Z*ro F*cks Fr*day–A Troll’s Tale

TL;DR: This is not a revenge post. Only arguments, nothing personal, save maybe this “sign of adoration of stupidity”—if you don’t get it, that’s okay, it’s food for troll.

Surviving leukemia taught me that immediate reactions are a waste of perfectly good neurotransmitters. So I try not to engage online folks with strong opinions and weak evidence. Still, everybody knows about broken clocks, right? Well, recently, a bad faith actor suggested that the complexity of Cortex RPG’s dice pools exceeds casual players’ understanding. In cases like that, I relapse (pun intended).

First, for bad faith: insinuations were used as bait—Cam Banks doesn’t understand his own system, I don’t understand combinatorics, I’m prejudiced against Finns, Hume has failed, etc. I swallowed some hook, line, and sinker wrote others off as random brain-farts, remained polite, steer clear of ad hominems, and eventually cornered my interlocutor into a contradiction. It was exhausting.

Second, for the suggestion. It “feels” wrong, but there’s something to it. The sheer number of possible dice pools and strategies for building them is overwhelming, so there’s muddiness to the resolution system, it’s undeniable. Plus, I have dyscalculia. I’ve been on it for a while and needed a fresh look. And the circumstances gave me one.

Broken clock talk

It all started with a comment on a Polverine post announcement on the Facebook Fate Community‘s wall (the public one). Soon after, the admins enforced the rules and removed a post or two, for verbal abuse of yours truly and Cam Banks. I retracted a few of my own replies, now without context. When the virtual smoke cleared, two potential arguments remained voiced against Cortex’s mechanics (Fig. 1).

The Troll: Yeah. I do agree it does work as intented : smoke and mirrors so complex you cannot do combinatorics analysis of its effects. But, just like any fanboy who cannot grasp any negative feedback, you did not reply or deny single one of my points.

The chance to succeed on even dice pool is less than 50%, as the player has to beat the game master on both Effect die number of sides, and the highest result on dice.
Fig. 1. Argument #1a & #2
  1. Obfuscation by Mathematics. Cortex’s dice pools and dice tricks are “smoke and mirrors so complex you cannot do combinatorics analysis of its effect” That are either easy to disprove, or beyond proof-or-disproof.
  2. Game-design bias. The “chance to succeed on even dice pool is less than 50%…” This one is vacuously true and self-defeating on the surface, but it has hidden depth.

I activated my Peter’s Principle* SFX and reached out to a friend to help me crunch some numbers for (1)—it later turned out we could have dispensed with that—went back to FB, answered with a sample of combinatorics—a refutation of (1), see next section and The Fine Prints—and handwaved (2) out, which led to the elaboration at the top of Fig. 2.

The Troll: The combinatorics analysis of good quality deals all combinations. Again, you use "one flaw disproves all" which is neither reasonable nor true. Do you understand combinatorics at all?

Me: Enough (External link to an article titled: Logical Dialogues with Explicit Preferences and Strategy Selection). 

Me:  I think, sir, that you tried to bite more than you can chew. Be gracious about it.
Fig. 2. Argument #1b

The article I linked analyzes strategic profiles (pairs of strategies) in games where players have nondenumerable action sets. In other words: “combinatorics of good quality [that] deals all combinations” is provably impossible for these games. It’s the proverbial pudding, proving that exhaustive enumeration is not the alpha and omega of combinatorial problems.

(A short aside on the problem: here, next-to-last paragraph in the “Classical Logic” section. TL;aDoRation of stupidity: solvable by exhaustive enumeration iff the Halting Problem is.)

Next, “one flaw disproves all,” sounds like a logical fallacy, but it’s not. Under the circumstances, it is a legit logical proof method (again, see The Fine Prints)—so “reasonable” by the standards of, you know, logical reason…ing. Not “true,” granted, but a method cannot be (or “false”, only a statement can).

There was more bad faith argumentation that I’ll spare you. Amid topic switches, moving goalposts, and piled up verbal abuse, the only discernible argument was a reiteration of (1)—discounting suggested “fixes” the letter of which eluded me (but I think I got the spirit).

Game-design bias: hidden depth

In an earlier answer to (1) and (2), I missed a few things. That’s an issue with toxic types: they cause tunnel vision. Embeds don’t work in WordPress anymore, but you can read the original in a follow-up post (second comment in the thread, after a sad face emoji). And now for what I missed.

Let’s start with nitpicking: assume two players, Alice and Bob, with two (finite) “even” dice pools A and Bi.e., with a one-one mapping between A and B based on dice side rating. For definiteness, assume that Alice is a player with a PC and Bob, the GM. Then:

  • in a test: Bob rolls B first, and collects his total (and effect). If Alice rolls A, she must beat Bob’s total to succeed.
  • in a contest:  Alice rolls A, and collects her total (and effect). If Bob decides to roll B, he must beat Alice’s total to succeed.

Ex hypothesis, the pools are “even.” So, the probabilities for total for A and B are the same (whatever they are). The outcome of the Alice-Bob game is biased toward the first roller (Bob in tests, Alice in contests) because a “tie” results in a failed con/test for the second roller. Among proposed solutions is the removal of biases, and it is an utterly cogent suggestion, easily implemented in Cortex.

Alice (in a test) and Bob (in a contest) can indeed spend Plot Points to include an additional die in their total, offsetting the bias against the second roller. Most Cortex situations are not “even” Alice vs. Bob con/tests, however—because dice rolls in Cortex are sequential, and the second roller builds a dice pool knowing the first roller’s result. This will become critical in a minute.

Let’s conclude on “even” dice pools: based on odds, a sound strategic principle for a second roller is to have plot points to spend on their total. So, the game is set “as if” Cam Banks had assumed rational Alices and Bobs, and had written the rules to encourage them to: (1) spend PP on “even” trials; and: (2) learn to avoid “even” trials altogether. 

Obfuscation: a legit concern?

In the middle of all this, I discovered Cortex Prime Calculator created by @HighDiceRoller (from the Cortex Official Discord), making obsolete the Excel sheet mentioned in the follow-up FB post. An issue raised along the way is that combinatorial analysis is no mere tool to obtain probabilities, but I don’t know that it applies, here.

  • I agree, for the general case. No choice: as Hume would put it, it’s a necessary relation of ideas (the mathematical equivalent of a fact). 
  • I disagree, for the special case. How can combinatorial analysis bring anything to the topic of Cortex dice pools without probabilities?

To belabor: the co-authored article I linked implements combinatorial analysis without probabilities because they cannot apply. But Cortex con/tests are games-in-the-game where strategic options are lotteries. So I can’t see how not considering probabilities could reveal, say, game-design flaws. Then again, that might be ignorance and the aforementioned tunnel vision.

However, the above question is a moot point anyway. And, unlike combinatorial analysis, the mathematical basis for that claim is smack dab in the middle of my domain of expertise. In Cortex, dice rolls are not simultaneous, turning con/tests into sequential games, thereby making me an expert in Cortex’s game-design analysis.

First, consider a simplified case, where Cortex runs on tests only—e.g. the free Hammerhead Highlight. Then, player-Alices always know GM-Bob’s result before choosing their pool. With test-only games (or TOG), the single strategic rule-of-thumb any Alice needs is:

(TOG) Alice should always have at least as many Plot Points as their largest |A|—where |A|, “the cardinal of A,” is the number of dice (of any rating) in dice pool A.


You can prove to yourself that some Cortex strategies are easily understandable by figuring out why (TOG) works—if you do, congratulations: you just performed “mental combinatorial analysis.” Now, if you’d rather protect your cognitive resources from the fallout of foreign keyboard wars, more power to you. Hit me on The Dirty Window, ask, and I’ll answer.

Contests introduce complexity, but to cut a long story short: Alices can learn from watching Bobs select their test strategies (and vice-versa). I have material on dice-pool-building strategies and how Alices and Bobs can learn by playing, rather than by analyzing, but I need a bit of reading and *hum-hum* combinatorial analysis. So that’s (almost) it for today.

And you know who I’ve given zero fucks about throughout? The troll.

Then again, there’s a charge against Cam Banks that moonlights as an epistemological hurdle, so I added a snapshot from the FB follow-up and a short comment in The Fine Prints.

I absolutely agree with you. But, let me be the devil's advocate here---the devil is smart, so it's just a metaphor---there is a valid concern: namely, that the math of dice pools is complex and that the game designer is just throwing dice around for "cool" factor without any notion of balance.
The reason it's a valid concern is that dice in Cortex are narrative devices: choosing the dice is choosing how you tell the story, so "optimizing" is never "just" a number game, but makes the player tell stories about their PCs.
So, if the dice pool math *were* broken, one part of the story engine would be broken, too.
Fortunately, it's not. And the math is not actually that complex: even with a limited understanding (that would include me until yesterday, as I had to ask someone for help) of the combinatorics, but a few rules of thumb (the ones I relied on then, and still do now that I understand the math), you can make informed choices of dice and of stories.
Fig. 3. A valid (but misguided) concern.

The Fine Prints

“One flaw disproves it all.” This sounds like “throwing the baby with the bathwater,” so a fallacy. But, as far as the claim under consideration goes, it’s not. The claim is: “[Cortex] smoke and mirrors [are] so complex you cannot do combinatorics analysis of its effects.” In logical parlance, this is called a negative existential statement, paraphrased: “there is no situation s where you could [this-and-that].” The only condition for disproof is one situation s where one does [this-and-that]. The situation analyzed in the FB post, pitching Alice vs Bob, where Alice always rolls 3d8 and Bob always rolls 1d10 and 1d8, is one such s where the combinatorics analysis of effects is possible. I’ve done it with my friend, done it again by hand to be sure I understood, and you could do it too and cross-check your results with @HighDiceRoller’s Cortex Prime Calculator. It is thus a disproof of the general claim. The Principle of Charity may compel to consider other reasonable interpretations (see Fig. 3). But certainly not to take shit about legit disproof methods or letting them be called a bad dog’s name.

Is Cam Banks a bullshitter? The post the admins deleted called bullshit on Cam Banks—in the technical sense, although not using the term, but the “smoke and mirrors” refer to the same concept (Fig. 3, first §). Since (1) is blatantly false as a negated existential, I’m okay to interpret it as saying something else, namely, that one cannot trust all “dice tricks.” The bullshit charge then paraphrases: “Cam Banks’ rules may work, but if they all do, it’s dumb luck.” Now, because the number of dice tricks, number of possible dice pools, and number of players who would play a game are all finite, this assertion is in principle testable by enumeration. But there’s no point doing it: the bullshit charge cannot be disproved. Even if all the dice tricks checked out, one could say: “You cannot prove it was not dumb luck.” Still, the Principle of Charity goes both ways. Given how Cortex Prime handles (2), I doubt that Cortex’s dice tricks work through dumb luck. I don’t have proof, and (again) may never have one, but my hypothesis that Cam Banks is a competent designer, is at least as solid as the opposite hypothesis.

Wrapping up: Just another day at the home office

Once upon a time, on Facebook, I engaged a bad-faith actor exploiting my content to gaslight folks who don’t know better, in the name of fighting obfuscation—the irony won’t be lost. In a Fate RPG group, where it’s sometimes fashionable to diss Cortex because it’s “too crunchy.”  I stuck around until he painted himself in a corner with no one listening. I had the means at hand, hence the responsibility.

Along the way, I reconnected with an old friend, had a surprisingly uplifting, low-drama parallel FB  interaction, and made a serendipitous discovery— @HighDiceRoller’s app. At that point, I’d almost be thankful for the circumstances.

And that will be all for today, folks.

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