TMI Tuesday–Contests in Cortex as Sequential Games

TL;DR: This post should have been titled: “Cortex’s Contests as Sequential Bayesian Games with Behavioral Strategies.” It was a bit much, so I left the Bayesian part out.

Cortex Prime RPG is crunchy—a consequence of dice pools with finicky probabilities, dice tricks with multiple decision points, and success, effect, and complications being tracked on separate dimensions (not necessarily a metaphor, see here). Still, Cortex is not “crunch for the joy of min-maxing” (looking at you, GURPS), and its strategic layer remains ancillary to narrative-crafting.

I usually relegate strategic matters to The Fine Prints, but on occasion, strategic stuff deserves the center stage. Tuesdays are perfect for giving a post-length treatment. Hence, a new series. And I’ll begin with words of wisdom from Lynn Jones, the other hemisphere of my Cortex (I love a terrible pun), as they popped up organically.

I appreciate that there is design merit that influences the narrative strategies by deciding what kind of strategy a given obstacle employs before the dice hit the table. Which means an enumeration and definition of those strategy paths is meaningful too.
Concede for Position - concede when the odds of winning are less than X
Brute Force - roll until fail
Aim for Effect - direct opponents who make a (figurative) statement when they get their way
Aim for Total - skilled opponents who'd rather win than punish
Hedge your bets - will trade some total for increased effect but not excessively

This post provides context for Lynn Jones’ Shortlist of Strategies™ for GMCs (Game Moderator Characters, Cortex-lingo for NPCs). My favorite applications—agent-based-model Threat maps (here and here)—would distract from the simplicity and elegance of Lynn’s idea, so I’ll keep them for another day. A final caveat emptor: with no Fine Prints to keep asides aside, you may want to take your ADHD meds.

Roll & Keep All the Good Stuff

Reminding readers of Cortex’s “roll and keep” mechanics is probably overkill. But I like to make believe that folks jump Cortex’s bandwagon through this blog on occasion, rather than the converse, and redundancy qualifies as “too much information” anyway.

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

The parameters n, m, and m’ in (R&K) stand for numbers of dice of any “side rating” between triangular pyramid (4-side) and dodecahedron (12-side). The default values for those numbers of dice are n=3, m=2 and m’=1, but can vary from one game build to another and with metacurrency spending (Plot Points, or PP). The criticals for today are:

the total determines success or failure via comparison to a difficulty also established by (R&K)—so, to another total;
on success, the effect represents the magnitude thereof, not its occurrence (which is, again, represented by the comparison of totals);
on failure, the effect still has a magnitude that may mitigate the fallout (if equal to or higher than the opposition’s, it steps down said opposition’s effect).

Handwaving optional rules and not-yet-canon rules, “success” in a task is assessed in one of two ways (upcoming editions will add a third):

tests, when the task model is a piecemeal decision problem;
contests, when the task model is a sequential decision problem.

Per the rules-as-written, “the key difference between tests and contests is who rolls the dice first” (CPGH, p. 19): the GM (tests) and a PC (contests, with rare exceptions). It’d be tempting to paraphrase this as a difference between non-strategic and strategic agents—or in colloquial terms, “passive” and “active” opposition. But I’ll resist for reasons I’ll leave for another day.

Contests as a 2-Player Game

I’ll focus on two-party contests without third-party interruptions because third parties are irrelevant to the preferences I’ll concern myself with. From a game-theoretic standpoint, a contest is a sequential, nonzero-sum, 2-player game with perfect information, and Fig. 1 is its extensive form. Each of those qualifiers calls for clarification.

“Sequential.” Contestants take turns and make decisions that respond to one another.
“Nonzero-sum.” If both C1 and C2 “botch” their rolls (i.e., roll all 1s), no one gets what they want, and the sum of payoffs is negative.
“2-player.” “Barring 3rd party intervention,” otherwise: n-player with n equal to or greater than 2.
“Perfect information.” No player has private information; equivalently (here), players have symmetrical information—like chess, unlike poker.
“Extensive form.” Fig. 1 is a fancy representation of a game tree (the other form, called “strategic,” is a matrix collapsing sequences of choices, thus irrelevant here).

Fig. 1: Cortex Contests (linear, recursive).

Fig. 1 does not mention effects explicitly, but I’ll come to them soon. Before that, a Captain Obvious moment: a contest is a game in itself, and there are strategies for that game. C1’s and C2’s action sets and preferences in that game can be considered abstracting from the narrative contribution of dice in the pool. And so, let’s abstract.

Both C1 and C2 have multiple (R&K)-compatible options (action sets) depending on Traits, SFXs, and available Plot Points. The action sets are finite, enumerable, and knowable by both players (for GT nerds: common knowledge). The issue is not uncertainty but combinatorial explosion (as in chess). For players: the cognitive load of anticipating possible moves and figuring out odds.

Tests as Decision Problems

Mechanically, a test is a single-turn contest where C1 is a GMC and C2 is a PC. Being single-turn, tests do not offer C1 or C2 the option to concede at a second turn. Two one-shot decision rules—or more precisely, families thereof, varying m and m’—apply here.

(Total) Keep the m highest-rolling eligible dice for total and the m’ highest-rated remaining eligible die for effect.

(Effect) Keep the m’ highest-rated eligible die for effect and the m remaining highest-rolling eligible dice for total.

Whichever best responds to C1’s total and effect is contextual, but (when they don’t coincide) knowing the outcome of C1’s (R&K) suffices to choose between (Total) and (Effect), up to and including boosting m and/or m’ with metacurrency spending.

Contests differ from tests because a contest initiator decides based on odds of total and effects, not known values—a topic of its own, for next TMI Tuesday actually—but only the last effect counts. Thus, if known, a GMC’s preferences over contests’ possible outcomes provide clues for strategy selection against that GMC.

Lynn Jones’ Shortlist of Strategies™ for GMCs

Lynn’s my reference on all things Cortex and one of few folks who patiently deal with my half-baked ideas and, rather than rubbing my face in their byproduct, help me work out better ones. So I was over the moon when I realized my game-theoretic mindset had rubbed off on him.

Below is a paraphrase of Lynn’s list based on subsequent conversations.

Brute Force. The GMC rolls at their turn until they get what they want or fail, no matter what.
Aim for Total. The GMC prioritizes the event of success (total), possibly at the expense of the magnitude of the effect.
Aim for Effect. The GMC maximizes the magnitude of success (if they get what they want) or minimizes the magnitude of incoming complications (if they don’t).
Concede for Position. The GMC concedes when the odds of winning fall below a given margin.
Bet Hedging. The GMC considers trade-offs between total and effect (up to a point).

Four remarks. First, the paraphrase edits out narrative counterparts of total/effect preferences. Lynn’s examples of narrative interpretations are natural but not uniquely so. Sticking to contests as game-in-themselves prevents turning Lynn’s examples into intuition pumps (for me) because I’d apply them to other cases, and so could you.

Second, the re-ordering reflects the test-contest continuum. Brute Force and Aim for [Total/Effect] collapse in tests (for GMCs), and the latter two to (Total) and (Effect) one-shot decision rules. Concede for Position, and Bet Hedging strategies only become available with contests and pay more attention to odds (and possibly, metacurrency) due to escalation.

Third, all strategies are available to PCs, and open to strategic reasoning. For instance, depending on dice pool makeup, Aim for Effect can do better against Aim for Total than, say, Brute Force or even Aim for Total. Therefore, knowing a GMC type is valuable strategic information. But rule-of-thumb reigns supreme here because…

Fourth, the game theory of contests as games-in-themselves is hellacious. Assembling a dice pool is choosing a lottery. Strategies for sequential games with lotteries in action sets (called behavioral strategies) are some of the most complex to compute.

And that’s where I’ll stop for today.

Wrapping up: Thanks, Lynn!

Until recently, I had fond memories of Cortex games I had GM-ed (Serenity, Marvel Heroic, and Firefly) and played (Supernatural), but viewed them as steps in a journey beginning with GURPS narrative-friendly foreplay and ending with Fate’s full-frontal fiction-first. The thing is, I misconstrued my fondness for Cortex’s crunchy side as nostalgia from my GURPS days, and would sum up my relation to it with an analogy (NSFW “Fate is sex, Cortex is porn.”)

Still, I suspected that I was missing something. Ironically, it took me about half a year of thinking about Fate and AW in game-theoretic terms to appreciate how Cortex’s design stands out. The same holds for Cortex’s online community, whose nicer aspects, compared to other TTRPG communities, might very well have to do with the system’s design (another insight from my day job).

This series is my geeky tribute to Cortex and its community. I have a few installments in-store, all prompted by conversations with folks I met online. And this one, in particular, was my nerdy way to thank Lynn Jones. So thanks, Lynn!

And that will be all for today, folks.