The Fallacy of the One Percent (A Thought Experiment)

by Ian Tregillis

Ian Tregillis author photo

No, I’m not talking about capitalism or high-finance here. In the world of Wild Cards, the “one percent” can only mean one thing: aces!

But what fallacy? Well, I’m a scientist (but with zero knowledge of biology, virology, and epidemiology, so everything that follows is 100% idle speculation from an unqualified layperson) and a fantasy writer, which means I spend a lot of my time thinking about edge cases. Either I’m looking for places where a scientific hypothesis might fail, or I’m looking for places where my magical world-building might hit a snag.  In the latter vein, suffice it to say that I subscribe to the idea of the “one big lie”: the central premise or crucial element of genre work from which everything else follows (ideally in a logical or at least plausible fashion).

In Wild Cards, our One Big Lie is Xenovirus Takis-A, and its effects.

When I first joined the Consortium, I quickly became acquainted with our epidemiological rule of thumb: of the infected people whose cards turn, 90% draw the Black Queen and die (often horribly); of that 10% who survive, 90% become jokers; and the remainder, that lucky 10% of 10%, become aces. Of 100 turned cards, that breaks down to a ratio of 90 Black Queens : 9 jokers : 1 ace. Very handy. 

While we’re highly (some might say inordinately) fond of card game terminology in Wild Cards, this sounds to me like the result of a dice roll: if your card turns, you roll the dice and hope to hell you get lucky. The 90:9:1 rule is perfectly suited to a single roll of a D100. And that’s entirely as it should be. After all, many Wild Cards fans know that our massive, sprawling, multi-multi-volume behemoth of a universe grew out of the Consortium old-timers’ (sorry, old timers) fanatical dedication to the role-playing game Superworld.  (As has been thoroughly and delightfully documented by others. Read GRRM’s account here, Superworld creator Steve Perrin’s account here, and the dearly missed Vic Milán’s account here.)  That was long before my time, so I’ve never played Superworldand have no idea how it worked. Only that dice were involved. But I when I asked John Miller, he confirmed that yes, indeed, the Superworldplayers occasionally tossed a D100. Neat!

But anyway, I love edge cases. And I also happen to know that in the sciences, category boundaries are rarely hard and fast. Often they’re more akin to useful guidelines, and they change over time. (Astronomy is rife with examples: look no further than Pluto!) And they tend to be fuzzy. They overlap. They’re rarely absolute. Nature is beautiful, but messy.

For instance, we sometimes talk about deuces: people bestowed with second-rate powers. Like poor Gary Bushorn, graced with the ability to ignite a fingertip as though it were a Bic lighter… and burn himself doing it. But from the point of view of our 90:9:1 ratio, it seems to me this is not a useful category. After all, if somebody’s card turned, and they didn’t melt to death, and they didn’t mutate, they’re automatically part of the vaunted 1%. Doesn’t matter if they can control the weather or turn water into cheap merlot. So, going forward, I’ll count deuces and aces together.

(And, really, what makes a power second-rate? Isn’t that context-dependent anyway? The ability to turn into a puddle of water might not be useful on a daily basis, but if you’re locked in a room, the ability to squeeze under the door might be infinitely more valuable in that moment  than limited-range telepathy. Every so-called deuce is just an ace waiting for their moment to shine.)

But deuces aren’t the only edge cases. We have plenty more: they’re called joker-aces (or knaves, over in the UK). Peregrine, with her wonderful wings, is a joker. But she can also fly thanks to telekinesis. So she lands in two of our categories: the 10% “survived but physically mutated” box, but also the “1% bestowed with inhuman ability” box. Ditto Rustbelt. His metal skin and steam-shovel jaw are a dead giveaway that the virus turned the poor lunk into a joker. But he’s also super strong and has the ability to rust things: ace. (Notice in both of these cases, the ace power is thematically related to the joker traits. More on this below, but suffice it to say it doescomplicate the thesis/thought experiment I’m developing here…)

To me, deuces and joker-aces are interesting because they highlight possible inadequacies of our simple (yet undeniably useful) 90:9:1 rule. It treats jokerism and superpowers as regions of a single spectrum. But, then, where do you put our many joker-aces? Do they contribute to the 9%, or to the 1%? (And, good heavens, to which box should we assign The Oddity?) The ratio is inherently correct (sprung from the Wild Cards creators’ minds to Dr. Tachyon’s lips, perhaps) but might it lull us into an overly simply view of how the virus manifests?

Personally, I’ve come to think that perhaps “jokerism” and “superhuman ability” belong on completely separate axes.  Or, if you prefer, that they’re determined by separate rolls of the dice. More on that below.

But before exploring that idea, let’s first introduce another heresy: cryptoJokers and cryptoAces. 

Consider this: in the real world there exists a medical condition known as situs inversuswhich, according to the Consortium’s resident retired E.R. doctor, Sage Walker, is “not all that uncommon.” People with this condition are not made ill by it (usually) and may live their entire lives unaware of their condition. But if they happen to undergo medical imaging, a bizarre truth reveals itself: their internal organs are mirror-reversed from normal human internal anatomy. (There have even been cases where this undiagnosed condition is discovered on the operating table. And Sage, who suggested the crypto- terminology, tells me that people with this condition sometimes “find it amusing to volunteer as physical diagnosis subjects for unsuspecting medical students.”) I would argue that these people are real-life jokers, without the influence of the Wild Card virus. And they might not even know it.

There’s no reason to imagine this condition doesn’t or couldn’t also exist in the Wild Cards universe. But there the mirror-reversal could be congenital, or it could, theoretically, be a result of Takis-A expression. Either way, the mutation could go undiagnosed for the entirety of a person’s life. These cryptoJokers, if you will, would present to the world — and themselves — no evidence of a turned card.  They would be unaccounted for in our 90:9:1 rule of thumb.

If it sounds like I’m nuts, don’t take it from me. When I was tossing these ideas around, Sage said, “Agree strongly that there may be undiagnosed jokers in the world.” Or take it from Steve Leigh, who told me, “I’m POSITIVE that there are almost certainly people out there who have been changed by the virus but in such a minor way that they’re just…people.” Maybe I’m crazy, but I’m in good company.

After all, consider the sheer complexity of the human body: there must be a thousand ways, and more, to hide a subtle mutation. A cryptoJoker might have racing stripes on their aorta but otherwise be perfectly normal. Or the Takis-A virus might have made their left iris a tenth of a millimeter wider than the right iris. Or the nail on their right pinky toe might grow 30% faster than their other toenails. These people would never know they’ve been mutated by the Wild Cards virus, and so neither would the greater world (barring a very detailed medical examination or an encounter with Digger Downs).  And if they present no evidence of a turned card, how do they fit in the 90:9:1 ratio?

So, okay, there might be people in the Wild Cards universe who don’t even know that they’re technically jokers. What about cryptoAces? That would be truly bonkers, right? 

Well, here’s another example from the real world: human tetrachromats. Researchers in the genetics of color vision believe a small fraction of the world’s women have four, rather than the usual three (or two in color-blind people) photopigment receptors in their retinas. Researchers also believe they have even identified women for whom these four receptors are fully functional and integrated into the way their optic nerves and brains process color information: they see the world in four primary colors rather than three like most people. These “functional” or “true” tetrachromats have superior color vision and are capable of distinguishing hues that are identical to normal humans. But unless they’re tested in very specific ways, they never know that they’re mutants with exceptional abilities. They might merely think they’re really good with colors. 

But it’s more than that: they’re natural-born aces. (Well, okay, maybe deuces. But I still think they’re incredibly cool.) 

The Wild Card virus could create a tetrachromat from scratch. How would we ever know? The virus could even create a male tetrachromat, something that is effectively impossible by natural genetics.  But again, how would these lucky guys know their cards had turned? They might only know that they have better color sense than many of their friends. Such tetrachromatic women and men would be cryptoAces unaccounted for by our usual 90:9:1 rule.

Note that these hypothetical cryptoAces are different from people keeping “an ace up the sleeve”. Those folks are hiding their powers from the world, pretending to be nats.  But a cryptoAce isn’t hiding because they don’t knowthey have powers. 

Hold on, Ian. How could somebody NOT KNOW they have a superpower?

Well, when was the last time YOU tried to fly? 

Granted, in the Wild Cards universe, people probably try this more frequently than in ours.

The observation that seeded my speculations here was raised in a discussion within the Consortium years ago. Some clever soul (and nobody I’ve queried can remember who said this; stand and be known, anonymous compatriot) raised what struck me as a very sharp question. Paraphrased a bit, they asked: What if the virus gives you the ace ability to communicate telepathically with whales… but you live in Iowa?Barring a lucky accident during a trip to the ocean, or Seaworld, how would you ever know that you’re an ace? You might never know. In fact, you’d be a cryptoAce.

And while we’re riding this train of thought… what about the dreaded Black Queen? It’s pretty obviously at fault when somebody just up and melts into a pile of eyeballs, or explosively turns inside-out, or dies of asphyxiation when their face turns into a slab of schist. But how many people die each year of “natural causes?” How do epidemiologists in the Wild Cards universe know there aren’t a ton of unidentified black queen deaths going unrecorded in their databases?

I’ve just argued that cryptoJokers and cryptoAces could be rife in the general population.  I’ve also argued, earlier, that it might be more fruitful to consider “jokerism” and “superhuman ability” as separate distributions, possibly orthogonal to one another.  In short, and putting it all together, I’ve started to consider the effects of Xenovirus Takis-A according to this extremely speculativecartoon:

Just to get the ball rolling, and for simplicity, let’s assume for now that virus-conferred abilities and jokerism are truly orthogonal to one another. Characters in the Wild Cards universe all start at the red dot. They either don’t carry the virus, or they do but their cards haven’t turned yet (they’re Latent). But when that card turns, they land somewhere on this plot. That final location depends not on a single random variable (as implied by the 90:9:1 ratio) but in fact is decided by a joint probability distribution: one part governs the distance traveled along the “Ability” axis, and the other governs the distance traveled in the “Jokerism” direction.  (One big caveat here is that I’ve denoted the Black Queen as the fatal limit of extreme jokerism. That’s a gross oversimplification. After all, one subtle alteration to the way a person’s body folds certain protein molecules — something outwardly invisible and thus close to cryptoJokerism — could be very deadly. Sage tells me many Black Queen deaths may boil down to septic shock.) 

The “noticeability threshold” is the hypothetical limit below which jokerism becomes unnoticeable: cryptoJokers live beneath this line. A similar boundary, an “awareness threshold,” exists for the cryptoAces. These limits are, of course, entirely subjective and not something that can be established mathematically. They probably depend on a person’s social and cultural environment, and thus change according to time and place throughout a person’s life, even day to day. But this is a Saturday-morning thought experiment, so let’s ignore that detail, too. The point is that a Latent carrier whose turned card doesn’t cross the crypto- boundaries effectively remains a nat. The crypto-boundaries, if they truly exist, aren’t hard and fast. Categories overlap and blur together.

This line of thinking is fun (for appropriately nerdy values of “fun”) because we can use this picture to back out how the 90:9:1 rule might manifest.  What can we deduce about the separate ability and jokerism probability distributions? We can’t solve exactly for the distributions — the problem is underconstrained, so there are an infinite number of possibilities — but we can lay some interesting constraints on the distributions.

You might have noticed that the 90:9:1 rule, as I’ve stated it, rules out the possibility that a person remains unchanged by the turn of their card. That is, the virus produces exactly 0 Nats. That situation might arise from something like this:

The hand-drawn blue and red lines are cartoon examples, but I think informative ones, of how orthogonal Ability/Jokerism probability distributions could combine to create the 90:9:1 rule. There are many curve shapes that could produce these results, but in order to do so they must conform to certain rules.  It isn’t hard to prove that in this “no Nats” scenario:

  • 90% of the Ability distribution falls below the “awareness” threshold
  • 10% of the Ability distribution falls above the “awareness” threshold
  • 90% of the Jokerism distribution falls within the fatal Black Queen regime
  • 10% of the Jokerism distribution is conspicuous but not fatal
  • 0% of the Jokerism distribution falls below the cryptoJoker threshold

(These percentages refer to the total area under the curves.)   We don’t know if there exist hard limits to the distributions at very high values of “Ability” and “Jokerism.” The latter, in particular, is unknowable, because when somebody lands in the Black Queen regime, we lose all information about their location on the (Ability, Jokerism) plane. That’s why I’ve shaded it out in the above cartoons. But even though the Ability and Jokerism axes extend without limit, there are curve shapes mathematically guaranteed to contain a finite fraction of the overall area even if they never go to 0. An exponential decay will do just that; many distributions in nature have such tails.

Interestingly, we find that the Ability distribution, by itself, actually puts 10% of cases above the “superpower” line, not 1% as we might expect from the 90:9:1 rule.  Meanwhile, depending on the shape of the tail, the Jokerism distribution could peak in either the “survivable jokerism” or even in the “Black Queen” regimes. It falls flat to 0 in the “Nat” regime. 

Earlier, I argued heavily for the existence of cryptoJokers and cryptoAces.  That would suggest  a turned card canplace somebody in the “NATS” sector of my cartoon plot.  This idle speculation teases a possibility I find very interesting: the 90:9:1 rule can only be observed to apply to identifiedcases of Takis-A expression.  After all, if you don’t know how many cards have turned, how can you calculate the percentages of various outcomes?

If you allow for cryptos while still imposing the 90:9:1 rule on knowncases of turned cards, things get mighty interesting. For example, consider a situation where only 75% of all cases of Takis-A expression are properly publically known as such. That is, let’s imagine that 25% of all card turnings are never identified as such– those cases produce cryptoAces and cryptoJokers who land in the “NATS” sector of our plot.  Now the situation looks something like this:

Now the jokerism probability distribution is bimodal: it contains big lumps in the “NATS” and “Black Queen” regimes, with only a sliver in the “JOKERS” regime. Meanwhile, the superpower distribution has become markedly slimmer: the fraction above the superpower line has fallen from 10% to a measly 2.3% (which is still better than the 1% we might have expected from 90:9:1). Notice that while we now have 25% of cases landing in the “NATS” regime, the new result maintains a Black Queen:Joker ratio of 10:1 and a Joker:Ace ratio of 9:1. So we’ve kept the 90:9:1 rule for the cases of Takis-A expression we can observe.Furthermore, Aces now represent less than 1% of all turned cards — hence the title of this blog post.

If you want to pull out a calculator and play around with the distributions in this extremely speculativecartoon model, they work out like so, where J is the Jokerism probability distribution, Ais the Ability probability distribution, and X is the fraction of all cases of virus expression that are correctly identified as such (the above thought experiment corresponded to X = 0.75):

Again, these numbers refer to the fraction, in each regime, of the total area under the probability curve (which is why the separate A fractions and J fractions add up to unity).

Of course, caveats to these speculations are legion. I’ve been assuming the separate manifestations of “Ability” and “Jokerism” are completely uncorrelated. That may be a vast oversimplification. After all, remember my earlier example of the joker-aces Peregrine and Rustbelt. If Peregrine had her joker wings but the ace mental domination power of Puppetman, they’d be uncorrelated. Ditto if Rusty had his jokery metal skin but the ace ability of Herne the Wild Huntsman. But that’s not the case: both of them have ace powers that are thematically related, for lack of a better term, with their joker traits. That screams correlation.  

This isn’t terribly surprising, for a couple of reasons. First and foremost, of course, and from a narrative perspective, there’s an irresistible aesthetic appeal to the many “thematically unified” cases like Peregrine, Rustbelt, and Herne. We writers are suckers for stuff like that. I also wonder if Wild Cards’s roots in the Superworld RPG don’t also influence our occasional tendency to draw connections between certain characters’ Jokerism and Abilities. There, great abilities came with great drawbacks. (Which is also narratively appealing!)

One could also imagine that certain forms of extreme jokerism dodge the Black Queen solely by virtue of an Ability. For instance, if the virus turns your blood into grape Kool-Aid, you’d die instantly if something else wasn’t going on. So that’s another argument for correlations, at least in certain limits. This suggests high jokerism may imply nonzero Ability, but not the other way around. 

Finally, and on a related note, for the Bayesian statisticians out there, it seems to me that the 90:9:1 ratio implies P(J | A) = 9 P(A | J). (I could be wrong.) That is, the odds of also being a joker, given that you’re already an ace, are 9 times higher than the odds of being an ace, given that you’re already a joker. Or to put it another way: if your card turns and you suddenly discover you can fly, you’d better look in the mirror, too; on the other hand, if your card turns and you suddenly discover your body is 50% snake, you’d better get accustomed to slithering because the odds are heavily against you teleporting anywhere.