Dice: Curve vs Linear

Back in the day what particular die expression your game used was such a sticking point because that was all we had. The games looked pretty much the same except that some used 1d100, some used 3d6, some used 10d10, some used 1d20 etc. These days there are a lot more nuance to system than just this basic question.

Just as a bit of game design basics for posterity, even though your game definitely shouldn’t start or end here, let’s bring out this old chestnut for one more go on the merry-go-round.

It is an oft repeated myth, maybe less so these days, that linear die rolls, such as 1d100 or 1d20, are more “swingy” than curve style die rolls, such as 3d6.

3d6 is basically a 1d216 — the three dice can fall in one of 216 different ways. That’s as swingy as they go. 2d6 is equivalent to 1d36—there are thirty-six different outcomes (for example one way to get 2, two ways to get 3 and so on).

Let’s take rolling 10 or lower as an example. On 1d20 and on 3d6 it’s both 50%. Same swinginess.

Or let’s say you want something that’s got 75% chance of happening. There’s no exact equivalent on 3d6 but rolling 12 or lower is close, at 74% and change. Of course on 1d20 it’s rolling 15 or lower.

You want curve when…

…you want to hide complex math behind small numbers

Games like Cthulhu Dark, Fudge and Shadespire use dice curves well. They have well–thought-out math where you can get rare events (like the 1-in-81 chance of rolling all pluses in Fudge, or the slowly decreasing Insight once you’ve started “supressing knowledge” in Cthulhu Dark) but not have to deal with a bunch of adding or comparing big numbers.

…the different outcomes have different meanings

Damage die in D&D is an example. 7 damage is meaningfully different than 4 damage than 1 damage because they all can kill different monsters.

Another example is rolling on a random table. Entry 7 is 3d6 wolves, entry 4 is 2 grumpy owlboars. Even the 3d6 wolves are different than 1d20 wolves.

When summing and counting up the number of wolves is an example where 1d20 is more swingy than 3d6.

The “myth” comes from a bad DM practice that was common in the past: to ascribe semantics to the natural die roll. A 4 or 3 was shameful, a 2 was banana-peel–slippingly ridiculous, a 17 or 18 was godlike elegance. The mod on the character sheet didn’t really matter, the al-mighty linear d20 ruled all. I can definitely understand why a lot of players would have a lot of lingering resentment towards linear after being subjected this!

You want linear when…

…you are adding a lot of modifiers

If you try to be all “+1 from the rain, +3 from the vegetation here, -2 for the exhaustion” on 4d3 (as per Fudge) you are in for a world of trouble. A net change of -2 take your chances of succeeding from 62% to just 19, in the typical case.

In curve systems, modifiers make more of a difference near the middle of the curve. A terrible or superb character in Fudge is less affected than someone near the middle of the pack, who can get completely messed up by a mod of -1 or -2.

This can sometimes be what you want, but, you are not getting transparent probabilities and you’re liable to mess up. A game like Burning Wheel where the difference between Ob2 and Ob3 differs wildly depending on amount of dice in the pool, for example.

…you want probabilities to stay familiar and consistent

A game that’s consistently using linear, like ⅙ this, ²⁄₆ that, or a d20 or a d100 or a d10 or whatever, will map to your players intuition of their odds reasonably well.

I know that enfranchised GURPS players know that they have 50% chance rolling 10 or lower on 3d6 but 75% rolling 12 or lower, but, many more casual players don’t know that and I’d like them to enjoy games too, which is why I suggest linear instead.

You are facing a difficult design decision when…

…you want a li’l of column A and a li’l of column B. Good luck my friends♥︎