RPG Errata: A New Kind of Die Roll

This is going to be a fluffy post, because my brain decided to ask a question that I needed to answer: Is it possible to do a different Powered by the Apocalypse die-roll system that has similar results?

The standard PbtA roll is 2d6 plus a bonus, such as a skill or stat. If the total of these dice and bonus is 7 to 9, you’ve rolled 1 hit. If the total is 10 or greater, you’ve rolled 2 hits. Moves have different results depending on how many hits you score, if any.

Ironsworn is a PbtA game that uses a different method of figuring out how many hits you score. Instead of having three “levels” of hits (2-6, 7-9, and 10+, for 0, 1, and 2 hits, respectively), you roll 2d10 and 1d6. You add your skill or stat bonus to the d6, and you gain 0, 1, or 2 hits depending on whether your result is greater than 0, 1, or 2 of the d10s.

What’s the difference between these two systems? Let’s take a look at Anydice. Here’s the program for comparing these two die-rolling methods:

function: pbta ROLL:s B:n{
 TOTAL: 1@ROLL+2@ROLL+B
 if TOTAL > 6 {
  result: 1 + (TOTAL > 9)
 }
 result: 0
}

function: ironsworn ROLL:s B:n{
DIEA: ROLL+B > 1d10
DIEB: ROLL+B > 1d10
 result: DIEA + DIEB
}

BONUS: 0

output [pbta 2d6 BONUS] named "PbtA"
output [ironsworn 1d6 BONUS+1] named "Ironsworn"

As you can see, these methods are pretty similar in terms of distribution, depending on the bonus. The biggest difference is that Ironsworn needs extra bonus points to more closely match the PbtA distribution, and after bonuses of 4, it really needs 2 extra points instead of just 1. This makes for a slightly grittier system, depending on how many bonuses a player gets on the average roll.

But that’s all math. What is the difference between the systems apart from probabilities? Why use one instead of the other?

Well, at its most basic, PbtA requires different kinds of cognitive load. First, you have to look at two dice and add them together. Second, you have to add a flat bonus. Then, you have to compare the total to two memorized break-points: greater than 6, then greater than 9. For Ironsworn, first you look at one die and add a flat bonus. Then, you compare the total to two break points: the 2 d10s.

Some people find different kinds of conative load more taxing than others. There are those who find too much math tiring, and so might find Ironsworn a faster system to play with, while others might chafe at needing to compare their rolled result to two different numbers every time.

So I wondered: is there another system that result in similar distributions of results, but uses a third kind of cognitive load? The answer is, yes.

I started from a couple basic ideas: rather than the binary success/fail of RPGs like D&D, PbtA games are trinary. They provide three results: miss, partial hit, or hit. We could use a d3 to represent those, couldn’t we? Then all we have to do is work out how to count the dice to see which of the three results we get.

Turns out, that didn’t work so well. I had the idea of rolling lots of FUDGE dice, reading the faces as hash-marks rather than minuses or pluses:

function: pbta ROLL:s B:n{
 TOTAL: 1@ROLL+2@ROLL+B
 if TOTAL > 6 {
  result: 1 + (TOTAL > 9)
 }
 result: 0
}

function: ironsworn ROLL:s B:n{
 DIEA: ROLL+B > 1d10
 DIEB: ROLL+B > 1d10
 result: DIEA + DIEB
}

function: newroll ROLL:s {
 T: [count 2 in ROLL]
 O: [count 1 in ROLL]
 Z: [count 0 in ROLL]-O
 if O > Z {
  result: 1 + (T > O)
 }
 result: 0
}

BONUS: 0
output [pbta 2d6 BONUS] named "PbtA"
output [ironsworn 1d6 BONUS+2] named "Ironsworn"
output [newroll 4d{0..2}] named "New Roll"

Now, look at that distribution. It look a little bit of tinkering to get it here, but I think that’s kinda cool. Roll 4dF, and remove blank dice equal to the number of single-hash’s you rolled. Whichever dice you have the most of, that’s how many hits you got. The fact that this kinda weird method of rolling dice comes up with a comparable distribution to the PbtA system, I think that’s neat.

But I hit a problem when I started trying to add bonuses to the system. It just didn’t work well, so I discarded the idea and thought about reading the highest rolled die, similar to Blades in the Dark, a system that is nominally PbtA, though with some radical differences.

What if you rolled a pool of dice and looked at the die showing the largest number: depending on it’s size, that would decide if it was a miss, hit, or partial:

function: pbta ROLL:s B:n{
 TOTAL: 1@ROLL+2@ROLL+B
 if TOTAL > 6 {
  result: 1 + (TOTAL > 9)
 }
 result: 0
}

function: ironsworn ROLL:s B:n{
 DIEA: ROLL+B > 1d10
 DIEB: ROLL+B > 1d10
 result: DIEA + DIEB
}

function: newroll S:n M:n L:n {
 if M > S {result: 1 + (L>M)}
 result: 0
}

BONUS: 0
output [pbta 2d6 BONUS] named "PbtA"
output [ironsworn 1d6 BONUS+2] named "Ironsworn"
output [newroll 1@3d6 1@2d8 1@1d10] named "New Roll"

Again, look at that distribution! The idea that rolling 3d6, 2d8, and 1d10, picking up the highest rolled die, and counting a d6 as a failure, a d8 as a partial, and a d10 as a full hit would map so closely to PbtA is wild to me. Dice are fun, aren’t they?

But those of you who are used to coding or double-checking other people’s work noticed my mistake already: the newroll function I came up with isn’t a “find the highest die” function. If I rolled a higher number on a d6 than I did on a d8, that’d count as a miss, no matter how big the d10 was. The fact that I made this same mistake with the FUDGE-dice function above means it didn’t really work in the first place either.

Here’s a different function that does what I really wanted.

function: newroll S:n M:n L:n {
 if L > M & L > S {result:2}
 if M > L & M > S {result:1}
 result: 0
}

Much less comparable, right?

Another interesting fact: to get this mechanic close to PbtA takes switching the dice around: d10s are misses and d6s are full hits. But again, adding bonuses became ridiculously complex, where instead of adding a flat number I was adding and removing dice to the pool, adjusting die-sizes, and ultimately creating a very complicated chart of different die-rolls depending on your skill level.

Now, as with most things, I was making it more complicated than I needed it to be. There is a very simple die-mechanic that uses almost no math and only a few dice to closely match the PbtA distribution…remember my last post, about Two Truths and a Lycanthrope?

Well, things didn’t end there…