I like making RPG systems. One thing I've noticed is that different kinds of task resolution systems make the game significantly different.
For example, games like D&D 3.X and Shadowrun 4E have a very details-oriented approach to task resolution. A typical die roll in combat might be something like 1d20+1+1+4+3+(7+2+3)*1.5+20-2 v.s. 10+8+min(4,1)+5+3+2+5, where each number comes from a different source and things like "I enjoyed breakfast greatly! +3 to hit" and "My shoes are freshly polished for +1 max dex mod to AC" matter greatly.
There are a limited number of modifiers and choosing the right combination for any given character is immensely important to the character's success in the game.
Other games, like FATE 2.0 or Amber Diceless, have a different approach. There a typical task looks like 5+4dF vs 3+4dF±2. All of the things that are tracked carefully in the first examples are abstracted away into a single modifier. This modifier generally does not exceed 50% of the base skill amount, and is generally regarded as less important than having a higher base skill amount. (In Amber diceless the 'rolls' are even more extreme: 1±1 v 3±1 is an example of a task's mechanical description there).
I am comfortable talking about this kind of difference between RPGs in general. We can talk about levels of abstraction, we can talk about focus, we can describe a system as 'high-level' or 'detail-oriented' or whatever.
What I am less comfortable with is the manner in which the stochastic character of a system's task resolution comes off to participants of RPGs run in it.
For example, I can tell you that the absence of dice in Amber significantly changes the feel of the game versus a similar setting modeled and run in FATE 2.0.
I'm much less articulate as to what the actual differences are, though. I'm aware of some popular pieces on randomness in RPGs, like the 'goblin dice' thing, but none of them really talk about the full space of stochastic design available to us as game designers. We can talk about how 2d6 is 'less swingy' than 1d13, but how that influences the feel of gameplay is not immediately clear.
I'm looking for a published overview of ways that different features of a task resolution system (in terms of stochastic analysis) are relevant to the feel of the overall game system from a game-design perspective. In particular I'm interested in the impact of the magnitude of the stochastic variance of the resolution system on the system, as well as the impact of greater or lesser volatility, and of polynomialization of the distribution (i.e. how binomail, trinomial, etc distribution graphs affect the feel of the game).
Basically, I'm looking to read published work addressing the question: How do we tie the stochastic characteristics of task resolution into a statement about the experience of using a particular role-playing game system?
What makes a good answer?
Answers will recommend further reading on the topic to support the claims made in their shorter overview. IJRP preferred. I'm looking for an overview, not a full discussion-- it's sufficient to provide references to appropriate academic literature and to explain how, and that, that literature answers the question. Also, since comments indicate that people are seeking primarily for online sources, let it be explicitly mentioned that offline sources like books are no less good for their being offline (RPGs may be young, but they most certainly predate widespread internet use).