## TL;DR

• The single-page rule book is here
• A simulator demonstrates game statistics here

## Background

I’ve been an occasional tabletop RPG player for years. My favorite teenage PC games were Neverwinter Nights and a Russian mod for Dungeon Siege called “Ледяной ветер”, so D&D was a natural first step when I turned to tabletop games. But I quickly realised that the game mechanics were a bit convoluted for my taste. A friend introduced me to World of Darkness and its Vampire games, which was a definite improvement. The simpler rules allowed for a faster-paced gameplay, the games tended to be less exuberant and subtler than D&D adventures, with an increased focus on strategising and negotiation. However, in the end, you are still playing a vampire, which can get pretty boring in the long run.

So I switched gears one again and started playing with a more experimental crowd. The focus there was almost fully narrative, with little or no combat. Disoriented characters were thrown into strange, dysfunctional worlds with complex faction systems which they had to explore, make sense of and ultimately exploit. You didn’t need a complex rulebook for these kind of stories, and I remember several occasions where the DM just ignored our throws in order to let us succeed at a key task, just for the needs of the story. At the time, we were using the Storytelling system, which is derived from World of Darkness rules. Quickly, we switched to Risus, a one-page system originally designed for more ironic/non-serious stories, which offers extreme flexibility.

Risus and Storytelling were the two systems I experimented with when I started DM-ing myself, along with other free-form RPGs such as Fate or GURPS. My first large-scale attempt at writing a game was something called “Dreamscape”, in which the characters were trapped in an unstable dream. The depth of their sleep was the determining game characteristic, and players had only little control over it. A lighter sleep made it possible for players to figure out they were dreaming, while a deeper slumber allowed them to bend logic to do seemingly impossible things. Sleep depth was updated by a random number after each player action, and understanding more about the plot made your sleep lighter, whereas just going with the flow made you more powerful, but also more unstable.

### Why another system?

Over time, our group ended up playing only story arcs where players’ characters were not supposed to be vampires, orcs or other beings with superhuman abilities. They were normal humans, with jobs, friends and families, thrown into a world that was mostly similar to our own. Some artifact or resource could be harvested or used (like the substance of dreams in Dreamscape) to perform extraordinary feats, but for the most part the characters were all pretty average.

Players were also asked to create pretty complex story arcs for their characters, and I felt the classical “skill point” system wasn’t subtle enough to describe the complexities of what makes a person good at something. In most games, you allocate a fixed number of points to a set of skills, and these points shift your ability at beating opposing throws.

This is not what happens in real life: usually, learning a skill is a combination of natural predisposition and training. As an example, I taught myself to play squash over the course of several years. I reached what could be described as a consistently mediocre level: although I excercised a lot, I lacked talent and guidance. On the other hand, I was often told that had I chosen to study literature, I would have become a fine writer/scholar/linguist or what have you. There, it’s not lack of talent but of practice that might make me fail at a given task. The key point here is that you don’t fail or succeed_in the same way_ in both those cases. When you lack talent, training still can allow you to achieve a consistent, although not necessarily impressive level at some skill. This means that both extreme failure and extraordinary success are less likely than just an average value, just like when I’m playing squash. When you lack practice, but have talent, you will tend to be better than average, but won’t be shielded against “rookie mistakes”, which will make your score much more random (I still haven’t given up on writing a great book some day). In other words, I wanted a game where training made you consistent, but not necessarily good, and talent would make you better, but not necessarily all the time.

## Consistently average

That made the specifications of the system pretty simple. It would be based on two characteristics: Skill and Aptitude.

• Increased Skill does not make you more likely to succeed at a given task, but it makes you less likely to be catastrophically bad (or good) at it.
• Increased Aptitude does increase your chances of success, but does not change the randomness of the outcome in any way.
• Only through a combination of Skill and Aptitude can a character become systematically better than the average at a task.

Intuitively, Skill reduces the variance of the score, while Aptitude introduces a positive bias. Reducing variance being quite hard with a set of dice, we turn to the central limit theorem. This tells us that the average of a sufficiently large number of i.i.d. variables will be normally distributed. Since the average is equivalent to the sum except for one multiplicative factor, we can understand the CLT as telling us that the sum of repeated throws of a dice will follow a normal distribution. A $\LARGE d20$ is discrete uniformly distributed with $\LARGE\mu=10$ and $\LARGE\sigma=\sqrt{\frac{399}{12}}$. A sum of $\LARGE n.d20$ will be approximately normally distributed $\LARGE\mathcal{N}(n\mu, \sigma)$.

Of course, we need to normalise the score, so we compute the average throw over $\LARGE S$ throws, where S is the skill point count of the character. This has the effect of reducing the variance $\LARGE\frac{\sigma^2}{n}$ as $\LARGE S=n$ increases.

Then we just add the aptitude points $\LARGE A$ to consistently shift the score, and we obtain a rudimentary realistic system. You can play with simulated throws here.

## Derived systems

Of course, I understand that some people do want to play superheroes or kung-fu masters all the time, so there are also ways to tweak the system to put an emphasis on different aspects of learning:

• the wushu mode takes not the average, but the maximum of $\LARGE S$ throws. This is as if experience gave you multiple chances at a given action. It implicitly values training and repetition. Training in a specific skill immediately and consistently makes you better at it, while the influence of aptitude is a constant that becomes less important as $\LARGE S$ increases.
• the superhero mode does the opposite. It keeps the convergent interpretation of $\LARGE S$, but gives you as many $\LARGE d3$ throws as you have aptitude points, and adds it to the score. This mirrors the belief that high-aptitude individuals will almost always beat perfectly trained, un-gifted individuals.

Of course, nothing prevents a DM from switching between the three throws in-game, or even assigning a given type of throw to specific characters.

In the end, each of these systems embodies a different world view, or at least a particular interpretation of how people learn and get better at things. I’d be curious to see which of these ends up being the most fun to play with, and above all which one players feel is closest to their experience of reality. Then again, sticking to reality is not necessarily what every RPG player will be looking for.