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.

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 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).

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    \$\begingroup\$ Comments are not for extended discussion; this conversation has been moved to chat. \$\endgroup\$ – nitsua60 May 9 '17 at 0:09
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    \$\begingroup\$ Based on the deluge of comments and flags on this Q&A I've gone ahead and opened up a meta question to figure out what's going on here. Please review the comments in the room above, but bring new discussion to the meta. \$\endgroup\$ – nitsua60 May 9 '17 at 0:10
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    \$\begingroup\$ Can I ask why you don't simply ask "how does the distribution of the conflict resolution randomness source impact the nature of the game?" Right now, you are making some very poorly formed and formulated assumptions about what distributions look like... \$\endgroup\$ – Shalvenay May 14 '17 at 19:44
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    \$\begingroup\$ @Shalvenay Cause I'm looking for academic literature, so "What can I read" is important. Also, I find that asking about distribution gets people focused specifically on deviation and I'm additionally interested in other characteristics like gradiation and volatility. Also, I'm not sure what poorly formed assumptions you are referring to; I generally consider myself proficient at basic statistics. Have I said something grossly inaccurate? \$\endgroup\$ – Please stop being evil May 14 '17 at 19:55
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    \$\begingroup\$ @thedarkwanderer -- more "too narrowly focused". Distributions are like RPGs in that they come in a bewildering variety of shapes and sizes... \$\endgroup\$ – Shalvenay May 14 '17 at 19:58

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:

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.

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    \$\begingroup\$ Today I learned there is an International Journal of Role-Playing, that its articles are in Google Scholar, and that it actually gets citations. \$\endgroup\$ – Novak May 8 '17 at 17:42
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    \$\begingroup\$ @Novak It is, in fact, my preferred source for academic discussions of RPGing, but I think Thanuir's answer makes it clear that they are a little lacking on this one. Time to email some strangers :S \$\endgroup\$ – Please stop being evil May 8 '17 at 18:02
  • \$\begingroup\$ @thedarkwanderer As far as I know, Carl Bergström is not in academia (he used to not be, at least, at some point). Lankoski, Montola and Torner are still active, I think. I don't know about Järvelä and Mizer. \$\endgroup\$ – Tommi May 8 '17 at 18:35
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    \$\begingroup\$ Please know that I've opened a meta about this question: your perspective may be particularly useful and I hope you'll contribute. Thanks! \$\endgroup\$ – nitsua60 May 9 '17 at 0:11
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    \$\begingroup\$ @KorvinStarmast Video games occasionally use random resolutions methods. There is a fair chance someone has investigated how the randomness influences player experience. The chance for the kind of study the OP wants is smaller, but not zero. One would have to adapt the findings to tabletop play, of course, but the key ideas might very well remain the same. \$\endgroup\$ – Tommi May 10 '17 at 5:58

This is also asking for a mathematical answer to a question about emotional reaction to a game's resolution style.

Simple response, however:

There are three main methods of resolution, two subtypes of resolution, and two types of modifier.


  • GM fiat based on player description and the needs of the story;
  • Flat roll (1d20, 1d100, 1d6; note: d66 and d666 are variants of this);
  • Bell curve (2d6, 3d6, 2d10).

Resolution subtype:

  • simple roll versus a value;
  • roll versus opposing roll.


  • Modifying the roll;
  • Modifying the target number.

All of these have a different feel, with the main differences being in player/character agency and arbitrariness of the result.

Excluding GM fiat, I see the main differences being between a flat roll and a bell curve.

With a bell curve the centre of the bell is where you've expect most reults to be, making the results at least broadly predictable. When you get a result at either end it's rare and therefore special. However, a modifer applied to a potential roll at either end will have proportionally more effect that if applied at the centre of the curve.

With a flat roll there's no differentiation between any possible result, although some systems (eg D&D) make the two end results special. However, they have no more or less chance of occurring than any other single result. This makes the majority of results essentially arbitrary in outcome. Flat rolls do have the advantage of making modifiers the same functional value wherever they are applied.

Roll versus roll adds to the dice being rolled, slowing the game somewhat, but increases the perception of tension. Roll versus value is faster and simpler, and most games aim for this as the speed and simplicity gains are larger than the tension loss. Some games make the other type an option (Eg one version of D&D suggests roll-versus roll as an option).

There is a perceptible psychological difference between modifying the rolled dice result and modifying the target number. The first changes the perception of PC agency, the second changes the perception of threat and difficulty. Many games use both, engaging both perception changes.

There's a simple and incomplete response that answers the OP as impersonally as I want to get it. :)

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    \$\begingroup\$ This answer does not fit the acceptance criteria of the OP \$\endgroup\$ – Doomed Mind May 8 '17 at 12:16
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    \$\begingroup\$ For your own edification, I recommend you take a look at systems like D&D 5E and Shadowrun (?every edition? 4th edition certainly, but I think even more so in 3rd) which present conflict resolution models omitted herein. "Roll 2, keep highest" is not a bell curve nor flat, and neither is "6's explode". \$\endgroup\$ – Please stop being evil May 8 '17 at 17:46
  • \$\begingroup\$ I will make the point that he's asking for a mathematical answer but then describing as what he wants an answer for as something better answered by an experimental psycholigist. Forgot Shadowrun, been too long. That's another, a one-sided bell curve, and has a similar psychological effect. Roll 2 keep highest is a skewed flat roll, similar to the one-sided bell curve of Shadowrun. haven't encountered D&D5, so can't comment. But all the systems I've met and seen are variations of flat and bell-curve, excerpt the GM fiat of Amber. \$\endgroup\$ – Paul May May 8 '17 at 22:52
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    \$\begingroup\$ Please know that I've opened a meta about this question: your perspective may be particularly useful and I hope you'll contribute. Thanks! \$\endgroup\$ – nitsua60 May 9 '17 at 0:11

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