Wednesday, July 20, 2011


I'm briefly sidetracked today by a comment on an earlier post which used a phrase I'm utterly delighted by. The poster was concerned about the variance in larger dice pools, but described it as "the mathematical whimsy of dice pool systems". That's a fantastic way to put it, and I'm totally filing that away.

But he raises a valid point, and he's not the only one to do so. Variance is a bit of a specter that has been raised more than once. For those unfamiliar, the concern is basically this: the bigger the pools of dice get, the less predictable the outcomes get. Once you're rolling 5d6, you've still got a curved outcome, but the curve gets shorter and fatter. You can see it when you map out the curves from 2d6 to 5d6, and it only gets more pronounced with time.

Now, this is totally a function of taste. I admit that so long as pools stay under 7d6 or so, the variance is still within my personal threshold, but I completely understand that other people's thresholds are elsewhere. The thing is that this is mostly something that math nerds are sensitive too, but gaming has no shortage of math nerds, so it's not so easily dismissed as all that.

So with that in mind, let me turn the question around a bit, and look at why we have dice in games in the first place. At heart, it's a matter of determining success or failure, with the uncertainty of things providing some of the thrill of play. Notably, that uncertainty is what puts games at a remove from pure narrative, and you can determine a lot about a game by how much of that uncertainty is in the game (determined by dice) and how much is in other sensibilities (such as drama or karma).

Now, this simple point has expanded into realms of nuance, with degrees of success and success with consequences and so on. There are piles of variations, but what's interesting to note is that there is often a divergence between results (as shown on the dice) and outcomes (how those results are interpreted). The best example of this is probably D&D, where in an attack, there are 20 possible results, but only 2 (maybe 3 with crits) outcomes.

This is an important point to bear in mind when you start looking at these die curves. It's not the specific numbers that matter so much as the bands of results. If hard rolls (13s and such) are common, then the variance starts becoming an issue - possibly a frustrating on - and that's where a lot of systems fall down. By having difficulties creep up along with die pools, you end up feeling like the treadmill is outracing you. Less consistent results combined with consistently escalating difficulties can make "high level" actions feel less heroic.

The solution to this is to take the base difficulty very seriously (Savage Worlds does a great job with this). If the target is really and truly 4 most of the time, then the big die pools feel powerful (especially when paired with the ability to "spend" unused dice). Using higher difficulties to represent specific circumstance is useful as a tool to manage exceptions, not as the default.


  1. I'm interested in the difference between fixed target numbers and opposed rolls when it comes to the impression math-sensitive folks have of dice pool systems. Cortex Plus doesn't use fixed TNs now because I have a fondness for opposed rolls (viz. Pendragon) and like the adding and subtracting of dice to be the GM decision factor, not the selection of a number.

  2. @Cam: Place me firmly in the opposed rolls part of the column.

    However that being said, the variation of results (variance of the distribution) with opposed rolls is Always going to be bigger than when making rolls against a fixed TN, as it is a function of the number of dice rolled as well as their size.

    [This is easily demonstrated if you look at the situation where one side rolls low and the other rolls high. You can get a greater difference than if you were simply rolling against a TN based on the average of the other side.]

    This "flattening of the curve" is something you have to look out for, which is why I find it a bad idea to mix opposed rolls and TN in the one system. Use one of the other.

    Some systems, such as Cortex Plus and Ironclaw get around this problem by limiting the number of dice that are actively read. In Ironclaw it is generally only one dice that determines the result (so you are not "multiplying" the distributions, but rather "adding" them). In Cortex Plus all dice rolls are effectively four dice (2 for you and 2 for me).

  3. Yay, I made a geeky contribution! It makes me very happy that Rob read my post and understood exactly what I was saying. To expound briefly: the distribution of of results in the game represents the randomness of the imagined world. It includes things like the chance the character is familiar with the matter at hand (never seen this type of lock before!), the favor-ability of the environment (dang jackhammer outside keeps moving my lockpicks!), and just whether the or not the character is at his best (haven't even had my coffee yet!). Some of these factors might be affected by the character's degree of skill, but to my mind most of them are not. That said, it's certainly reasonable that a more skilled lockpick learns to account for randomness, making the variation of his attempts tighter. So I suppose I'm not completely opposed to changing distributions - as long as its thoughtfully implemented vice just using a bunch of dice cause its fun.

    I realize this is a very simulationist sort of concern to have, and I'm usually much more concerned with the game being fun than worrying about simulating things accurately. Like Rob says, math nerd. :) I also think I've been burned in games where the variation seems wildly inappropriate and takes away player agency. So what rob says about looking at the bands of success is a good point - as long as frustration doesn't occur, things will probably be fine.

    @Cam LOL, yes math-sensitive is a decent term for the likes of us. Pavane describes the effect of opposed checks well.

    @Pavane I agree that systems should pick opposed or TN and stick with it. I'm not in agreement about preferring opposed rolls, but I think that's more a function of preferring quicker systems than mathematical concerns.


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