Whenever a character in a tabletop role-playing game attempts an action and the outcome is uncertain the system steps in to determine the outcome. Arguably resolving that ambiguity is the primary purpose for the existence of the mechanical half of an TTRPG so it's not an unreasonable place to start the design process.
While there are systems that use things such as playing cards or dominoes for task resolution the most option is to roll some number of dice. Normally in one of the following three ways: SINGLE, roll a single die; SUM, roll a pool of dice then add them together; and SELECTION, roll a pool of dice then select a subset to be the result. Each method has a different likelihood producing any given result, a different probability curve. And it is entirely possible to calculate these curves in advance.
Rolling a single die of any size has the same likelihood of producing any result within its range, if rolling a d6 each number has an equal 1-in-6 (or 6-in-36, to frame it in a way that will be helpful later on) chance of coming up, creating a perfectly flat "curve". Rolling and sum produces something resembling the classic bell curve, 2d6 has numbers looking something like the following: 2 = 1/36, 3 = 2/36, 4 = 3/36, 5 = 4/36, 6 = 5/36, 7 = 6/36, 8 = 5/36, 9 = 4/36, 10 = 3/36, 11 = 2/36, 12 = 1/36. Increasing the number of dice rolled both increases the range and flattens the curve, makes the central peak less pronounced. Calculating the probability for a selection method is a little more complected, requiring some assumptions to be made, but produces a curve that can only be described as spiky. If you roll 2d6 and care only about the highest result the odds look something like this: 1 = 1/36, 2 = 3/36, 3 = 5/36, 4 = 7/36, 5 = 9/36, 6 = 11/36. Adding dice to that pool does nothing to affect the range but does increase the likelihood of a maximal result. Which might have utility.
There are two main ways a character's traits can impact task resolution: it can either modify the dice pool, changing the number or size of dice involved, before the roll, or modifying the result after the roll. Changing the dice pool of either the single or sum method changes the range of possible results making it much harder to calculate difficulties. Which should be avoided. There are systems that do that, that change up dice pools (some of which I even like), but it should still be avoided. There is no such drawback with the selection method, as long as you stick to a single size of die, meaning you're free to use both forms of resolution modification, you can have different traits modify the same roll in different ways.
A useful framework for examining TTRPG systems is to divide a character's (task resolution modifying) traits into broad primary ones and narrower secondary ones. The more or less default approach is to have both types of traits affect task resolution in the same way; having them both add dice to the pool or value to the result (mathematically increasing the result is the same as decreasing the target number). This is completely serviceable, hence its position as the default, but it's more interesting if you can create a greater distinction between the two classes of traits. One method I've seen used by lighter, more narratively focused, games is it treat secondary traits as a simple binary; primary traits may have numerical value but secondary traits are only ever trained or untrained. But since there are two methods of modification at our disposal why don't we use both: one trait can determine the number of dice and the other can act as a bonus to the result. Since the number of dice in a pool has the biggest impact on probability that should be determined by the primary traits, leaving the secondary traits to act as bonuses, and bringing us our first actual game rule.
Basic Task Resolution: When determining the outcome of an action the controlling player will roll a number of dX 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).
There are still things to be worked out even in that short paragraph; the type of die used needs to be nailed down, the specifics of the primary and secondary traits (both individually and as classes), the various difficulty target numbers need to worked out (at least partially based on the die used), and finally we most consider whether success will be binary or have degrees.
It should maybe have degrees.
-Comments welcome.
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