The Primacy of Dice

[Lee Short]

I have to disagree about FUDGE putting primacy on skills.  Maybe it is in the text, but in actual play, the dice are terrifically variable; perhaps one of the most common topics on the mailing list, if not the most common, is how to mitigate  a really evil "whiff factor."

--JB

I agree.  Given the scale of the skill ratings, using 3 FUDGE dice works much much better.

[Lee Short]

To start with -- is there some trick to editing in this little reply box?  I seem to keep deleting more or less than I want to, and I'm getting pretty tired of retyping stuff.  Or am I better off just copying stuff over to a text editor?  

Interestingly, you say that the FUDGE method is better psychologically. Do you have any evidence for this? You admit that they are mathematically similar in some cases. So in those cases it's only psychology that gets in the way. But, other than personal bias (I could tell you that I don't feel that way, but that would just be my bias), do you have any evidence to back this up? I don't believe it's true, personally. If they are mathematically the same, then they seem exactly the same to me.

Let's just say that the last is not true for everyone.  IME, only strongly Gamist players have not found the skill-centered distribution easier to relate to (I rarely play with strongly Narrativist players, BTW).  

I should also note that skill-centered systems do not necessarily use names instead of numbers for skill levels.  My system uses numbers, because it has no cap and it has too fine a grain.  

I think that FUDGE has had some considerable impact. Considering its distribution scheme, the amount of talk it generates, and the relative lateness of its arrival, I think it's generated quite a lot of buzz. You aren't the first person to laud its design merits here. Do a search on the term Transparency to get an idea of how often this comes up.

In addition, I think that the Sim crowd is exactly the crowd that looks at FUDGE most often (it being highly Simulationist). Who else is looking at it more closely?

Perhaps I'm just out of the loop.  Can you point me at some games that you think show its influence, or is its influence limited to "buzz"?  

To begin, let us examine what those dice represent in a Simulationist game.  For the game to qualify as Simulationist, the dice must represent something inside the game world.  Otherwise they should not be used at all.  

Why is this true? Why can't dice be the whim of the gods? Or the luck of the adventurous? Why must all Sim resolution systems be based on "reality" when, in fact they are usually set in unrealistic settings? I think this is very much a preference.
[/quote]
See my earlier reply for my views on this, in general.  In specific, the dice could represent, in part, "the luck of the gods."  But I've never seen a game that said "the dice represent both the 'laws of entropy' and 'the luck of the gods', and that's why the random factors in this game are so huge."  Maybe I'm just oblivious, but I've never seen it (other than AD&D1).  

Commonly, what the dice represent in the game world are the numerous micro-scaled factors that effect task performance.  Informally termed ?luck?, these factors are too small to have an effect individually, yet have a macro scale effect in toto.

Yes, commonly. But this does not have to be the case. They can represent meta-game concerns. Yes, even in a Sim game. Or other things. This should not be an assumption.

You are correct here that dice can be used to represent other things in a Sim game.  I would be interested in seeing a game where the dice represent a Simulationist metagame concern, rather than a non-Sim concern in a largely Sim game.  

I had one ex-player comment that he didn?t like my game system because ?the dice don?t count for enough.? It was music to my ears.

Odd statement. Isn't player satisfaction what we're looking for here?

I suppose some explanation is in order.  The player in question really was not appropriate for my game.  I didn't have time to screen them, they didn't have time to talk to me about the game and see if they wanted to play -- they were dragged in for a few sessions for social reasons, and their spouse was one of my regular players.  What they wanted in a game was AD&D1.  Period.  They just didn't fit, and the whole game collapsed shortly as several of the principals no longer had compatible schedules.  There were and are no hard feelings between me and the player; that was just his way of saying that my game did not suit him, and he wasn't interested in playing in the new campaign I was starting up.  

Lee

[Lee Short]

I guess my basic point here is that any game that includes rules for skill performance is, in Clinton's words, "attempting to appear to simulate realistic situations" to some degree or another.  Why not do a good job at it?

My last reply to Mike Holmes made me realize I have overstated my case a bit here...in the case of Ars Magica and other settings where "luck of the god(s)" is a tangible force, certainly my criticisms do not apply...and there are other possibilities.  What I should have stated above is "just because a game is not aiming for hard-core realism, does not invalidate my criticisms."

Lee

[Walt Freitag]

Hi Lee,

Interesting thread on an interesting topic.

I'm inclined to agree with your core idea, that there are psychological factors that can make a system seem more "dice primary" or "skill primary." However, I believe those factors are more varied than you've hypothesized. In particular, I'll show you a system that appears to have the characteristics you regard as definitional for dice-primary-ness (one evaluates the situation, determines a probability of success, and then rolls against that probability), and yet has all the mathematical properties you associate with skill-primary-ness (it's centered on a 50% chance, is open-ended, has a smooth bell-like curve, and is easy to adjust for the appropriate degree of performance variance).

First, though, the psychological factors. One of the most basic, which you've implied but not stated outright in your analysis, is the order in which actions are performed. Consider two different resolution procedures:

A. Add 6 to your skill level, then subtract the difficulty, to get your target number. Roll the target number or higher on a d10 to succeed.

B. Roll a d10. Add your skill, and subtract the difficulty. If the result is 6 or greater, you succeed.

I submit that procedure B is more skill-primary and less dice-primary than procedure A. It's natural to pay the most attention to the most recently performed action. In A the die roll is the climax of the whole process. If the outcome is not successful, the player will tend to attribute that to the roll not being high enough rather than to the situation factors that caused the target number to be high. In B, the player will tend to see a failure as the skill (relative to the difficulty) not being high enough rather than the roll being too low to overcome. This is a subtle effect, but we're talking about subtle effects here. (Perhaps this is too obvious to mention, but many players like the drama of a climactic deciding dice roll at the end after the TN is determined.)

The relative wording of A and B is also an example of another type of factor. Notice the second sentence in A. What do you do to succeed? You roll. Thus only the act of rolling is directly associated with succeeding, with all those additional instructions about how to arrive at the TN being clearly secondary. In B, you succeed by meeting a condition. That condition comes about based on, let's see, the difficulty, the skill, and oh yeah, the die roll. A very different feeling.

Another psychological factor is the dice-handling time (which is some portion of the overall handling time that you noted as a factor). In particular, time spent reading and interpreting the results of the roll itself. The extra die used to smooth the curve in a die minus die mechanism could be counterproductive in that regard.

Finally, I agree with you that associating the roll with what it represents in-game does make a difference (a subtle one, as all of these are). That's where the die + skill vs. die + difficulty mechanism (mathematically equivalent to the die minus die mechanism) shines. The die added to skill can represent the performance uncertainty, while the die added to difficulty can represent the amount of resistance the world puts up  -- the performance of an opponent, or that portion of the task's difficulty that can't be known "until you try it." (Note that when interpreted that way, neither single die has the bell curve it would need to realistically represent human performance variation. Oh well. Also note that the third die mechanism is hard to fit within this interpretation, and kind of pulls the whole thing back to an abstract number-juggling level.)

By contrast, I don't see the Fudge dice as particulary good (or bad) in this regard. Dice pools in some simulationist systems (especially opposed dice pool vs. dice pool rolls) can have far clearer in-game meanings. Often each die in the pool represents a specific factor in the situation being resolved. If you wanted to (and some new indie systems discussed here have begun doing things like this) you could keep track of which dice represent which factors, and use that to help narrate the details of the outcome.

[Note: Those who have already seen all they want to of Symmetry can skip the rest.]

The system I mentioned earlier that seems to cross your categories is one I've used in many of my homebrews. It's based on an integer score derived from the situation (e.g. skill minus difficulty), where a score of zero (skill = difficulty) represents a success probability of 50%. The chance of failure decreases exponentially for positive scores, while the chance of success decreases exponentially for negative scores.

p (probability of success) as a function of m (score):

p = 1 - ((1 / (a ^ (m/b))) / 2)     when m >= 0
p = (1 / (a ^ (-m/b))) / 2    when m < 0

The parameters a and b determine the rate of exponential decay as a function of the score (effectively, the performance variance). The probability of success/failure decreases by a factor of exactly a for each decrease/increase of b points in the score. (One point added to/decremented from the score decreases the chance of failure/success by a factor of the b-th root of a.) Most often I use a = 2 and b = 4.

The advantage of using exponential decay functions is that the influence of situational modifiers becomes consistent and easy to understand and handle, a property that most systems don't have. (Dice pool systems do have this property as long as the the pool isn't too small and/or the modifiers are in the character's favor.) So not only is it easy to know what difficulty will give a character a 50% chance -- whatever difficulty results in a score of zero (usually a difficulty equal to the character's skill score) -- it is also easy to assign modifiers for individual situational factors, which remain correct and well-behaved when combined. A negative modifier of b points causes the chance of succcess to decrease by a factor of a (when the score is negative), and a positive modifier of b points causes the chance of failure to decrease by a factor of a (when the score is positive). Thus, if a = 2 and b = 4, a modifier of -4 points makes the task "twice as hard" as it otherwise would be, to as consistent an extent possible, regardless of what the score is initially or what other modifiers also apply. A -1 modifier is exactly one fourth as powerful. And there are absolutely no edge effects whatsoever, since there are no edges anywhere.

There are two different procedures I've used to implement this mechanism. My original method many years ago was to use the formulas to create a (one-dimensional) table of probabilities, and roll percentile dice against the probability indicated in the table for a given score. With this method, it would be relatively easy to make the table two-dimensional with varying values of a or b to represent situations of different performance variance, although I never found it necessary to do so. The alternative method I use now is to convert the score directly into a dice pool roll that yields the same (or approximately the same) probability of success as the table. The pool contains one 50-50 die, and a variable number of modifier dice depending on the score. The modifier dice in the roll directly represent the modifying factors (actually, only those modifying factors not offset by opposing modifying factors). It would be very awkward to have different dice to roll for different variances, but it's so easy to re-scale the scores instead as needed that this shouldn't be necessary anyway.

(Lots more details and rationale for this mechanism on the Symmetry thread.)

It would be interesting to see where you'd place this on the dice primary to skill primary continuum (actually, I prefer to think of it as situation primary instead of skill primary), and why. (My main concern in its design was the handling of cumulative modifiers, not the psychological nuances.) And is there any significant psychological difference between the table method and the dice pool method, even though they have the same knowledge going in (the score), the same results coming out, and most of the same information in between? In the table method the exact probability is known; in the dice pool method the approximate probability is fairly easy to deduce from the number and type of modifier dice in the roll.

- Walt

[Walt Freitag]

For example, 12-sided dice with 6 blank sides and one side labeled each of: +1, -1, +2, -2, +3, -3 will create a smooth bell curve if used appropriately.

Actually, if you roll three or more they create an otherwise smooth bell curve with a big spike at zero. Roll two and you get a peculiar stair-step distribution with an even bigger spike at zero. Why so many blank sides?

However, I agree with the general idea. It would be very convenient to have available, for system designs, "centered" dice of varying sizes. This would allow you to add dice or change the die size situationally, to represent degrees of performance variance or situational certainty/uncertainty, without having to deal with the annoying offsets to the mean that occur when you try to use regular dice this way. This would allow you to set up almost any sort of [skill + performance vs. difficulty + (optional) difficulty uncertainy] roll you wanted, quickly and easily. If all the dice involved are centered, then only the player's skill shifts the mean result in the skill + performance roll, which would appear to promote a skill-primary feel. Also, the performance roll can be several dice creating a zero-centered bell curve without the need for subtraction. (OK, you have to add negative numbers which is equivalent to subtraction, but the magnitudes of the numbers are less, and more important, you don't have to remember which of several dice rolled is supposed to be the one subtracted.)

A truly centered die with the same range and linear distribution as a conventional die would end up with all x.5 fractional values (unless it had an odd number of sides). But two zeros and +/-1, +/-2, ... +/-(n - 1) would be pretty close for most 2n sided dice.

For those with their own basement plastic foundries, let me also suggest the "3dF d20" numbered -3, -2, -2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3.

- Walt

[Lee Short]

Hi Lee,

Interesting thread on an interesting topic.

I'm inclined to agree with your core idea, that there are psychological factors that can make a system seem more "dice primary" or "skill primary." However, I believe those factors are more varied than you've hypothesized. In particular, I'll show you a system that appears to have the characteristics you regard as definitional for dice-primary-ness (one evaluates the situation, determines a probability of success, and then rolls against that probability), and yet has all the mathematical properties you associate with skill-primary-ness (it's centered on a 50% chance, is open-ended, has a smooth bell-like curve, and is easy to adjust for the appropriate degree of performance variance).

First, though, the psychological factors. One of the most basic, which you've implied but not stated outright in your analysis, is the order in which actions are performed. Consider two different resolution procedures:

A. Add 6 to your skill level, then subtract the difficulty, to get your target number. Roll the target number or higher on a d10 to succeed.

B. Roll a d10. Add your skill, and subtract the difficulty. If the result is 6 or greater, you succeed.

I submit that procedure B is more skill-primary and less dice-primary than procedure A. [snip]

[snip]

Another psychological factor is the dice-handling time (which is some portion of the overall handling time that you noted as a factor). In particular, time spent reading and interpreting the results of the roll itself. The extra die used to smooth the curve in a die minus die mechanism could be counterproductive in that regard.

I agree with everything you've said up to this point.  I, too, believe the handling time to be very important.  I think that die minus die mechanics will require too large a handling time for some players -- it depends on if the player picks up on the mechanic and makes it 'second nature.'  If the gaming group meets irregularly or if skill rolls are called for infrequently, that will be difficult for some people to do, IME.  

Finally, I agree with you that associating the roll with what it represents in-game does make a difference (a subtle one, as all of these are). That's where the die + skill vs. die + difficulty mechanism (mathematically equivalent to the die minus die mechanism) shines. The die added to skill can represent the performance uncertainty, while the die added to difficulty can represent the amount of resistance the world puts up  -- the performance of an opponent, or that portion of the task's difficulty that can't be known "until you try it." (Note that when interpreted that way, neither single die has the bell curve it would need to realistically represent human performance variation. Oh well. Also note that the third die mechanism is hard to fit within this interpretation, and kind of pulls the whole thing back to an abstract number-juggling level.)

By contrast, I don't see the Fudge dice as particulary good (or bad) in this regard.

The reason I think FUDGE dice are good is because they have a very low handling time (particularly if the number of dice is 3 or fewer), and IME players can easily relate the dice to a skill modifier.   I've never tried running a game with the "die+skill vs. die+difficulty" mechanic....that might avoid the problems I've had in the past with players getting confused by die minus die, plus it would reduce the handling time by removing the time necessary to differentiate the plus die from the minus...that might work very well indeed. I'll put it on my list of things to try when I get the chance.  

The system I mentioned earlier that seems to cross your categories is one I've used in many of my homebrews. It's based on an integer score derived from the situation (e.g. skill minus difficulty), where a score of zero (skill = difficulty) represents a success probability of 50%. The chance of failure decreases exponentially for positive scores, while the chance of success decreases exponentially for negative scores.

p (probability of success) as a function of m (score):

p = 1 - ((1 / (a ^ (m/b))) / 2)     when m >= 0
p = (1 / (a ^ (-m/b))) / 2    when m < 0

The parameters a and b determine the rate of exponential decay as a function of the score (effectively, the performance variance). The probability of success/failure decreases by a factor of exactly a for each decrease/increase of b points in the score. (One point added to/decremented from the score decreases the chance of failure/success by a factor of the b-th root of a.) Most often I use a = 2 and b = 4.

The advantage of using exponential decay functions is that the influence of situational modifiers becomes consistent and easy to understand and handle, a property that most systems don't have.

I agree with you here, and that is also an important criteria for me.   It handily avoids all kinds of boundary conditions.  Open-ended FUDGE dice display the same robustness.  

(Dice pool systems do have this property as long as the the pool isn't too small and/or the modifiers are in the character's favor.)

...and the modifiers are not too large.  IME, dice pools run against these boundary conditions too often, though I admit I have never played a dice pool vs. dice pool game, where some of the problems would disappear.  I think simply the rolling and counting of so many dice would tend to make such a game dice primary, but that's just my off-the-cuff feeling.  Once again, this may be alleviated with experience with such a game system.  

So not only is it easy to know what difficulty will give a character a 50% chance -- whatever difficulty results in a score of zero (usually a difficulty equal to the character's skill score) -- it is also easy to assign modifiers for individual situational factors, which remain correct and well-behaved when combined. [snip]

[snip]

It would be interesting to see where you'd place this on the dice primary to skill primary continuum (actually, I prefer to think of it as situation primary instead of skill primary), and why. (My main concern in its design was the handling of cumulative modifiers, not the psychological nuances.) And is there any significant psychological difference between the table method and the dice pool method, even though they have the same knowledge going in (the score), the same results coming out, and most of the same information in between? In the table method the exact probability is known; in the dice pool method the approximate probability is fairly easy to deduce from the number and type of modifier dice in the roll.

- Walt

I think it would depend on the individual gaming group.  I think that my gaming group would be bogged down enough in the resolution mechanism that it would be dice primary (or maybe 'mechanism primary'), but for the right gaming group, it could certainly be skill primary ('situation primary' is also a reasonable name alsi, IMO).  That's an important point -- different players  will have a greater or lesser tolerance for dice math, before it cranks the handling time to obtrusive levels. So I believe that the very same system can be dice primary for some players and skill primary for others.  

My current gaming group has a very low tolerance.  We have 2 players who are completely new to RPG, and 2 who have not gamed for some time.  The other 4 are all hard-core vets.  

I agree with your other post.  I would love to have some "3dF d20"s.  The previous version of my game used almost exactly those dice (one less 1).  I'd be willing to put $500 in for 2000 of them, if we can find 4 more people for the cooperative (koplow's minimum order is 10000 custom dice for $2470 fob Boston).  

thanks for the thoughful reply,
Lee

[Paganini]

Hey Lee, I'm going to ramble on a bit, and it's possible I've totally failed to get the point of your post. If I have, I appologize in advance, and please correct me. :)

First off, I don't agree with you that it's limited to simulationist games. IMO, the concept is important regardless of your preferred play style.

A related topic that I've discussed many times is whether or not to use a universal or unique rating system. That is, whether or not each character is rated with a common set of categories (D&D attributes), or a set of unique traits (Pool traits), or some combination thereof (most attribute + skill systems). D&D characters often appear to be very similar, even though their in-game abilities may be quite different, while each Pool character is extremely unique and flavor-filled. (In case you haven't noticed, I prefere the non-categorical method. ;)

I think your idea is almost paralell with this idea. A die mechanic can have appearance in exactly the same way character representation can. I almost think that this topic would fall into the category of "color," because that's mostly what it deals with... flavoring the game.

[Forlarren]

Fist off Lee I completely understand where you are coming from. Part of the reason for this is because I am not a math wiz. Another reason is because I am very open minded to this new way of doing things.

Try to follow my analogy without nitpicking I'm not having a very good morning.

The search for the PERFECT RPG rules is like the search for the grand unified theory. A straight chance system (roll one die every face is an equal chance) was a very early understanding of how chance worked. It's like Newtonian physics, it works for most problems, and where it dose tend to fall apart additional rules can be tacked on. Then came along the bell curve systems (personal favorite is FUDGE by the way), this was like Einstein coming up with E=mc^2. On the surface it seems less intuitive, that and its new and unproven. It took a long time for science to accept this new theory mostly because that meant unlearning all the tricks they were using for Newtonian theory. In a way it also set science back several years as everything had to be reevaluated. I think that the straight chance systems have been tricked out so to speak, there is not much room for growth. The FUDGE-like systems are new and are forcing a rethinking of how things are done and why on a more basic level than most of us are accustomed to thinking about. I am ambitiously rewriting the basic FUDGE rules for a Sci-Fi RPG. I hope to show with it that FUDGE-like systems are more optimal for realistic settings (though with lots of gamer elements thrown in).

[Le Joueur]

The search for the PERFECT RPG rules is like the search for the grand unified theory.

Except one is subjective and the other objective.   There might actually be a verifiable Grand Unified Field Theory; the "perfect role-playing game" is only a matter of opinion.

Fang Langford

[Lee Short]

Hey Lee, I'm going to ramble on a bit, and it's possible I've totally failed to get the point of your post. If I have, I apologize in advance, and please correct me. :)

First off, I don't agree with you that it's limited to simulationist games. IMO, the concept is important regardless of your preferred play style.

I certainly think it can be applied to Narrativist games -- though Narrativist games will have entirely different criteria for what makes a game Dice Primary.  Of the top of my head, I would say that handling time will be of paramount importance.  

For Gamist games, I think that being Dice Primary (or mechanism primary) is quite possibly a benefit.  Manipulating the mechanics within the strictures of your resources, is, to my eyes, the heart of Gamist play.  So focussing on the dice/mechanics during the course of play is entirely appropriate.  

A related topic that I've discussed many times is whether or not to use a universal or unique rating system. That is, whether or not each character is rated with a common set of categories (D&D attributes), or a set of unique traits (Pool traits), or some combination thereof (most attribute + skill systems). D&D characters often appear to be very similar, even though their in-game abilities may be quite different, while each Pool character is extremely unique and flavor-filled. (In case you haven't noticed, I prefere the non-categorical method. ;)

I think your idea is almost paralell with this idea. A die mechanic can have appearance in exactly the same way character representation can. I almost think that this topic would fall into the category of "color," because that's mostly what it deals with... flavoring the game.

I'd never looked at it like that before.  

Lee

[Jeremy Cole]

Lee,

With FUDGE or a similar system it isn't easier to produce reasonable difficulty numbers.  With the standard system you can get the same information by simply adding the average dice value to the skill.  The average expected value is skill plus die average, if the die average is zero, ie FUDGE, well it doesn't really matter.

Further, it is far harder to calculate the probability with system using a bell curve during play, so you may not know the probability of a player succeeding at a difficulty two points above his current level, whereas with a d6, or any other single die, is very easy to find.  If you want a system that models real performance, then a bell distributed system is wise, but appropriate difficulty numbers are always harder to find, never easier.

The psychology aspect is interesting, but isn't it based more on std dev of skill vs std dev of dice, rather than the order they are added together?

Jeremy