#4: Dice Pools

[RPGnet Columns]

http://www.rpg.net/columns/rollthebones/rollthebones4.phtml

Summary:

Looking at ability-based dice pool systems.

Go to the column (http://www.rpg.net/columns/rollthebones/rollthebones4.phtml) for more information.

[Paul DuPont]

I have been looking much more into the possibilities of dice pools before. Despite that, there were a few things that you pointed out which were new and helpful to me. I like your point about the low ability characters getting the chance to do a masterful job (as much as a high ability character), this points out that masters are simply more reliable. Your method of reducing the speed at which it holds true was good. I had forgoten the old (count multiples of a value), it bears remembering.

By far the most enlightening aspect of your column was your last point about dice pools being appropriate for games where you don't want much rolling of dice. I think this is very appropriate, though there are exceptions to be sure. I am still testing a system that uses dice pools for difficulty and the skill is the target number. Since this is a roll under system, and since the number rolled is limited to the skill of the character, no one can accomplish a task better than their skill level. Magical enhancements give bonus dice (picks the best die value) while dificulty modifiers add penalty dice (picks the 'worst' die value). Players are ussually hoping that they get exactly of close to their actual skill level.

I am not sure if this type of system would fit your next column or not. But if you see any potential difficulties, let me know. Players don't roll for character actions unless it is a 'high drama' or 'high stress' circumstance, otherwise, they are assumed to accomplish at their normal skill level. Latter I added rules for Masters who attained their full skill potential to get multiple successes (this make their action bigger though not better). Of course, even Masters still have a small chance of failure.`

I was trying to keep the number of dice low (hence penalty or bonus dice with a base of one die) but wonder if I can come up with better granularity for difficulty modifiers. Any sugestions?

[torbenm]

I am still testing a system that uses dice pools for difficulty and the skill is the target number. Since this is a roll under system, and since the number rolled is limited to the skill of the character, no one can accomplish a task better than their skill level. Magical enhancements give bonus dice (picks the best die value) while dificulty modifiers add penalty dice (picks the 'worst' die value). Players are ussually hoping that they get exactly of close to their actual skill level.

I'm not sure I understand exactly how your system works. You say you use a pool for difficulty. Does that mean that the number of dice rolled depends on the difficulty? If so, does a harder task mean more dice (in which case I assume all have to be under the skill) or does a harder task mean fewer dice (in which case you would need only one to be under the skill)? Also, I'm not exactly sure how your bonus and penalty dice work. Maybe if you went through an example it would help.

[Paul DuPont]

Ok, a 'standard' roll is one die to roll under the difficulty. If there are enhancements but the difficulty has not changed, then they get bonus dice. In which case they need only to roll under one their skill on one the dice. On the other hand, if there are difficulty modifiers and no enhancements they add penalty dice. In which case they have to roll under their skill level on all the dice in the pool.

Enhancements (bonus dice) and difficulty (penalty dice) cancel each other out. If there are more difficulty modifiers, the enhancements reduce the number of penalty dice and vice-a-versa.

It was designed this way to reduce the total number of dice being rolled, also, most modifiers are caused by characters 'pushing' their skills, this means self induced penalty dice but increases the effects of that action. Enhancements are likewise player tracked as often as not, since they mostly come from magic objects and magic effects. This reduces the GMs need to track and decide these issues once the players understand the system. Of course, the whole mechanic is unused most of the time since most characters are assumed to function within their skill level unless it is a high drama or high stress situation. So the GMs roll is largely to tell players whether to roll rather than how to roll.

[torbenm]

Ok, a 'standard' roll is one die to roll under the difficulty. If there are enhancements but the difficulty has not changed, then they get bonus dice. In which case they need only to roll under one their skill on one the dice. On the other hand, if there are difficulty modifiers and no enhancements they add penalty dice. In which case they have to roll under their skill level on all the dice in the pool.

Enhancements (bonus dice) and difficulty (penalty dice) cancel each other out. If there are more difficulty modifiers, the enhancements reduce the number of penalty dice and vice-a-versa.

I think I now see how it works. Adding one penalty or bonus die will have quite a dramatic effect. If you one one die have 50% chance of success, you will with a bonus die get 75% of success and with a penalty die only 25%. Generally, if your success chance is p on one die, N penalty dice will make your success chance p^(N+1) and N bonus dice will make your success chance 1 - (1-p)^(N+1).

QUOTE]Of course, the whole mechanic is unused most of the time since most characters are assumed to function within their skill level unless it is a high drama or high stress situation. So the GMs roll is largely to tell players whether to roll rather than how to roll.[/QUOTE]

While you should, indeed, only roll when it is important, you should be careful not to use it as an excuse for a broken system. I have heard people say "It doesn't matter that it is broken, you don't use it very often".

I don't say your system is broken. It seems to work fine with the provision that adding a penalty or bonus die has a very large effect, so it is suitable only when this is what you want.

It is a bit like the "highest of N dice" systems, where going from one die to two is very dramatic, but where you quickly get to rolling maximum almost all the time.

My suggestion to that was using the second-highest die. This can be modified to using both bonus and penalty dice for a roll-under system in the following way:

- You normally roll three dice and take the middle result (this has the same average as just rolling one die, see more in the next column).

- With bonus dice, you take the second-lowest result.

- With penalty dice, you take the second-highest result.

So, for example, with one bonus die you roll four dice and take the second lowest. If you, using d10s, would normally have 50% change of success (i.e., you must roll under 6), you will with one bonus die have 68.75% of success and with two bonus dice you will have 81.25% chance of success. Similarly, adding one and two penalty dice will decrease the success rate to 31.25% and 18.75%.

Compare this to 75% and 87.5% for bonus and 25% and 12.5% for penalty with the unmodified system.

[smascrns]

Magical enhancements give bonus dice (picks the best die value) while dificulty modifiers add penalty dice (picks the 'worst' die value). Players are ussually hoping that they get exactly of close to their actual skill level.
I've been using the core idea behind this (and writing about it in my RPGnet columns) for years - just check the links below. It was already present in Sillcore but in a limited way.

One of the advantages is that it reduces the number of dice in a dice pool. For instance, if one has a range of values for the ability that goes from 1 to 7 and uses a 'pick highest' dice pool, than the number of dice can go from 1 to 7. On the other hand, if one uses a 'pick eighest/lowest' dice pool, it works this way:
Ability 4 is the average value and requires 1 die (I call it the Base Die). For each level of ability below average one gets a penalty die; for each level above average one gets a bonus die. This means that at ability 1 one uses 4 dice (base die plus three penalty dice) and likewise at ability 7 one uses 4 dice (base die plus three bonus dice).

[Paul DuPont]

I had thought of using the multi-die base roll and using a pick second highest, second lowest but felt that keeping track of the number of dice rolled was too cumbersome for the advantage it gave me. There are sevearl aspects of my system that I first felt were flaws but latter saw as features. Since my die pools are not tied to attributes or character ability beyond 'comparative' ability (a character twice the size will get bonus dice for damage and penalty dice to hit) I don't feel that it is particularly problematic. I was hoping someone would have another sugestion. Then again, playtesting may show this method as best.

1 bonus= roll 4 dice. 2 bonuses= roll 5 dice, ... I feel like that would require a table, but I would rather not use a table for basic skill rolls in a storytelling game like this one. Yes I know it is only +3. Maybe I just need to adjust to the idea. Another complication is that highest and lowest are not always the best or worse dice since players want to roll under their skill by as little as possible and since other rules allow them to make use of multiple values it becomes complicated to remove 'best' or 'worst' dice.

If my system is broken, I want to fix it. I actually use it at some of the most important parts of the game so it needs to work well in those instances. At the climax or other times the characters (and players) are under stress wondering 'what will happen next?' My comment was based on the fact that it won't slow down gameplay in general, it is designed to slow down the game only when players are in the tension of climax (like slow motion in movies).

It is nice to know others are using this mechanic successfully, though one always wishes to blaze new ground. :D Oh well!

[smascrns]

I prefer simplicity myself. Pick second highest/lowest requires larger sets of dice. 1 Bonus only works with 4 dice, and so on. So I stick to pick best. Yes, we go up the ladder quite fast (but not as fast as implied in another post or the column) but why not?

I may introduce an optional rule where if the character is average he rolls three dice and picks the middle result, though. But depends on implementation since some variants of the way I use these dice pools don't require it.

[Paul DuPont]

Upon further thought, I have decided that I don't actually want the increase to be diminished. One reason is because I want to keep the number of dice low, I would rather have each die really 'mean' something to the player. Somewhat associated with that, my affinity system is designed to encourage players to make fun and interesting descriptions of character actions. The system does this by giving them a 'free' bonus die. I want that to 'mean' something to the player.

I also prefer the idea that unless something is trully significant, it won't change the die roll. That will keep the game focused on the significant things rather than bogging down in detail.

Thank you both for your feedback. It was quite helpful and gave me the opportunity to think through my options 'out loud' and confirm my current approach.

[mindstalk]

My variant, which Paul has as part of his: roll a fixed number of dice, probably 4 or 5. Successes are dice equal or under one's skill level. So, one might have skills ranked 0-9, and roll 5d10. Skill of 7 and a roll of 3,8,7,1,2 would be 2 successes. # of successes goes from 0 to 5, which is annoyingly coarse, but I love the curves. And performance is an S-curve based on linear experience, like in Sergio's old columns. Expected value is trivial to calculate; general distribution is easy to visualize, not so much to calculate.

Sergio's +b/+p system I re-read last night, and I liked the elegant use of low numbers of dice, and thought it was basically an inversion of my system (skill being # of dice, result being number you read off) with the penalty of being really hard to analyze. But i realized this morning it's actually pretty easy, and as was mentioned but not emphasized in the column, it goes straight to making the extreme value the most likely. For max of 2 dice, the chance of rolling n is (n^2 - (n-1)^2)/n^2, and chances rise linearly with n. For max of 3 dice, change all the squares to cubes, and chance rises quadratically.

Actually calculating the expected value for a skill level... isn't that hard with a calculator, but tedious. E.g. expected value of max of 2d4 is 7*4 + 5*3 + 3*2 + 1, divided by 16. For d20? Bleah.

For my system, a next variant, inspired by description of Riddle of Steel, was to replaced the fixed number of dice by an attribute. So Dex 2, Agility 9 would roll 2 dice, looking for 9 or below; Dex 5 Agility 5 would roll 5 dice, looking for 5 or below. I like how this makes a role for attributes which isn't just a symmetry of the skill role, or a linear shift.

[Daztur]

Hmmmm, never thought about this subject much before. I'm really liking the "roll bunch of dice and the second highest one is your result" since it makes it hard for fluke-ish beginner luck to win the day and it has built in diminishing returns.

[mindstalk]

Hmmmm, never thought about this subject much before. I'm really liking the "roll bunch of dice and the second highest one is your result" since it makes it hard for fluke-ish beginner luck to win the day and it has built in diminishing returns.

OTOH, whereas "take max" makes the high score most likely right away, "take second" apparently takes 14 dice to get there, which for my taste is too many dice.

[Daztur]

OTOH, whereas "take max" makes the high score most likely right away, "take second" apparently takes 14 dice to get there, which for my taste is too many dice.

Depends what sort of game you're playing I guess. With a low-powered game you don't want the highest possible result to be very likely.

[mindstalk]

Not trivially very likely, no. I actually like my experts to be near their peak, even in a mundane game. Passion/effort/inspiration might let them surpass normal limits, but basically they'd be always very good, with a duel decided mostly by who makes the first minor mistake. Which is easy to get if you fiddle the target number in success counting.

[Daztur]

Not trivially very likely, no. I actually like my experts to be near their peak, even in a mundane game. Passion/effort/inspiration might let them surpass normal limits, but basically they'd be always very good, with a duel decided mostly by who makes the first minor mistake. Which is easy to get if you fiddle the target number in success counting.

Hmmmm, with that sort of thing maybe having the "roll a handful of dice" mechanic would work well with mabye different sizes of dice depending on different things. Maybe number of dice being skill and size of dice being the stat? It would especially work out if getting a very low number on your roll was very very bad since playing a character with a "result is highest of 2d10" skill (whiz kid) would be very differently than a character whose skill is "result is the highest of 6d6" (seasoned but over the hill professional).

[mindstalk]

My variant, which Paul has as part of his: roll a fixed number of dice, probably 4 or 5. Successes are dice equal or under one's skill level. So, one might have skills ranked 0-9, and roll 5d10. Skill of 7 and a roll of 3,8,7,1,2 would be 2 successes. # of successes goes from 0 to 5, which is annoyingly coarse, but I love the curves. And performance is an S-curve based on linear experience, like in Sergio's old columns. Expected value is trivial to calculate; general distribution is easy to visualize, not so much to calculate.

Sergio's +b/+p system I re-read last night, and I liked the elegant use of low numbers of dice, and thought it was basically an inversion of my system (skill being # of dice, result being number you read off) with the penalty of being really hard to analyze. But i realized this morning it's actually pretty easy, and as was mentioned but not emphasized in the column, it goes straight to making the extreme value the most likely. For max of 2 dice, the chance of rolling n is (n^2 - (n-1)^2)/n^2, and chances rise linearly with n. For max of 3 dice, change all the squares to cubes, and chance rises quadratically.

Actually calculating the expected value for a skill level... isn't that hard with a calculator, but tedious. E.g. expected value of max of 2d4 is 7*4 + 5*3 + 3*2 + 1, divided by 16. For d20? Bleah.

For my system, a next variant, inspired by description of Riddle of Steel, was to replaced the fixed number of dice by an attribute. So Dex 2, Agility 9 would roll 2 dice, looking for 9 or below; Dex 5 Agility 5 would roll 5 dice, looking for 5 or below. I like how this makes a role for attributes which isn't just a symmetry of the skill role, or a linear shift.

Huh. So I was, by implication at least, critical of how quickly Sergio's max function zoom to the top (or bottom, if you're taking the min.) And thought my system did similar things more nicely. But I was wrong! My system isn't even diminishing returns, except if you look at proportional increase. Expected value is linear with experience, or at least with skill number, which I'd thought would be linear with experience. Doh. While Sergio's system does in fact do an S-curve, as he wishes; max of 2 dice may suddenly make doing well most likely, but that's what S-curves do: shoot from bottom to top with only a brief time in between. One could ask if it's fun, but that's another matter. :)

Not sure I could adopt it without fiddling; the midpoint is just rolling one die, which is flat, which is ennnh for me; I like my bell curves. Admittedly midpoint is someone who's right at the cusp between casual amateur and professional, so one might expect a broad range, but flat? Which I guess would be why Sergio mentions considering "take middle of three" for the midpoint.

[smascrns]

Huh. So I was, by implication at least, critical of how quickly Sergio's max function zoom to the top (or bottom, if you're taking the min.) And thought my system did similar things more nicely. But I was wrong! My system isn't even diminishing returns, except if you look at proportional increase. Expected value is linear with experience, or at least with skill number, which I'd thought would be linear with experience. Doh. While Sergio's system does in fact do an S-curve, as he wishes; max of 2 dice may suddenly make doing well most likely, but that's what S-curves do: shoot from bottom to top with only a brief time in between. One could ask if it's fun, but that's another matter. :)

Not sure I could adopt it without fiddling; the midpoint is just rolling one die, which is flat, which is ennnh for me; I like my bell curves. Admittedly midpoint is someone who's right at the cusp between casual amateur and professional, so one might expect a broad range, but flat? Which I guess would be why Sergio mentions considering "take middle of three" for the midpoint.
Yes, that's the point if I want all the numbers in the dice roll to be meaningful. What I mean is, I have basically two ways of using the dice pool:

Way one, the range of game results is equal to the range of die results. If I'm using a d10 there are 10 different results; if I'm using the d6 there are 6 results; and so on.

Way two, the range of game results is smaller than the range if die results. For instance, I have game results that go from A to E (these can be mapped into qualitative results instead of letters, of course). But I use dice with a larter set of results, say the d10. In this case A = 1 on the die; B = 2/3; C = 4/7; D = 8/9; and, E = 10.
What happens is that I'm simulating a veru crude bell curve in the way I distribute results, so I don't need to roll multiple dice, pick the median for average abilities. Furthermore, if I use the d20 I minimize the problem with getting to the top of the scale very fast with larger dice pools.
On the other hand, I get a more coarse scale of game results, something that some players dislike. I'm personaly more than fine with it.

[smascrns]

Hmmmm, with that sort of thing maybe having the "roll a handful of dice" mechanic would work well with mabye different sizes of dice depending on different things. Maybe number of dice being skill and size of dice being the stat? It would especially work out if getting a very low number on your roll was very very bad since playing a character with a "result is highest of 2d10" skill (whiz kid) would be very differently than a character whose skill is "result is the highest of 6d6" (seasoned but over the hill professional).
!!! I'm currently working on a game that combines my bonus/penalties dice pool with different dice. Basically the attributes represent raw talent and are mapped into the type of dice, from d4 to d12. Next skill is represented with dice pools from lowest at 2 penalty to best at 2 bonus. This means that a character with high skill is able to get operate consistently at the top of his natural ability, but he is also limited by the latter.

For instance, take someone like Conan. He is a natural fighter, so his combat attribute is set at d12, he can get the best results possible in combat. he is facing a less naturaly endowed fighter that only gets a d10 for combat talent.
The young Conan is naturaly talented but he lacks the skill, so he gets a 1 penalty for combat, meaning he rolls two d12 and retains the lowest result. He is fighting an experienced fighter that gets 1 bonus and thus rolls two d12 and retains the highest value rolled. On average the fighter is able to beat the young Conan but the latter may from time to time come out with an attack that is just behind the fighter's capabilities.
Of course, when Conan matures and becomes an expert fighter himself (at 2 bonus), he really becomes a fighting machine that is on a part with the best fighters in terms of skill and beats them in terms of talent. Or we can assume that Conan is the rare individual that takes skill to new eights at 3 bonus; and that when he is really prepared he takes his talent behind the usual range of human capabilities, and he gets a +1. So he rolls the best of 4d12 pus one, something that no one is able to do...

[mindstalk]

Me, if I went Sergio-like, I think I'd have 3d6 as base, and bonus or penalty dice being "add best/worst 3". Make curviness intrinsic -- though only journeymen (middle) would have a normal normal, everyone else will be skewed left or right. So like my system in skew, but with the S-curve of experience. And you can deal with arbitrarily large experience easily, it's just more bonus dice, and doesn't get out of hand.

Drawbacks: there's no natural zero -- one could in theory have arbitrary amounts of inexperience (penalty dice), which doesn't make sense. Have to guess what a reasonable starting point is for untrained skills.

My system allowed for fairly fine grained skills, and a natural but asymmetric interaction with attributes or other "powers", but had very coarse successes. Sergio allows for fine range of results but a pretty limited range of skill classes, and thus of modifiers. And reading the columns didn't tell me how attributes would be used; I could see just adding or subtracting a fixed amount, e.g. Str adds 2 but inexperience means you're at -1, so you roll 4d6, add the worst three, then add 2 to the result. But it doesn't feel as clean as my system, though maybe that's familiarity.

One could completely separate the functions, e.g. have a resolution of skill + 5(biased d2), with the bias controlling your reliability: normal people would have a fair d2, more trained ones would be rolling successes under 5/6 or 9/10, but you could easily have high power and high variance, but low power and low variance, or any combination. Drawback: more complicated, makes advancement less obvious.

Bah. Not sure anything looks perfect to me right now.

[smascrns]

Me, if I went Sergio-like, I think I'd have 3d6 as base, and bonus or penalty dice being "add best/worst 3". Make curviness intrinsic .
It's always a tough call. I really prefer small sets of dice, though, like a personal bias.
Drawbacks: there's no natural zero -- one could in theory have arbitrary amounts of inexperience (penalty dice), which doesn't make sense. Have to guess what a reasonable starting point is for untrained skills.
True. The way I look at this is that I fix it arbitrarly in terms that attempt to represent the distribution of skills in the population. So, I assume that there are 5% of people with very low skill, 20% with low, 50% with average, 205 with high and 5% with very high. Of course, this corresponds to -2, -1, Base Die, +1 and +2. The advantage of this approach is that it also allows me to distribute the likelyhood of a particular interaction with persons of a certain skill level. I know that there is one in 20 fighters, for instance, with very high skill. Note, this only represents people that have learned the skill. It does not include the masses that didn't learn it. So, if I'm looking at speakers of Latin I'm not considering in the distribution the millions that don't know Latin at all.
reading the columns didn't tell me how attributes would be used; I could see just adding or subtracting a fixed amount, e.g. Str adds 2 but inexperience means you're at -1, so you roll 4d6, add the worst three, then add 2 to the result. But it doesn't feel as clean as my system, though maybe that's familiarity.
My personal approach has always been to have skill plus attribute. This means that attributes map into modifier dice as well. If one has skill +1 and attribute -1 one rolls two dice, pick lowest.
Not sure anything looks perfect to me right now.
I suppose it's never perfect. Each time I start to think I've made it something comes that stops the process.

[smascrns]

Me, if I went Sergio-like, I think I'd have 3d6 as base, and bonus or penalty dice being "add best/worst 3". Make curviness intrinsic .
It's always a tough call. I really prefer small sets of dice, though, like a personal bias.
Drawbacks: there's no natural zero -- one could in theory have arbitrary amounts of inexperience (penalty dice), which doesn't make sense. Have to guess what a reasonable starting point is for untrained skills.
True. The way I look at this is that I fix it arbitrarly in terms that attempt to represent the distribution of skills in the population. So, I assume that there are 5% of people with very low skill, 20% with low, 50% with average, 205 with high and 5% with very high. Of course, this corresponds to -2, -1, Base Die, +1 and +2. The advantage of this approach is that it also allows me to distribute the likelyhood of a particular interaction with persons of a certain skill level. I know that there is one in 20 fighters, for instance, with very high skill. Note, this only represents people that have learned the skill. It does not include the masses that didn't learn it. So, if I'm looking at speakers of Latin I'm not considering in the distribution the millions that don't know Latin at all.
reading the columns didn't tell me how attributes would be used; I could see just adding or subtracting a fixed amount, e.g. Str adds 2 but inexperience means you're at -1, so you roll 4d6, add the worst three, then add 2 to the result. But it doesn't feel as clean as my system, though maybe that's familiarity.
My personal approach has always been to have skill plus attribute. This means that attributes map into modifier dice as well. If one has skill +1 and attribute -1 one rolls two dice, pick lowest.
Not sure anything looks perfect to me right now.
I suppose it's never perfect. Each time I start to think I've made it something comes that stops the process.

[mindstalk]

Yeah, I like small # of dice too. Relative to Shadowrun or Exalted pools, anyway.
I was thinking a roll and keep could work well. Roll attribute + skill, keep the smaller number. Att 3 Skill 1, roll 4 keep 1. Att 1 Skill 3, same. You don't get low-skill people doing ridiculously well out of raw talent; att and skill always matter; skill can grow unboundedly without getting out of hand; diminishing returns (rapid rise in power up to your attribute cap, then just get more reliable.)

Pools would get up to the high units though, and somewhat coarse.

If I'm being realistic enough to care about expertise curves, I feel I do have to think about representing the masses. "No Latin" isn't a big deal -- autofail -- but other skills can be tried with no or minimal training...

[Paul DuPont]

In my system, (called Opus by the way), I use attributes as a definition of the effects when the skill is successful. In fact, there are no attributes on the character sheet with the basic rules. That is part of advanced/race creation. When two characters oppose each other and one has a higher 'average result' because of their 'invisible' attributes, then either they get a bonus die or the opposition has a penalty die. The system has evolved so the character can make use of skills, proficiencies and knowledges. Thus, a single die roll (with any number of bonus or penalty dice) can result in a failure, or 1 to 3 successes. One success means the person has achieved their desired result (add flavor like, just barely, through rote, etc.), 2 successes adds a level of 'magnitude' thus raising the effect of the result above what is normal for their 'attribute level', three successes raises it twice. Many actions involve various result levels, for instance, throwing has both distance and impact as values, not to mention accuracy. So a person with multiple 'additional' successes can apply it to extra impact (often damage), increased range, increased accuracy (like critical hits or circumventing armor, etc).

In general, the bonus and penalty dice are nothing more than modifiers, fighting someone of vastly different strength or speed (or whatever), simply counts as a modifier to your roll (or theirs). From this vantage point, the dice pool has nothing to do with personal talent or skill level (either personal or statistical). Although I do have an afinity system that grants a bonus die for describing actions within the affinity of the character. Mix and match then! :o