So what die are we using?
The three most common types of dice used in TTRPGs are d6s, d10s, and d20s (in some sort of order) and if I was smart, if I maximize uptake of my new system, I would use one of those. Instead I’m going with d12s. I admit that part of the reason is my desire to go with an atypical, though still readily available, die type but I do have a fig leaf in the form of factors.
In mathematics a factor is a whole number that divides evenly into another whole number; ignoring 1 and itself, which we shall be doing for all these examples, the factors of six are 2 and 3. Eight and ten are no better still only have two factors each (2 and 4, and 2 and 5 respectively) but twelve has twice as many (2, 3, 4 and 6). More factors make for easier mental arithmetic hence the existence of a dozen as a numerical unit and the doomed dozenal movement.
Twenty has just as many factors (2, 4, 5, and 10) but they’re not, arguably, as evenly distributed. You could argue that the greater gradation, having more numbers on the die, has value but not a lot; there’s not a big percent shift between the two. And if gradation mattered I’d be thinking about a percentile system (given how many such systems use five percent increments they’re mostly just d20s with extra steps). There is actually an argument that a d20 as a rounder die would be preferable as it rolls more true, the closer to a sphere a die is the less impacted by starting conditions it is, but these are very marginal gains. Will only really manifest after thousands of rolls under conditions much more tightly controlled than a human can do so I’m sticking with the d12s. Meaning I can update my first rule:
Twenty has just as many factors (2, 4, 5, and 10) but they’re not, arguably, as evenly distributed. You could argue that the greater gradation, having more numbers on the die, has value but not a lot; there’s not a big percent shift between the two. And if gradation mattered I’d be thinking about a percentile system (given how many such systems use five percent increments they’re mostly just d20s with extra steps). There is actually an argument that a d20 as a rounder die would be preferable as it rolls more true, the closer to a sphere a die is the less impacted by starting conditions it is, but these are very marginal gains. Will only really manifest after thousands of rolls under conditions much more tightly controlled than a human can do so I’m sticking with the d12s. Meaning I can update my first rule:
Basic Task Resolution: When determining the outcome of an action the controlling player will roll a number of d12s equal to the governing primary trait, add the relevant secondary trait to the highest die rolled, and compare the result to the difficulty's target number (TN). If it is more than the TN it is a success.
Now that’s not much of an update, one word, but it is the first link in a chain. If we have a rough idea of how difficult we want an untrained unmodified roll to be we can derive a base difficulty and method; a 6 would have a 50-50 chance under those conditions which seems like a good starting point. This could change, this number could go up if things are found to be too easy (I can’t imagine going down) but that is what playtesting is for.
That is only the average or base difficulty situations will require this to float up and down. Well maybe not float perhaps move in steps and to figure out how big those steps should be we could look at our factors. If we make a degree of difficulty equal to 3 (a factor of both six and twelve) then each step of difficulty change equals a 25% change in probability of success from guaranteed success (TN 0) to guaranteed failure (TN 12), on an unmodified roll, in five steps.
That is only the average or base difficulty situations will require this to float up and down. Well maybe not float perhaps move in steps and to figure out how big those steps should be we could look at our factors. If we make a degree of difficulty equal to 3 (a factor of both six and twelve) then each step of difficulty change equals a 25% change in probability of success from guaranteed success (TN 0) to guaranteed failure (TN 12), on an unmodified roll, in five steps.
There maybe a desire to modify the difficulty of an action by less than a full degree and there are only two numbers smaller than 3 (1 and 2). Which might be a good thing as it easily maps onto Minor and Major Complications (or Bonuses if we want to move in the other direction). There is a danger of these modifiers getting away from us, of them piling up to infinity and making calculating the difficulty of any given action more trouble than it’s worth, so we need to limit their ability to stack.
We could say that they don’t stack at all, that only the largest Complication or Bonus is applied to any roll, but I think I want things to be more flexible than that. Instead we could say that only the greatest Complication (or Bonus) of any give Type applies; both smoke and darkness might negatively impact visibility but we should only really care about the more severe of the two at any given time.
There will have to be a cap on how many different type of Complications there are, there should actually be a list of sample Complications but feels like a task for another day. For now we’ll just say no more than six (another factor) Complications.
We could say that they don’t stack at all, that only the largest Complication or Bonus is applied to any roll, but I think I want things to be more flexible than that. Instead we could say that only the greatest Complication (or Bonus) of any give Type applies; both smoke and darkness might negatively impact visibility but we should only really care about the more severe of the two at any given time.
There will have to be a cap on how many different type of Complications there are, there should actually be a list of sample Complications but feels like a task for another day. For now we’ll just say no more than six (another factor) Complications.
