What can I read about how we tie the stochastic characteristics of task resolution into statements about a game system's aesthetics?

Question

I like making RPG systems. One thing I've noticed is that different kinds of task resolution systems make the game significantly different.

Background

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.

The problem

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 using one or the other more commonly for some hypothetical ruleset would influence our aesthetic perception of that ruleset 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' (i.e. the perception of aesthetic qualities) 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 binomial, trinomial, etc distribution for a game's randomizer affects the game's overall aesthetic).

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).

Answer 1

I am not aware of academic studies that directly address this, but maybe some exist for video games.

I am an interested amateur with completely different academic background.

Here's where I looked and what I am familiar with:

• International journal of roleplaying: There is an article on the effect of rules on group creativity by Karl Bergström, and an article about embodiment by Järvelä and Lankoski, which might be classified as vaguely related articles.
• Analog game studies: Non-immersive roleplaying by Nick Mizer discusses kinds of fun not related to immersion. Evan Torner has written about uncertainty in roleplaying games, but there is no analysis of stochastics going on (it is a multi-part series).

Here is what I am roughly familiar with:

• Solmukohta books are focused on larp. There might be something there, but I would not hold high hopes. I would start the search with the earliest ones, personally, as larp studies as a field have matured significantly since the first ones were published. The article of Markus Montola on chaos theory applied to roleplaying might be as close as you get. But maybe not.

Video game literature is vast and unknown to me. Find an expert and ask them, or get familiar with the literature by yourself. You might want to start with DiGRA, for example.

When you find something somewhat interesting, see what it cites and check if those are relevant. Also use Google scholar to see what cites the articles you found, and check if any of those is interesting. (That is, expand your search forwards and backwards in citations from the most interesting article you did find.)

Evan Torner was easy to communicate with and still an active academic. You might also ask them, or some other author of an even vaguely related article.