check to see something more sufficient?

##### Heretic of The Seventh Circle
You've stated that nothing else ever adds to the rolls.

Does anything subtract from the rolls? For example, would fog make a check to see something more sufficient?
Penalties and bonuses exist in the form of +d or -d, rather than static modifiers. So, I guess it isn’t totally accurate to say nothing else ever adds to a roll. Well, not anymore. Before seeing the stats, I wasn’t sure if +/-d was a good idea. I had considered having a penalty reduce your ceiling by making you reroll max results on the die, or using basically advantage/disadvantage but only for the “Action Die”.

I may still use the adv/disad idea, but we will see what playtesting feels like.

Another way to go might be adding an extra die, and either dropping the highest or lowest rank die result.

##### Heretic of The Seventh Circle
To sum up where I'm at now, 1d12 Action Die plus [rank]d6 rank dice. Success tiers at 10, 16, 20, total ranks from 1-5 (maybe 6, but a 6th rank is very diminished return. You're better off ranking up in related specialties and skills).

This makes it easier to keep straight ranks vs dice rolled, and allows the game to use the d12 Action Die to determine things like damage, as part of the roll.

It also might make the system I'm replacing the old Health system with work a little more smoothly, but that is a whole 'nother discussion.

#### Argyle King

##### Legend
Penalties and bonuses exist in the form of +d or -d, rather than static modifiers. So, I guess it isn’t totally accurate to say nothing else ever adds to a roll. Well, not anymore. Before seeing the stats, I wasn’t sure if +/-d was a good idea. I had considered having a penalty reduce your ceiling by making you reroll max results on the die, or using basically advantage/disadvantage but only for the “Action Die”.

I may still use the adv/disad idea, but we will see what playtesting feels like.

Another way to go might be adding an extra die, and either dropping the highest or lowest rank die result.

Are you familiar with FFG Star Wars?

Numerically, it handles things a lot differently than your system, but the idea of adding or subtracting dice is something that system uses.

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