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

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).

Any good RP systems out there for a Azure Lane RP? [closed]

Kinda a weird question for sure, but to put small context this all began after a small joke that got way out of hand. By the end of it I was "encouraged" to put together a one-shot campaign for Azure Lane with some friends. Looking around though at the few I know such as DnD & Pathfinder, none of those really work for something like Azure Lane.

So my question is then does anyone have some good recommendations regarding a RP system to use for a Azure Lane focused setting and mechanics?

Is deciding solvability of systems of quadratic equations with integer coefficients over the reals in NP?

In the book ‘Computational Complexity’ by Arora and Barak the following question is posed (exercise 2.20.):

Let REALQUADEQ be the language of all satisfiable sets of quadratic equations over real variables. Show that REALQUADEQ is NP-complete.

I know how to show NP-hardness, but I’m stuck when it comes to proving that this problem is in NP, in particular how to show that we can describe a solution using a polynomial number of bits.

I did some research and found out that over the complex numbers, it remains an open question if the problem is in NP [1]. It also seems closely related to the existential theory of the reals, which again is not known to be in NP.

Thus my question: Is this problem known to be in NP? And if so, could somebody point me in the right direction regarding the proof.


[1] Pascal Koiran, Hilbert’s Nullstellensatz is in the Polynomial Hierarchy, Journal of Complexity 12 (1996), no. 4, pp. 273–286.

What are some advanced background topics I’ll need for distributed systems and networks research?

I am a new graduate student in Computer Science who would like to be able to read and understand modern and new distributed systems research papers. My current background / courses and understanding is in the level of undergraduate and beginner graduate level courses in:

  • Networks (TCP/IP stack and applications)
  • Distributed Systems (Graduate level course with Time (logical/vector clocks), 2PC and 3PC, Multicast and membership, election, Consistency , Consensus and Quorums (Paxos), DHTs and Overlays and some modern applications like ZooKeeper etc)
  • Undergraduate Algorithms, Discrete Mathematics and Theory of Computation (basic DFA/NFA and intro to Turing Machines with no rigorous mathematics)

However, I find this background insufficient to read modern research in networks and distributed systems and in particular, I am not aware of modern protocols like QUIC and the formal methods mentioned in the papers which I believe include some sort of model checking and the likes. Also many of the topics I have mentioned above in distributed systems – I lack the background to verify and prove correctness of these protocols and even follow the proofs that they have given.

Any suggestions on a reading list that can prepare me to be in a position to understand modern research in this area would be very helpful.