Quote from: SpikeI had an idea roughly midway through my aborted sabbatical. Roughly speaking, it is this: the way games use dice fall into distinct and easily catagorized patterns. This is worth an in depth study, both as an intellectual study (for amusement) and on a more practical level as a means of identifing useful and useless mechanisms when discussing game design.

Of course, dice are not the only means of resolution/randomization in games, but they are the primary one.  

In a couple of your categories, either your descriptions are unclear, or your examples are wrong:

D20 System is "single die additive", not "single die vs."

ShadowRun has always been "roll multiple dice, and count how many of them are higher than X" (your Seperate Dice-Fixed Target, rather than Single High Pool).

I'd say Silhouette (Heavy Gear, Jovian Chroncles, Tribe 8, etc.) is definitely single-high dice pool, but, in common with the other such game that comes immediately to mind (Deadlands), it is not a pure example. (See below for suggested modifiers to layer on top of your categories). That is, it is more like a single-high system than a multiple-high system.

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Now, comments on the categories, etc.

Single die subtractive: well, there are lots of systems where you roll under (your single die vs.), and the amount by which you roll under is the degree of success, rather than simply reading the result on the die. So, effectively you're subtracting the die roll from a character stat, though most don't explain it that way.

Likewise, there are a few systems where you roll vs. a skill value (rather than adding to the skill value), but you're trying to roll over it, rather than under.

"Comparative Dice" is really just a bell curve. Well, not strictly, since it takes 3 or more dice to generate a bell curve; two dice is the degenerate case. But, nonetheless, the subtractive really makes no difference [vice additive]. To use an easily-shown example: 4d3-8 is identical to 4dF. Likewise, d6-d6 is the same as 2d6-7. Which is also why systems like Feng Shui don't use a single die--just like a 3d6 is used for more-normative results, a single smaller die would not be the same.

Also, keep in mind that dice pools where you use all the dice (whether adding them up, a la WEG Star Wars--a category i just noticed that you missed completely--or counting successes, a la Storyteller) also display bell curved results. Well, mostly. When one die can affect another (a 1 on one die cancelling a success on another, frex), it gets trickier. That might be a worthwhile category distinction to make: whether the dice in the pool are truly independent events, or whether they interact (1s cancelling in Storyteller; additional 6s raising the result in Silhouette; perhaps other cases).

Dice pool systems where you use a subset of the dice will produce a skewed result--it looks sort of like a bell curve, but with the peak shifted to one end, and a very long tail to the other end. Roll-and-Keep, Silhouette, Deadlands, Over the Edge once you add modifier dice, all do this. Generally such systems skew high, representing increasing ability with a higher skew, rather than a higher maximum, but not necessarily--OtE skews low when you've got penalty dice.

I'm not sure of the value of distinguishing systems based on the relative sizes of the die and the stats. Or, rather, i don't think you should roll that into the other distinctions, at the first order level. Rather, I would make that a second axis. IOW, two systems might both be additive single die, but one has stats in the 30-50 range and a d20, while the other has stats in the 0-10 range and a d20. Of course, the first one is high-level D&D3E, while the second is low-level D&D3E, which is why i think it's a separate axes of quantification. Yes, it makes a huge difference, but it's much less intrinsic to the dice system. Similarly, a lot of dice pool games vary drastically in their behavior between very low and very high pools, but they're still fundamentally the same mechanics.

I wonder if rather than distinguishing whether the entire die pool is used or only a portion of it (Multi High pool, vs. Seperate Dice-Fixed Target and Many dice-variable target), and then between fixed-target and variable target, if maybe those should be two different axes of differentiation. After all, the "multi high pool" category is, AFAIK, all variable-target, but there's no reason it couldn't be fixed target. Plus, you completely missed Ghostbusters, Star Wars, Over the Edge, and any others that use that system--namely, dice pool where you add up all the dice. Also, i think a system like Roll-and-Keep has more in common with Star Wars than with Deadlands or even Silhouette, but your current nomenclature implies that they are more alike, due to the similarity of category names.

So perhaps the dice pool systems could more usefully be broken down into three subcategories: single-highest, additive, success-counting. Within the single-highest, you either have modifiers/add-ons/gimmicks or subcategories to identify things like Deadlands, Silhouette, and Jadeclaw.  Within additive, the variable is whether you add all the dice (Star Wars), usually add all the dice (Over the Edge), or usually add a subset (Roll-and-Keep). Within all 3 categories, you could potentially distinguish between fixed and variable target numbers, but it perhaps makes the most sense to only do so within the success-counting category, since (1) i'm not aware of any examples of the other two types with fixed target numbers and (2) how you roll isn't affected as drastically in those systems, it just means you did or didn't succeed.

I'm not sure depleting pools, like Dying Earth, really belong in the dice pool category at all, since you only roll a single die at a time, so the statistical behavior ends up either indistinguishable from single-die systems, or looks sort of like a degenerate case of the single-highest dicepool systems--which, in a certain sense, or the least-dicepool-ish of the dicepool systems, since success range doesn't really change with increasing numbers of dice in the pool.

People wondered about fixed-size die pool, where other variables are used. First, the hypothetical example: everyone rolls N dice, and the size of the dice is dependent on stats. Now, the possible actual examples:

In a sense, Ironclaw/Jadeclaw, Usagi Yojimbo, and a few others are exactly this: you always roll, say, 3 dice (for Jadeclaw: race + skill + profession, IIRC), but what size each die is depends on the relevant scores. And it's a true dicepool system, because you're just taking the value of the largest die, not adding them together, plus, it's not a perfectly-fixed-size pool: you can sometimes roll fewer or more dice.

Four Colors al Fresco: every character has 4 numeric stats, and rolls all 4 of them any time a die roll is called for. You neither add them up, nor compare them to a target number. Rather, you order them according to result. The variables come in in that when you create your character you choose what size each die is (that stat's value); depending on what you're trying to accomplish, you'll want different dice to come out on top; and modifier dice which are rolled in addition to the pool, but sorted by value, too, rather than added.

Which, in case it wasn't obvious, points up a very different sort of dice mechanic, i think. In Four Colors al Fresco, you're not only determining whether or not the character succeeds, you're determining how/why they succeed (or fail). And, like i said, you're not comparing the dice to anything external (like a target number), but rather simply ordering them within the character's pool of dice.

Don't Rest Your head has a similar mechanic: you roll dice for various stats, which exact stats depending on the roll. It's a dice pool system, all d6s, so the better you are at something ,the more dice you roll when it comes into play. You then look for the highest *and* lowest dice--1s,2s,3s are successes, and you count the number of dice that do so, just like many other dice pool systems. But you then look at the type of die (i.e., what  stat it came from) that has the highest result, and that tells you the how/why of the result. Basically, the innovation/deviation from previous dice pool systems is tracking where the dice came from, rather than just lumping them all into one big pool.

Actually, now that i say it that way, it's not all that new. In addition to Four Colors al Fresco, Immortal did it before Don't Rest Your Head. Immortal is another one that i'm not sure how it fits into your system. You have 6 stats, each with a static value. When you try to do something, a target number is assigned, you roll a d10 and add the appropriate stat, and see if you succeeded. So far, straight forward. Here's where it gets wonky. Difficulty of a task increases the target number. Complexity of the task adds another stat into the mix. So, if swinging a sword is a red task (the stats have colors), swinging a sword at a smaller target is a higher-difficulty red task. You roll a red die and add your red score. But swinging a sword at a target in the dark is a red & blue task, so now you roll a red die and add your red score, beating the difficulty for hitting the target, and roll your blue die and add your blue score, beating the difficulty for the degree of darkness. And if you're trying to do this while wading in slippery mud, you also roll the die for movement actions (yellow, i think), adding that to your yellow score, and comparing to a 3rd difficulty, based on how much the mud is impeding you. Each difficulty can be separate. It would just be an elegant way to handle multiple actions, if they weren't all tied together: you can shift excess from one result to another (blue 12 vs. diff 7 and red 4 vs. diff 8 could be turned into a success by shifting 4 points from your blue result to make up for the crappy red roll), and you have a bunch of "free motes", which are extra (um, dice?, points?--i forget) which you can shift aronud from round to round, further shifting the probabilities, but only within the overall pool of dice.

That points up what might be a useful secondary axis: how much control the player has over the dice rolled. Frex, ShadowRun has a couple pools of dice that you can shift around from round to round, affecting how many dice you have for various types of actions. Fireborn has a similar concept of allocating your dice pool. As a degenerate case, the Storyteller system uses such a model for multiple actions.

If Roll-and-Keep is distinct from Star Wars, and you want to put Burning Wheel and Storyteller into separate categories, then ORE is definitely yet another sort of beast. It's not just a gimmick--counting the highest set of multiple dice, plus the player's ability to decide between multiple sets when they are present, leads to results that are every bit as distinct from the other dice pool systems as they are from each other.

There's yet another sort of die roll, which is a hybrid of single-die and bell curve: mid20 is the only example i can immediately think of. Roll 3d20, and toss out the highest and lowest dice. So, you're only adding a single die to your stat, but the results will be like a bell curve, sort of (it's actually a different sort of curve, and tapers less dramatically).

In addition to magnitude of the variable component vs. the fixed components, and fixed vs. variable target numbers (both variables apply to every category you've identified), there are some other "secondary" things that could be used to qualify dice methods. Here are some that i've thought of:

• exploding dice: Best result on a die results in a reroll-and-add. Could also happen in some fashion with particularly poor rolls. ex: ShadowRun, Deadlands, Rolemaster.
• cancelling: I think it only applies to success-counting dice pools, but where poor results on one die can cancel out good results on another. ex: Storyteller
• boosting: Can a good result on one die boost another. ex: Immortal, Silhouette.
• criticals and botches: Is there a way to get an extraordinarily good or bad result, beyond whatever the value on the die would indicate. I.e., is rolling a 10 on d10 with a stat of 7 the same as rolling a 9 with a stat of 8? Does it take additional rolls? ex: D20 System, BRP.
• special dice results: not sure if this is a special case of exploding dice and/or criticals and botches, but i'll toss it out there. Using the singles digit in some percentile systems to determine degree of success; a 1 in Ars Magica meaning reroll and double; doubles meaning a critical success; etc.
• wild die: a particular die, distinct from those determining success, that determines degree of success, or otherwise modifies the whole roll. ex: Star Wars, Hercules & Xena RPG.
• modifiers: are they in the form of static numbers, or more dice? Most game systems modify your skill with numbers (D20 System, Deadlands); a few modify by adding or subtracting dice, and not all of them are dicepool systems (Alternity); a few modify by modifying the number of dice rolled, but not the number counted/added (OtE).
• zero-centered vs. positive: most dice systems generate a number from 1 to something, or occasionally 0 to something. Others are zero-centered (Fudge, Feng Shui).
• success levels: does the mechanic generate a simple binary result, or degrees of success.
• result shifts: some mechanics, rather than  simply adding more to the number the die generates on a particularly good result (or subtracting on a particularly poor result), instead shift the entire result. Aria, frex: if you roll a 10 or 1 (on a d10), you then roll again, and if the new roll is a failure or success (respectively), the result is one step worse or better than it would've been just by applying the 10 or the 1 to your skill. And it can repeat, if you continue to roll 10s or 1s. What's distinct about this is that (1) it does this even if that first roll isn't a failure/success, so you can turn a failure into a success, and vice versa, in this way; and (2) it shifts by steps of result, rather than simply adding more numbers to the [numerical] result.

Thank you for that long post. It's going to take me a while to wade through it all, and I will freely admit that you left me behind in a few spots. Maybe I'm tired?

Can't believe I forgot about WEG's dice pool mechanic. If anything it is most represntative of it's type, while 'roll and keep' is a subset of that type.  The wild die, naturally, is a Gimmick effect, not that it's a bad one.  

I have had to think on the older editions of Shadowrun. I think I was mistaken here, as while typically a single 'high result' was always a success, multiple successes were necessary to accomplish tasks with any degree of proficiency... still I will also add a 'margin of success' overlay in there somewhere as well.

I think the Single vs. catagory is a fine catagory, however, you are correct that I sould include a roll over/roll under distinction, or addative/subtractive.  I tried to initially start with just the die mechanic itself, and not worry excessively about the 'fixed numbers' that are applied to them.   However, as such numbers are not a feature of every die mechanic (many dice pool systems, for example...), then obviously I should make a note of them somewhere.

On the Die - Die topic: A very good point, and when I update the OP to reflect the changes (when??? Dunno...) the catagory will remain, due to the route used to get it, but will reflect that. To my knowledge the d-d mechanic has not been used,for example, with alterations to the die sizes in play, which would necessitate keeping the catagory as the variables would change.

Color Dice and Jade Claw and others: Not concerned so much with how the dice are assembled, but I will have to look deeper before I comment more. JadeClaw sounds like a fixed dice pool, roll high with variable dice?    


Once I've worked my way through all this and processed it I will certainly have to look towards a rewrite to get it all in there.

Quote from: SpikeThank you for that long post. It's going to take me a while to wade through it all, and I will freely admit that you left me behind in a few spots. Maybe I'm tired?

Let me know--i'll be happy to clarify anything.

Quote from: SpikeOn the Die - Die topic: A very good point, and when I update the OP to reflect the changes (when??? Dunno...) the catagory will remain, due to the route used to get it, but will reflect that. To my knowledge the d-d mechanic has not been used,for example, with alterations to the die sizes in play, which would necessitate keeping the catagory as the variables would change.

Well, there's Alternity: i forget your base die roll--a d20, maybe?--but modifiers come in the form of additional dice added or subtracted, rather than numbers added or subtracted. Those modifiers are mostly a single die, but can range as high as +3d20, or as low as -3d20.

Quote from: SpikeColor Dice and Jade Claw and others: Not concerned so much with how the dice are assembled, but I will have to look deeper before I comment more. JadeClaw sounds like a fixed dice pool, roll high with variable dice?    

Without pulling my books out to confirm--yeah, mostly. You sometimes roll fewer dice, i think, and maybe also sometimes more than 3 dice.

The Immortal dice system is maybe nothing more than a cool gimmick for complex/multiple actions--i'm not sure. OTOH, it seems like it has as much in common with small-dice-pool systems like Silhouette as it does with single-die systems.

Before dismissing Don't Rest Your Head and Four Colors al Fresco, i'd take a look at them--especially the latter. I think it's a very distinctive way to deal with the randomizers, even in the contexct of my fairly extensive RPG collection.

I have a question, if there are any statistics gurus out there who can help.

I'm trying to figure out how to simulate a multi-factored game mechanic.  To give an example:

Standard d20 mechanics use Roll & Compare.  There are 2 factors: (1) the # rolled, and (2) the DC.  Both can be manipulated with additions and subtractions.

Dice Pool mechanics are similiar, but with 3 potential factors: (1) the DC, (2) the # of dice that beat the DC, and (3) the # of dice rolled.  As above, each factor can be manipulated before the roll.

My question is in reference to a mass combat system I've been toying with for d20 as I've read all the systems in print or PDF (more than a dozen).  For me, they all suck to one degree or another.  Just my opinion, mind you.

In simulating mass combat I use the dice pool 3-factor system for: (1) attack, (2) defense, and (3) # of attackers/defenders.

The real difficulty comes in with area effects (and this problem seems to occur in every mass combat sim).  d20 spells affect a variable number of opponents based upon: (1) DC, (2) saves, (3) size/shape of area of effect, (4) creature/item size, and (5) # of creatures/items.

Currently, I've been thinking of a 3-factor dice pool roll with 1 or 2 multiplications against a 2-factor table.  

Essentially, (1) # of creatures in unit = # of dice rolled, (2) number of successes vs. (3) the DC = the creatures affected (A).  (A) is multiplied by (B) a number 1-10 on a table with factors (4) creature size & (5) spell area.  (the table offers creature density within a spell area based upon creature size).


My question is: Are there any dice mechanics with 4 or more factors out there?  Dice pools were all that came to mind.  Clipping factors down to three always seem to require me to rewrite the d20 system, not appealing to me or potential users.


EDIT - Also, as this is for d20 games, I can't really use scaling dice pools as a 4th factor.  Buckets 'o d20 dice are already enough.  I don't need the d4 bucket, d6 bucket, d8 bucket, etc.