Theory Thursday–Success or Failure? Yes

TL;DR: Cortex Prime changes the very concepts of success and failure, there’s a cognitive science theory that can prove it, and a few visuals are all that’s needed to show how.

When it comes to rolling the dice, the recommended policy of most narrative-friendly TTRPGs is to roll when things could go wrong in a dramatic way—Fate would be my go-to reference here. “Going wrong” is often interpreted as a type of failure, with some TTRPGs introducing partial or costly success, sometimes as optional substitutes for failure—Fate does that well, too.

Apocalypse World and Cortex Prime break away from that logic—see here, for instance. Still, until recently, I had missed a theoretical connection with conceptual spaces, a tool I’ve dabbled with professionally (and in a previous life of hobby blogging). Through that lens, Cortex Prime changes the concepts of “success” and “failure,” same as scientific revolutions change scientific concepts. 

Now, that’s a tall claim, and a popular exposition of conceptual spaces explaining it is, to be honest, still beyond the time and effort I’m able to devote to that blog. Fortunately, that’s unnecessary: the framework is geometrical, i.e., visual-friendly. So I can make my point with simple visuals—lines and planes—with the theory doing the work under the hood.

And in this post, I’ll do just that. Pedantically (that’s going to come up often), I’ll offer what philosophers call a “rational reconstruction”: I’ll show how theory could have brought the same result an organic development—the evolution of the Cortex ruleset—and in the process, highlight some under-appreciated features of said development.

1D Stuff: Linear ordering of success and failure

Apocalypse World is revolutionary in ninety-nine ways, but success ain’t one. PCs roll 2d6+[stat] where stat ranges from -2 to +3, to results within the (4-15) open interval—open, not close, because of further possible ongoing and forward modifiers from moves. Since the GM never rolls, there is no PC-to-NPC comparison.

Given the above, results are linearly ordered (or strictly partially ordered, for pedantic folks like me), so we merely need a linear representation. Actually, we don’t even need all the numbers: a discretized line with four cut-off points standing for intervals suffices, as in Fig. 1. (12+ applies when advanced moves are in play, and so 10+ remains the general case).

Fig. 1. Apocalypse World (discretized) success-and-failure line

AW’s 7-9 results (and sometimes, 6- too) grant success with complications. But the magnitudes of success and complication are correlated: the higher the dice roll, the less severe the complication. The same holds for Fate RPG, mutatis mutandis, with its “Success at a Major Cost” alternative to failure. Still, conceptually, we could separate the performance, as measured by the dice roll, and the consequence, as represented by the narrative outcome. So let’s do just that.

Going 2-dimensional

With conceptual spaces theory working under the hood, the last suggestion boils down to tracking performance and consequence along different axes. Using AW for reference, that’s Fig. 2. Note that I inverted the order of outcomes for a more readable picture—-steps rather than nested rectangles (there’s an ulterior motive).

Fig. 2: An idle refinement.

The 2-dimensional picture is, at that point, an idle refinement. Performance on the y-axis is constantly correlated to consequences on the x-axis. But now, the x-y axis correlation becomes something we can play with. We have a visual medium to support questions like: “could a PC have a moment of grace performance and yet need to prepare for the worst?” All we need is to split the outcome between the x- and y- axes. 

And that brings us to Cortex Prime territory. Cortex Prime’s resolution mechanics, which uses a dice pool, allows for splitting the outcome of any action between effect and complication, identifying them with different dice in the pool. But under the hood, that’s really changing the concept of “outcome”—because the 1D representation does not suffice anymore.

The Success Plane

The effect-complications distinction is Cortex Prime’s novel contribution and builds upon our old friend, the Roll & Keep rule. It’s coming so often in that blog that I actually made it a re-usable block in the WordPress editor, and I can’t wait to re-use it, so here it is.

(R&K) Assemble a dice pool of n dice, then: (1) roll the n dice, discard all 1s; (2) keep and add their display value: that’s your total; and: (3) keep m’ and note the side rating(s): that’s your effect(s).

Since the default values for (R&K) are n=3, m=2 and m’=1, too many 1s can reduce the number of eligible dice to the special case of m’=0—and that’s all the probability reasoning I’ll need for today. Both players’ and GM’s rolls obey (R&K), but I’ll consider cases where the GM’s roll merely sets a “difficulty” and I’ll handwave vigorously everything else—in particular, the discussion GM’s 1s and effect.

With that said, let’s get back to the co-stars of today’s show: player-rolled 1s, called hitches, and players’ effect dice. Qualitatively, hitches are not “all bad”: the GM “activates” them by paying the player a Plot Point (CP’s metacurrency) to create complications. They are represented by a die, starting with a six-sided rating, and are thereafter available, as dice-pool builders, against the PCs (see The Fine Prints for some strategic refinements).

Let’s consider the simplest Cortex Prime resolution case, when a PC takes unopposed, low-stake action: the GM rolls, their total is the difficulty to beat, and their effect is mostly irrelevant. For demonstration’s sake, let’s define it even further:

  • The action is Easy, which in Cortex Prime is a dice pool with an m=2 average of 7.
  • The PC’s dice pool has an m=2 average of at least 9.

Now, recall the simple-minded narrative-friendly logic mentioned in the introduction’s first paragraph. we have a straightforward case for the GM’s waiving the dice roll because, you know, unchallenging, can’t go wrong, yadda-yadda-yadda. But that’s only the case if probabilities of success and complications are strictly correlated. When they’re not, we can have the situation depicted in Fig. 3.

In Fig. 3, the rolls fall in the expected range, but the twelve-sided die, that should have been a total builder, hitched, leaving a ten-sided die for effect. If the GM buys the hitch, that’s an above-average effect with “strings attached.” Still, success trumps complications: a hitched dice, whatever the rating, yields a six-sided complication, hence the transparency and the six-sided die in Fig 4, but thing can get worse from there (see The Fine Prints).

A plane with a Cartesian coordinate system, with an Effect y-axis and a Complication x-axis, both with five equidistant coordinate identified by a polyhedral die size, the closest to the origin being four-sided and the farthest being twelve sided. Two bands, one vertical, one horizontal, are singled out, both between the axis and a parallel line perpendicular to the other axis at the four-sided die position. The vertical band is identified as "Straight Effect Band" and the horizontal band, as "Straight complication band" while the origin of the axes is labelled "uncomplicated failure point."
Fig. 4.: The Success Plane

Now, for bells and whistles. First, the “standard” notion of success is “effect without complication” and is the Straight Effect Band of Fig. 4. Due to variation between dice pools, the band’s surface is not proportional to the probability of a straight effect. Pedantically: Fig. 4 is a conceptual space, not an event space. Second, the Straight Complication Band is a conceptual possibility, but in cases considered so far, the effect defaults to a four-sided die “floor” (see The Fine Prints). Third, and not represented, Cortex is actually 3D: Fig. 4 has a hidden 3rd axis for total comparison, and what happens on the success plane holds when the total exceeds the opposition, so the “Success Plane” is actually a “success volume” in a 3D result space.

The Fine Prints

Complication strategies. If multiple hitches occur at once, the GM can buy them for one PP apiece and create multiple six-sided complications, or spend a single PP and step up the complication once for each hitch beyond the first. Too many hitches in the same pool may step up a complication beyond d12, taking out a PC. If it’s not narratively appropriate, the GM might prefer to create multiple complications. But otherwise doing so may seem suboptimal, as it increases the odds of GM-rolled 1s that players can buy (with PPs) to step down and possibly eliminate complications (they’re called opportunities for that reason). So there’s a potential negative feedback loop: a batch of “small” complications created from a single roll may lead to fewer complications later on. It is, nevertheless, a sound tension-building strategy: it divides the PCs’ attention between multiple complications and incentivizes players to spend PPs on stepping them down (because they’re easier to eliminate). It may even encourage players to generate more PP, often through Hinder—which, substituting a d4 to whatever die rating would otherwise be used, can create new complications.

Straight Complications. The Straight Complication Band of Fig. 4 maps to the standard notion of “failure,” but cannot turn a success into failure. Consider what would have happened if, in Fig. 3, the ten-sided die had rolled 1 rather than 3. Then, we’d be left with a (nominal) success per total comparison, but only hitches. A similar situation with even more hitches could be enough to take the PC out (cf. previous Fine Prints). This could be a dice-pool interpretation of a Pyrrhic victory. Then again, Pyrrhus took the Roman army out at Heraclea as well as his own, and that’s an “effect” to go with the “complication.” Following a similar logic, for pools with a success-granting total but no eligible dice for effect, CP defaults to a d4-rated effect. Symmetrically, effect dice are relevant to failure: if a PC fails to beat the GM’s total, but their effect die is equal to or higher than the GM’s, the complication they’d take is stepped down from the GM’s effect die. Thus, CP modifies the concepts of failure, too: “straight complication” becomes a special case of failure—when the losing party’s effort is insufficient to lessen the winning party’s success.

Wrapping Up: Flipping things around

Cortex Prime introduces radical changes to the concepts of success and failure, with unique consequences on gameplay. One of them is to turn on its head the simple-minded advice with which I started, to “only roll if failure could have dramatic consequences.”

Here’s how. Imagine a PC assembling a dice pool with multiple X-or-higher rated dice against a GM’s dice pool of mostly Y-rated dice, where X>Y—which is just a pedantic generalization of the example of Fig. 3. The larger the PC’s pool, the greater their chance of success—but, also, the odds of hitches.

I’ll leave the next-to-last word to s my friend @Bro (any/all) from the Apocalypse World Discord server, who summed up those consequences better than I could.

“[Cortex] flips things around to you [the player] deciding to roll becoming a moment of dramatic importance by that decision.”

@Bro (any/all)

And that will be all for today, folks.

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