Probability Curves

[Henri]

Well, these are meant to be broad categories, so weird things could be either special cases, hybrids (like Sorcerer), or maybe we'll need some new broad categories.

I think you have a very good point about how an underlying distribution can actually just lead to a binary "succeed, fail" result.  I definately like systems that allow for degree of success.  However, as John points out, you can allways use the distance from the Target as degree of success for fixed-dice systems.  

I'm not familliar with Shadows, but if both the dice and the target number are fixed, what varies?  There has to be something that varies in order for you to represent the difficulty of the task and the ability of the character.  I can't think of a system that doesn't incorporate these two variables.

[Mike Holmes]

I'm not familliar with Shadows, but if both the dice and the target number are fixed, what varies?  There has to be something that varies in order for you to represent the difficulty of the task and the ability of the character.  I can't think of a system that doesn't incorporate these two variables.

Actually, I think Shadows is a d20 vs d20 or something. Can't remember. What happens is that you use points after the roll for re-rolls. There is no "difficulty."

I've even seen games where you just flip a coin for every resolution. I mean, that's way more rules than most freeform games have where there is no resolution system (does that represent a category - null?).

Also, are we only looking at traditional resolution systems? I mean, what about methods for rolling for damage? Or any of the myriad other mechanical systems that exist out there that are not strictly success/fail determiners? When does a system become something more than the resolution? TROS combines the combat resolution system with the damaga system. Are these all resolution, or is just the calculation of the "success" portion of things the "resolution"?

Again, what about matching systems, and other "odd" systems? How would you characterize Unknown Armies system, where you want to roll as high as you can but still remain under the target (aka The Price is Right method). Would you differentiate between how Deadlands does Step Dice, and how Earthdawn does it? What about the Immortal system, where does that fall? Dreamspire isn't out yet, but the basic idea of the mechanic is that stat provides the die type, and attribute provides the target number. What I think I'm getting at is that we need to have a more descriptive system, and less a categorization system.

And, as long as we're at it, what about systems that resolve using playing cards (lord knows there are tons of them)? Or Dragonstrike the CCG RPG? Or are you only interested in dice? What about games like Throwing Stones with collectable dice? Or The World, The Flesh and The Devil (or Ron's new game) which have customizable dice?

Mike

[M. J. Young]

I'll toss out Scarlet Jester's Diverse Lunacy system. d10's are rolled, but the faces are altered to a center-weighted five-step outcome and then always used as opposed rolls. (It will appear for the first time in what I think is a modified form in Legends of Alyria--I think LoA reduces the probability of rolling the center from 40% to 30% to create a 10% chance to botch, but I'm sort of extrapolating backwards to get that.)

I also agree that there are a lot of questions about what should be included. I think this thread is about "dice-based fortune task or outcome resolution systems" exclusively. Character creation rolls are not included despite their impact on resolution; factors determined by the same roll (e.g., relative success (including damage), relative failure, botch, crit, and color) are incidental except as they relate to resolution.

Even so, there will be systems that defy simple categorization. Obviously, Multiverser's skill checks (percentile, roll under but as high as possible), simple attribute checks (peaked 2d20 curve roll under) and difficult attribute check (straight d30+10 roll under) are all resolution systems, as they determine success or failure (although they also determine relative success and relative failure). What, though, of the General Effects Roll? This 3d10 roll determines whether events, situations, outcomes, or other aspects favor or disfavor the player's desires. The simple example is the character who facing a crowd of apparently intelligent creatures of which he knows nothing fires a gun in the air to get attention. Do they flee in terror, turn to focus on him, attack him viciously, stare at the sky looking for the source of the sound, cower on the ground, or something else? The GE roll resolves this situation by guiding the referee in determining what happens. In application it can be as close to a resolution mechanic as deciding the outcome of a battle in which the player character plays only a minor part, or as far from it as deciding whether the night is quiet or interrupted by a rainstorm or a wandering bear.

So what are we after here, really?

--M. J. Young

[Rob Carriere]

I think that if you want a very realistic game, you want a fairly low variance.

Just one quickie remark: A _very_ realistic game would probably have variable variance. In many tasks, newbies have much larger variance in their results than do experts. You could simulate this with a system where increasing expertise raises the mean and drops the variance. (Sounds like a candidate for a computer solution to me, but maybe somebody has a clever die-roll solution.)

SR
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[Andrew Cooper]

I think this is on-topic.  Anyway, I just wanted to say that I've written a Windows program that is a Dice Analyzer.  I essentially allows you to pick die types, number and type of analysis and then gives a nice little graph of the results.  It's for those folks who really hated statistics.  Instead of doing the problem mathematically, the computer just rolls 100,000 iterations and compiles the results.  They're pretty accurate too.  If anyone wants a copy of the program, send me an email address and I'll send it to you.  It's only about 50kb so it's not hard to send.  It zips up to 14kb.  I'm always willing to add features to those who like the program and want to see different types of results.

[Henri]

A couple of people have brought up several interesting ideas, but I wanted to point out that the topic of this thread is intended to be about probability curves.  Broader system issues like IIEE are not the topic, although if someone wants to start a new thread about that that would be cool.  Also, drama and karma systems are not part of this thread.  The topic is simply what is the diversity of dice rolling mechanisms out there, what kind of probability curves do they create, and what are the salient characteristics and effects of these curves.  

Even with such a narrow focus, there is a lot of diversity out there.  For this reason, I thought it would be useful to start out by looking at what those systems have in common, and creating broad categories.  Then we can look at differences within categories to create more refined categories.

John's article identifies three categories at the highest level: fixed dice, dice pool, and step dice.  Then he breaks fixed dice into flat and bell-shaped.  Then (this is a slight modifcation on my part), dice pools are broken down into additive, fixed target number, variable target number, and highest die.  

Allow me to restate the question is a way that I hope is more focused.  At these two upper-most levels, is the system complete?  I suspect not.  Can we come up with any other broad categories?  At the highest level, are there any other classes that cannot be fit within fixed, pool, or step?  What about at the next level down?  I suggest that we don't add a third level yet, until we are happy with the top two levels.

[John Kim]

Also, are we only looking at traditional resolution systems? I mean, what about methods for rolling for damage? Or any of the myriad other mechanical systems that exist out there that are not strictly success/fail determiners? When does a system become something more than the resolution? TROS combines the combat resolution system with the damaga system. Are these all resolution, or is just the calculation of the "success" portion of things the "resolution"?  

My intent with my dice essays was to cover common choices for RPGs.  The idea being that if a technique has appeared in, say, three or more unrelated RPGs, then it should be at least analyzed and considered.  Of course, RPGs can and should invent new techniques -- but they should be compared against the relatively well-tested and understood techniques of earlier games.  

John's article identifies three categories at the highest level: fixed dice, dice pool, and step dice.  Then he breaks fixed dice into flat and bell-shaped.  Then (this is a slight modifcation on my part), dice pools are broken down into additive, fixed target number, variable target number, and highest die.  

Allow me to restate the question is a way that I hope is more focused.  At these two upper-most levels, is the system complete?  I suspect not.  

I don't think that completeness is necessarily desirable.  My intent wasn't to make broad labels which can be attached to any possible dice mechanics, but rather to explain how specific known dice mechanics worked.  For example, Godlike isn't sufficiently covered by these choices -- nor is FVLMINATA.

[Mike Holmes]

I was refering to Henri's efforts here, John, your article does a good job at what it intends to do. And now that I've got a better idea of what Henri is looking for - sorta like a morphology of dice rolling - I get where he's at. I'm not sure where to proceed with it, but at least I think he's got a well defined task in front of him. Basically, I see him using your work as a jumping off point. If your point is that it's not the best point to jump from given your goals for the article, then I may be with you. Not sure.

Mike

[Thierry Michel]

A couple of people have brought up several interesting ideas, but I wanted to point out that the topic of this thread is intended to be about probability curves

You need to narrow that further.

Probability of what ? The bell curve for 3d6 does not represent the same type of result that the graph of the number of success in a dice pool.

[Henri]

Probability of what ? The bell curve for 3d6 does not represent the same type of result that the graph of the number of success in a dice pool.

I'm not sure that I agree.  Although there are important differences (which is why they are in different families of dice systems), they are fundamentally doing the same thing.  Lets say the GM looks at my skill and the difficulty of the task and says, okay, you need a 14 or better on 3d6.  The higher above 14 the better, the lower the worse (so we care about degree of success).  Or we are playing a different game and he says, roll 3d6 with target number 4 and you need to get at least two successes.  If you get 3, its better, and if you get none, its really bad.  

Fundamentally, these are doing the same thing, although there are differences.  The first gives a much smoother bell curve, whereas the second is more rough and blocky.  Hence the first example has a much finer granularity for determining degree of success.  Also, in the first my skill affected the targert number of 14, whereas in the second it affected the number of dice.  

As for your more general point that I need to narrow my focus, I apologize that I was somewhat vague at the start of this thread, but that is because I was still trying to figure out what I was trying to do.  Mike nailed it.  I'm looking for a "morphology" or "taxonomy" of dice rolling.  I am using John's essay as a "jumping off point."

Mike suggests that this may not be the best jumping off point, and I get the feeling from several people that this attempt may be somewhat misguided or at least quixotic.  I hold that a taxonomy of dice systems would be a good, useful thing to have.  However, I am willing to concede that it may be far more difficult a task than I am really up to tackling in my free time and with my limitted breadth of experience.  If that is the conclusion of this discussion, I'm okay with that, since I feel like it has already been helpul to me in sorting things out in my head.

[Mike Holmes]

I think it's potnetially a good idea, Henri. For a little history, it's been tried before, BTW (I'm remiss for not having looked up the thread). The question is what will be the outcome of the terms developed? I think that the usual idea in these attempts is to come up with a common shorthand for refering to systems to make communication of them from person to person simpler, and so that the types can be discussed in groups.

Is that where you're headed?

If so, I'm not sure that John's headings don't already sorta cover it. And there is an informal jargon that has developed around these things. Rollunder, and rollover, for instance are pretty commonly used and fairly well understood (the assumption for rollunder, for instance, likely actually means roll the TN or less, so, ironically not really an accurate description). I guess the question is whether or not more specific description doesn't cover things. Then these terms can be used in combination. For example, you'd just have a jargon like:

Additive: Dice results are added
Individual: dice are considered individually
Pool: More than one die is rolled
Set: the number of dice do not change
Variable: the number of dice are dependant on some factor
Target Number: the results of each read die are compared to some number
Rollover: result is a success if it is equal to the target number or more
Rollunder: result is a success if it is equal to the target number or less
Matches: Matching dice rolled are successes
MOS (margin of success): successes are determined by the difference between the TN and the roll

Etc

Then we say things like TROS is a two stage method where you start with a rollunder variable pool opposed by another rollunder variable pool where the MOS is calculated as the difference in successes generated by each pool.

Just an example, it would need a lot of work. The advantage here is that you can accurately describe most systems with the shorthand. The disadvantage is that you can't really speak to "rollunder" systems because they're all vastly different depending on the other variables.

But I think that's going to have to be the case. Because there so many variables at work here.

Still, I may be wrong - maybe some of these combinations can be declared "categories" in some fashion that could lead to effective discussion of the categories. But I'd personally be fine with just defining a category for discussion by conglomerating the terms that are needed to define it accurately.

Mike

[Henri]

I think it's potnetially a good idea, Henri. For a little history, it's been tried before, BTW (I'm remiss for not having looked up the thread).

I'm sure it has.  I'd like to see the results of those attempts.  

The question is what will be the outcome of the terms developed? I think that the usual idea in these attempts is to come up with a common shorthand for refering to systems

Well, that's part of it.  I was also hoping for nested groupings as well as just a short hand for descriptions

If so, I'm not sure that John's headings don't already sorta cover it.

Heck, maybe they do.  That is one of the questions I was posing.  

And there is an informal jargon that has developed around these things.... The advantage here is that you can accurately describe most systems with the shorthand. The disadvantage is that you can't really speak to "rollunder" systems because they're all vastly different depending on the other variables. But I think that's going to have to be the case. Because there so many variables at work here.

This is a good point and may be why an attempt at classification is quixotic.  Essentially, we have to arbitrarily pick certain features and say that they are more important than others.  John's system priveleges fixed vs. variable number of dice rolled and makes these two his most important categories.  This isn't a problem with a shorthand, because you are just trying to describe features individually, not organize them into groups based on shared features.  

In an earlier post I wrote that I wanted to come up with a taxonomy and then discuss the advantages and disadvantages of different groups.  But it occurs to me that we don't strictly need a taxonomy to do this.  Perhaps the short hand you are referring to is sufficient.  Basically, what I wanted to do was the examine a subset of Ron's claim "System Does Matter."  There is more to system than just the way in which dice are rolled, but I wanted to look at just this feature and see how it matters.  According to the principle of System Does Matter, when deciding on a dice rolling mechanism for your game, you need to take a hard look at the probability curve it generates and think about whether it is what you want for the design goals of your game.  Rather than having people reinvent the wheel, I thought it would be useful to have a classification system that could then point people in certain directions depending on their design goal.  

So lets say we have three games.  A Purist-for-system Sim game that we want to be a very realistic and do a reasonable job a modeling the results of tasks.  A zany, off-the-wall gamist game with a strong element of self-parody (like Munchkin or something).  An Nar game with an intense, character-driven premise that's way over the edge.  

These are very vauge and somewhat stereotyped examples, but I think it is obvious that we don't necesarily want to use the same dice mechanic for each one.  So what are some features that you would want in the dice systems of these games?  Or, just ignore the examples and get to the heart of the question, which is "How do the various characteristics of dice systems matter to a game's design goal?"

I started to adress this question in a previous post, where I wrote that I think a lower variance is going to be more realistic, but that making the outcomes of rolls more predictable might make the game less interesting.

[John Kim]

Then these terms can be used in combination. For example, you'd just have a jargon like:

Additive: Dice results are added
Individual: dice are considered individually
Pool: More than one die is rolled
Set: the number of dice do not change
Variable: the number of dice are dependant on some factor
Target Number: the results of each read die are compared to some number
Rollover: result is a success if it is equal to the target number or more
Rollunder: result is a success if it is equal to the target number or less
Matches: Matching dice rolled are successes
MOS (margin of success): successes are determined by the difference between the TN and the roll  

Good start there.  One comment -- in common usage of published systems, the term "dice pool" always refers to a variable number of dice.  For example, systems using 3d6 (like GURPS) are never referred to as being "dice pool" systems.  Thus, I contrast "fixed-die" with "dice pool" -- which seems pretty clear and matches how most systems call themselves.  

Just an example, it would need a lot of work. The advantage here is that you can accurately describe most systems with the shorthand. The disadvantage is that you can't really speak to "rollunder" systems because they're all vastly different depending on the other variables.

But I think that's going to have to be the case. Because there so many variables at work here.  

It seems possible to have shorthand for common choices, like "rollunder percentile system".  The vast majority of published systems use one of a half-dozen basic approaches, so it seems worthwhile to have these as reference points.  But yeah, I agree that a complete taxonomy isn't practical.

[Thierry Michel]

I'm not sure that I agree.

That's because I was unclear, probably (eh). What I meant is that one has to be specific about which random variable is being mapped. I gather from your posts it is the degree of success and not the random number(s) generated by the dice.