Rolling 2d6 in PDQ and Apocalypse World: Learning the Numbers

I am supervising two students in independent study projects this semester. One of them is working on a tabletop RPG, and I want to share here a topic that came up on our group's online chat.

I have fiddled with Chad Underkoffler's PDQ a few times over the years, running some short-lived campaigns with my boys. I wrote about one of my favorite aspects of PDQ several years ago, how it models the psychology of learning in a more realistic way than many mass-market games. You can find the PDQ Master Chart in this free PDF, and I'm reproducing it here for convenience:

I remember that every time I played a PDQ session, I would have this simple chart in front of me. I never got to the point where I internalized it, although I'm sure I would have with time. Let's look at some of the structural properties that make it learnable. First, "average" quality is 0, which is simple: a regular person has no bonuses or penalities. Going up or down in quality is in steps of two, which I like from a mathematics point-of-view because it's statistically meaningful in a way that, say, a +1 on a d20 is almost insignificant. For the Difficulty Ranks, there is a sensible centering on 7 as "a straightforward task." Anyone who picks up the rulebook is going to know that 7 is the most likely result on 2d6, so this gives a memorable default. Difficulty Ranks also move up and down in steps of two, which again I think is a much better choice than fine-grained quanta, especially since this is supposed to be a narrative-heavy game rather than a simulationist one. (PDQ stands for "Prose Descriptive Qualities" after all.) I never had problems with the centers of these scales, but I did find it hard to remember, say, the difference between a Difficulty Rank of 11 and an 13. Also, for reasons I cannot quite explain, I find -2, 0, +2, +4, +6 to be much easier to remember than 5, 7, 9, 11, 13, even though they are the result of the same function, just applied to different inputs.

My student who is exploring tabletop roleplaying game design has been inspired by the Powered by the Apocalypse movement, which, briefly, describes a family of designs that are inspired by Vincent and Meguey Baker's Apocalypse World system. I backed the Kickstarter for the second edition of Apocalypse World a few years ago on a forgotten recommendation from a respected designer: I think it was someone like Robin Laws or Richard Bartle who posted about the campaign, saying that anyone serious about game design should support it. It's a riot to read, but it's certainly not the kind of thing my kids are quite ready for yet!

The mechanisms of Apocalypse World that I want to focus on here, though, is resolution of moves through rolling 2d6. These are the only dice used in the system, and it works like this: with less than a 7, it's a failure; between 7 and 9, it's a partial success, and 10 or higher is a complete success. That's it. This is truly elegant for a system that is designed for narrativist gameplay.

A funny thing happened when my student was testing his RPG with the research group. In order to make the game learnable to new players, he put this dice resolution system into a chart and set it in the middle of the table. He himself referenced the chart a few times while we played the game, despite his being the designer and a regular player of Blades in the Dark, another PbtA game. Curiously, the Bakers don't actually have a chart in Apocalypse World second edition at all; they just describe it in prose.

This got me thinking about the specific values used by Apocalypse World, similar to how I analyzed the PDQ Master Chart. Once again, we have 7 as a prominent number: it's the most likely value on 2d6, and it sits at the threshold between failure and partial success. It is, in a way, the easiest number to remember as being significant on 2d6. The next threshold value is 10, which marks the lowest value that represents a full success. Ten is the first double-digit number possible on two dice. It's also, for most people, the number of fingers you have. It's the base of our counting system. A "perfect 10" cannot be beat. 7. 10. Got it. Two numbers, that's the whole system in a very small amount of memory.

Just to be clear, I think this is brilliant. I don't think you could pick two different numbers that would be better for breaking down 2-6 in a more memorable way. I wonder if the Bakers chose these numbers because of their interesting properties or if it was done with intuition and luck.

We had a brief discussion in my research group meeting last week about adding 2d6 vs. counting success on variable numbers of d6. For example, the question was raised, can most players more quickly add 2d6 or count how many of an arbitrary number of dice have rolled above 4? I argued that for anyone who had spent any appreciable time playing tabletop games, rolling 2d6 can be done purely with pattern matching: I don't add five pips and the three pips, I just see a representation of the quantity "8". I mention this here because I think it's a good games research (or perceptual learning) question, but I haven't checked to see if anyone's explored this yet.

Finally, I'll mention that, with the little bit of testing we've done on my student's game, I've grown quite fond of the "partial success" idea. My favorite expression of this as a story device is that you succeed, but at a cost.

In case you were wondering about the dearth of posts here: I've been meaning to write more about my research group activities this semester, since it's been very rewarding. I hope to write up some kind of summary at the end of the semester at least. However, the past few weeks, my attention has been pulled away into a departmental self-study report. I think the sections I have been spearheading are strong, but it's had a significant impact on my research time as well as my reflective writing time.