Hobby gamers of a certain age know exactly what this is:
It’s the bell curve for Attribute distributions generated by rolling 3d6, which was how many a D&D session began. Throw three dice six times, record the scores next to the Attributes in sequence, and charge into the dungeon with your voulge drawn.
In addition to looking pleasantly symmetrical, that bell curve says something. It says that, when you roll multiple dice to obtain a single outcome, you’re likely to see a cumulative number in the middle of the possible range of outcomes. That’s why an average Attribute in D&D is a 10; it’s why you rolled 3d6 instead of 1d20. Indeed, if you rolled 1d20, the bell curve would look like this:
That’s not a curve at all. That’s an equal likelihood of any given outcome, with no range more common than any other. In the 3d6 bell curve, a 10 or 11 is more likely the outcome than a 3 or 18. In the 1d20 curve, 3, 10, 11, and 18 are all equally likely (as are all other numbers in the 1-20 range), at a five-percent chance of occurrence each.
Now, everyone around the table is disappointed when a cleric calls up a healing spell and, after much anticipation, rolls a 1. Rolling 1d8 for cure light wounds or cure wounds, depending on your edition of preference, is a bit of a letdown. It’s good for creating a hardcore, let-the-dice-fall-where-they-may moment, but it’s not good for creating a heroic moment. That standard 1d8 curve looks almost exactly like the 1d20 curve. Each outcome is equally probable, since you’re rolling only one die.
Taking a cue from that 3d6 bell curve, we can make it more likely for the cleric’s spell will generate a greater number of hit points cured. By making the cleric’s cure spell heal 2d4 hit points as opposed to 1d8, the flat curve instead becomes a peaked line, with the most likely outcome being a 5 — and, most importantly, that 5 is four times more likely to be the result than the lowest yield, the humble 2 (which, itself, is still twice the recovered hit points than the possible 1 from 1d8 allows…).
In fact, the 5e rules have an element of this in place. Cure wounds still operates on a flat 1d8 roll, but potions of healing do indeed use a 2d4 base roll, with an additional +2 modifier to that roll, which keep the peaked line but just shifts the range of values up by two.
But you know this, so let’s get to the point.
Deciding how to distribute your randomized outcomes plays a large part in supporting the essential experience of your game. If you want more of those satisfying, “heroic” moments in which a supportive character can generally be relied upon to give a substantial boon to the other characters, consider house-ruling to a 2d4 per level roll instead of the standard 1d8 per level. To represent those high-tension, what-does-Fate-have-in-store moments — a decidedly old-school flavor in which the gods’ favor is fickle, even for their chosen — the 1d8 method works well. Think about the campaign you’re running. Are the players’ characters considered to be “heroes”? Or are they more morally ambiguous, dime-a-dozen “adventurers”? Later editions of D&D embrace the former, while earlier editions and games like Dungeon Crawl Classics posit the latter.
Obviously, working with your probabilities and value ranges need not stop with D&D. Using the Life Sphere in Mage, for example, a Storyteller may set the difficulties for healing magic at 1 lower than standard, if she wants the chronicle to feature more durable characters, or if the theme of the game revolves around healing or nurturing. A Call of Cthulhu Keeper may grant a bonus to an experience check to represent characters who rapidly increase in competency. A Dungeon World GM may halve common monster damage rolls but increase the number of monsters the characters encounter, to give a sense of high-powered adventurers possessing advantage over lesser foes, while keeping the damage rolls of boss-type monsters unmodified — or even increased, to highlight the disparity between monstrous rabble and more significant antagonists.
That essential experience is key, and I’ll return to it frequently when discussing design. The systems of the game must support what the game intends to communicate, otherwise the rules won’t convey the setting, nor will they help communicate what the game is “about.”
Thanks to anydice.com for the dice probabilities calculator.