Someone who know what they're talking about, please, please, banish the ignorance over at this this thread about dice pools vs. linear models on the Hârn Forum.

Sorry if this is the wrong place for this.

Hi Shane,

Ron will probably chip in on this, but: It's no one's business here to go "crusading" on other sites. If there's something at the site that you'd like to bring up as a topic of discussion, I think that'd be worthwhile, but the Forge is most definitely not about winning converts or "bringing the light to the unwashed heathen masses".

Actually, we're probably doing the best we can until someone brings the light to us :)

Chris

Well, ok, how about discussing here what's being said over there and then I can crusading on my own. ;)

Seriously, it's not about the crusdading; I'm a regular at the Harn Forum and I know those chaps pretty well. There are 'facts' being bandied about in that thread that strike me as suspisious at best, though, and I was hoping someone here who knows about this sort of thing, could point out and correct any errors, should there be any.

Agreed in full with Chris.

However, I don't see anything wrong with having a discussion here to the effect of, "I'm interacting with others about issue X, they hold opinion Y which I disagree with, I believe Z but I don't think they're understanding me; what would be a good way to explain my position?"

If it's a question of correct calculation of outcome probability distributions for dice pools versus, say, d20s or percentiles, I'm sure I or other people here could come up with some accurate numbers or equations. On the other hand, if the issue is one of personal preference, then there's not much chance of (or need to be) convincing anyone of anything. Sometimes the latter looks deceptively like the former: someone claims "Dice pools are more random," there follows a five-page thread on probabilities and variances and the mathematical definition of "random," and just when you think a case is made one way or the other, someone points out, "yeah, well, they feel more random to me and that's the only important thing" -- and that person is correct, that is the only important thing to that person, and attempting to argue otherwise has been a waste of time.

So, can you state briefly what the issue is? (I'd just go read what it is myself, but for some reason I haven't been able to receive my registration confirmation e-mail to log on to the site.)

- Walt

EDIT: Cross-posted with Shane

Nah, I don't do exclusive forums. Bah. If you want to paraphrase the discussion for us paranoids here, go ahead.

Hello,

Shane, consider this an invitation to raise the issue that you'd like some dialogue about. In fact, let's more or less forget about the other forum discussion entirely; assume that no one is going to click on it and needs your input here.

I'm also going to assume that we are not being milked for ammunition that will enable you to return to that discussion and kick ass. Let's have a valuable discussion here for its own sake, concerning the issues that you raise.

Best,
Ron

Well, ok, then...

And this isn't about ammunition, either. I'm a very prolific poster on that other forum and I almost always hop in a good argument, but I haven't even posted on this thread and I don't intend to (that's why I wanted someone else to do it). I'm not for or against die pools, BTW. I just think there's a lot of misinformation being bandied about as fact.

Some Guy wrote: The other advantage it has from the narrativist sections of the hobby is that not many people have the math skill to min-max (i.e. game) the system. Of course, the bad side of that coin is not many game designers have the math skill to make sure it doesn't get goofy at the extremes.

And This Other Guy wrote: (In reply to the above) And the bad side is VERY bad. Further the mathematicians get a huge power up as it is possible to derive algorithms which quickly answer questions (unfortunately they can be a bit hard for non-mathematicians to use, so they are of strictly limitted utility to the community at large).

This Other Guy wrote: The sole advantage of using dice pools where each die is counted against a dificulty, is that you no longer have either a lot of calculations with the dice thrown or a chart for mandatory reference. Given the abyssmal math skills of many people, having the limit of mathematical sophistication for the players rest at adding 1 to a difficulty number or counting the number of dice which suceed is perhaps a better explanation of the popularity of such games.

This Other Guy wrote: "Linear" systems are mathematically indistinguishable from "Dice Pool" systems if the mechanics are handled correctly by the game designers, a simple proof can show that. Even the dreaded +5 Sword in the novices syndrome can be smoothly handled (Look the + from the sword is dependent on the skill of the wielder, for a D&D system). HArnmaster can easily handle the problem because a Sword with +5 Impact is only going to have an effect if the wielder can get in a strike, hence the peasant with a Sword skill of 27% will have a tough time striking someone wiht his +5 Greatsword.

This Other Guy wrote: One alledged advantage is that these systems allow you to vary the probability of an event occuring by changing either of two elements - the number of dice thrown OR the difficulty of any die being counted in the success group. Another Alledged advantage is that somehow it is the ONLY way to force characters to 'divide their attention' (by allocating a portion of their dice to each of several actions/options).
The first claim is, of course, pure illusion. That is where a mathematical proof comes in handy - a linear transformation can change any "Dice Pool" System into a % system with less than 1% rounding errors for any event. With a recursive % system you can get rid of even the round off error.
The second claim falls flat when judged against a system which has existed since 1980 (or so). To wit "Champions" by Hero Games. In the champions system a skilled character will have "Overall" levels which must be allocated between all the things they want to accomplish in a particular action - spotting something, dodging, making a difficult acrobatic aneuver, defending against a mental attack, and Hitting, to name a few. Even lowly combat levels must be allowcated between Offense and Defense.

ShaneNINE wrote: Well, ok, then...

And this isn't about ammunition, either. I'm a very prolific poster on that other forum and I almost always hop in a good argument, but I haven't even posted on this thread and I don't intend to (that's why I wanted someone else to do it). I'm not for or against die pools, BTW. I just think there's a lot of misinformation being bandied about as fact.

Some Guy wrote: The other advantage it has from the narrativist sections of the hobby is that not many people have the math skill to min-max (i.e. game) the system. Of course, the bad side of that coin is not many game designers have the math skill to make sure it doesn't get goofy at the extremes.

And This Other Guy wrote: (In reply to the above) And the bad side is VERY bad. Further the mathematicians get a huge power up as it is possible to derive algorithms which quickly answer questions (unfortunately they can be a bit hard for non-mathematicians to use, so they are of strictly limitted utility to the community at large).

I think that's off. Discuss...

I don't want to focus too much on the selected quotes since it's out-of-context pulls from people who aren't here to explain themselves. But I'll take a shot at what I see as the topics Shane is addressing. By the way, I'd suggest my system design pages on dice methods at
http://www.darkshire.net/~jhkim/rpg/systemdesign/

I'd split this up into a four subtopics:

1) Difficulty to understand / non-intuitiveness of dice pools

On this point, I pretty much agree with the posters that Shane quotes. Most players and even game designers that I've talked to don't seem to understand the probabilities which dice pools generate. For example, when asked "With a dice pool of X and a target number Y, is it better to get +1 die or -1 target number?" I know that some people do consider this a pro for dice pools -- i.e. it encourages certain players to just guess rather than minimaxing.

2) Ease of use of dice pools

Resolving dice pools can be easier in mental operations, particularly for determining degree-of-success. In a fixed-die scheme, you generally have to do a subtraction (i.e. stat + roll - difficulty) to get a degree of success. With dice pools, you can operate by physically moving dice around the table. It's more physical operations but simpler conceptually.

3) Equivalence of dice pools and linear systems

It is trivial to convert a linear roll to roughly the same probability curve as a dice pool -- for example through a universal chart. You roll percentile dice, look on the chart, and see the number of successes. This can generate the same curve as a dice pool roll. I suspect this is what the poster meant by the two methods being "mathematically equivalent".

Now, a fixed-die roll (like 3d6 or 1d100) without a chart or other conversion does have a different probability curve than a dice pool. My test is this: describe the kind of probability curve you want first without any reference to dice. Then you can come up with the type of roll that will come closest to that.

4) The advantage of being able to split dice pools between actions

In a dice pool system, you can put 3 dice for defense and 4 dice for offense. However, this is the same as splitting linear bonus between rolls in a fixed-die system. This was done in RoleMaster and shortly later in Champions. i.e. You have a total of +7 levels, and you put +3 in DCV and +4 to OCV. The advantage of dice pools is presumably having the dice as tokens to shift in front of you. However, presumably a HERO player could also just count out pennies or whatever for his combat levels.

Hmm.... well, ok, maybe I'm the ignant one.

Doh! I've been banished!

Guess I was drawing all my inspiration from this:

Mike Holmes wrote: Probablility curves. One die is very linear, which models very little in reality. Multiple dice work to produce the sorts of higher orser functions that model life more accurately, and are often more interesting in terms of output. For example, if I roll d20 +10 I have a range that goes from 11 to 30. I cannot roll a zero.

In Jake's system, no matter your TN or the size of your dice pool you can always roll a zero, up to the number of dice rolled. This allows for all sorts of mechanics to come in that would otherwise be impossible.

The reason dice pool systems have a reputation for being "non-intuitive" is that many of them, historically, have mixed (used simultaneously) two or even all three of the most common variables:

- number of dice rolled
- target number of individiual dice needed to score "successes"
- total number of "successes" needed to succeed at the in-game task

(And if you really want to muddle things up, you can also vary the size of the dice.)

However, when the number of dice rolled is the only variable, I find pool rolls to be a worthwhile intuitiveness trade-off with linear rolls. With linear rolls, the question "what roll would give about a .6 probability of success?" is easy, but the question "what effect will a +2 modifier have on a character's success rate?" is hard. With a simple dice pool, for which modifiers are dice added to or removed from the pool, it's exactly the other way around.

- Walt

I challenge the claim that probabilities should be able to be grasped intuitively by the players. Why is this something desireable? Yes, the designer should clearly understand the implications of mechanics. Why do the players have to even know about probability at all?

Paganini wrote: I challenge the claim that probabilities should be able to be grasped intuitively by the players. Why is this something desireable? Yes, the designer should clearly understand the implications of mechanics. Why do the players have to even know about probability at all?

The "advantage" of linear rolls is that the effect of modifiers is easier to see, and more constant. And for the "Realistic" "Sim" of Harn, this is a Good Thing.

Paganini wrote: I challenge the claim that probabilities should be able to be grasped intuitively by the players. Why is this something desireable? Yes, the designer should clearly understand the implications of mechanics. Why do the players have to even know about probability at all?

To follow up M.J.'s point, let me note that we all, in ordinary life, strategize. That is, we have some sort of goal, and we try to achieve that goal. Since there are a zillion possible factors involved, we can't know the odds terribly clearly. But we can, and do, with amazing success, correctly guess the general likelihoods of our desired results coming from a particular course of action. Debating how we do this is one of those huge, painful areas of epistemology and the philosophy of action, but it seems pretty clear that we do this pretty well.

But we, the players, can't always do this as well as our characters. So it's helpful to have at least a solid sense of the basic probabilities.

M.J., that wasn't quite what I was getting at. More like... why do the probabilities have to be easy to calculate exactly? Why not assume that experience with the game will give all the information you need to know? I mean, like, if I play TROS, some of the dice pool probabilities get pretty complicated with all the sliding scales. There might be some holes and breakpoints and things that I'm not aware of. But in general, I know that more dice is good, lower target numbers are good (or whatever the specific case is for TROS, I forgeT), and so on.

So, that is, I have an intuitive grasp of the probabilities, in the sense that I know the scale and the effects. But I don't know the specifics, and I can't figure them in my head (which is what I think most people mean by "intuitive grasp of probabilities). Like... it's trivial to figure the probabilities of d20 system rolls. Why is that necessarily a good thing? For something that's supposed to facilitate tactical choices and player competition and skill, I'd think that something a little less obvious would be more appropriate.

Most heavily tactical systems have layers of complexity that scale up arbitrarily high. The difference is basically whether the introductory level is easy to grasp or not, and I think there's a big playability advantage in systems that make it easy to work out how successful a basic action is.

This doesn't necessarily mean the whole thing is a solved problem, either. Like you say, it's trivial to work out in D&D that if you have attack bonus X and the monster has armor class Y, your chance to hit is Z -- but if you're using power attack, how many points of attack bonus should you sacrifice for damage bonus if you want to optimize your average per-round damage? Or maybe you'd be better off wielding a second weapon instead, or using aid another to help your buddy hit.

By comparison, 7th Sea's system doesn't get nearly as complex at the high end since there's not that much tactical stacking, but the basic die roll is hard to analyze, and this makes it difficult to design characters or figure out how likely you are to succeed at things in play. Sure, you can tell that having a high trait is good, and it seems to be better than a high skill, but it's not obvious to a new player that raising your skill past 2 is virtually useless, or when it's better to add a drama die before you roll and when after.