Heads I Win, Tails YOU DIE: Thanos’ Plan is Even Worse Than You Know

(Obviously, full spoilers for Avengers: Infinity War ahead.)

Thanos is bad with numbers. And justice.

There’s a subset of antagonists that I call “probability villains,” who claim Fortuna’s help in making the decisions for their dirty work. Usually, they choose the simplest, most “random” way possible: a coin flip.

Like Harvey Dent and Anton Chigurh, who kill by the coin, Thanos acquires his MacGuffins through his own force, but then allows Luck to choose the victims of his genocide.

As Infinity War is technically a Disney movie, I’m reminded of a Carl Barks comic called “Flip Decision”1, in which Donald Duck is suckered into a belief system called Flipism (seemingly in preparation for his mathemystical journey a few years later2), deciding every action on the flip of a coin. This doesn’t go well for Donald, as you might expect: he disrupts traffic by flipping to choose which way to drive, crashes his car, ends up in court and fined, and accidentally breaks a date with Daisy. Professor Batty, the scammer at the heart of the Great Society of Flippists, gets away with Donald’s dollar.

Thanos economicus clearly takes his work a step further, by expending tremendous amounts of effort toward the goal of allowing the allegedly apolitical probability of coin flips to sort everyone out: he decides not who, but only how many, live or die.

Even our War’s actors are familiar with this trope: not only is Josh Brolin in No Country For Old Men (along with Two-Face Forever Tommy Lee Jones), but Chris Evans has dealt with a randomized death scenario resulting from resource allocation concerns: in Snowpiercer’s climate-manipulation-leads-to-train-based-caste-system scenario, Tilda Swinton’s front-class Mason tells Evans’ tail-class Curtis that “precisely 74%” of his troops will perish3 in an imminent fight.

74% (nearly 2/e, since we are discussing population models) is probably a bit closer to the actual death toll involved in Thanos’ plot.


Whither “Life”?

We desperately need to know the parameters of Thanos’ magical death mechanism. Is it half of “sentient” life that will die? Half of “all” life? And who defines “life” here?

Are human fetuses privy to this criterion, Mr. Gemfist? If so, up to what level of development? Cows? Cockroaches? Corn? You declared that survivors would have “bellies full” after all populations suddenly dropped to half, presumably with twice the resources they had minutes before?

Amidst witnessing helicopters careening into buildings and SUVs spinning through traffic, I imagined horrific offscreen scenarios. Half the world’s buses just careened off the roads. Half of all trains just lost their brakemen. How much of the world’s population is in transit at this moment? How many people are being operated on at this moment? Due-in-hours pregnant women suddenly feel much lighter. What about someone vanishing on their way to the hospital, leaving their healthy, just-about-to-be-born charges falling to the ground?

For this “full belly” hypothesis to work, the survivors need to know how to fill those remaining: how to maintain suddenly-fractioned governments and economies, universal panic and ensuing madness. But Big T simply walks away, abandoning them to several short-, medium-, and long-term global infrastructure crises.

If an alien ship shows up and procedurally kills half of the people on your world, at least you know how they died, and can start to plan after they’re gone. If that many people just… vanish… we are all going mad quickly. So much for survival.4

Collateral damage due to accidents will eliminate a fair percentage of the remaining 50% immediately. Then, in the upcoming weeks, infrastructure failures will claim many more. Loss of most basic services, including but certainly not limited to: electricity, water and waste treatment, food transportation, processing, and service, access to emergency services, hospital care, medical supply delivery, hospice care, will impact millions more. Will these losses “fairly” impact all, as Thanos claims to intend?

TOTAL DEAD > 50% + (immediate accidents)% + (infrastructure failures)% + (undetected)%

Did Thanos kill you?

Did Thanos kill you?

All this built on the theory of one world (Titan), which collapsed due to internal stresses from its own population. Hell of a sample set, Dr. T. Your prescription really lines up with the prognosis.

There is one dubious positive from all this, I suppose: at least we have several more philosophical questions answered. MCU Earthlings have already received recent answers to such questions as:

  • Are we alone in the universe? (No. In fact, the aliens are hostile, and have reached us several times now.)
  • Does God exist? (Yes. Many of them.)
  • Should we fear the mutant threat? (Um… let us have a few more meetings with Fox, and we’ll get back to you.)

We now know what “life” means in the MCU. While we all go mad from the extreme loss and allegedly full bellies, we no longer have to ponder:

  • Are animals sentient? (Did any of them suddenly vanish? If so, those were sentient, and the remaining like them are as well.)
  • What about plants? (Did any of them suddenly vanish? Ditto.)
  • When does human life begin? (You’ve given us an actual measurement, down to the week. Planned Parenthood and the Catholic League will have a field day with that public information.)

Thanks, Thanos, you just answered all those questions in one shot for us with your ill-defined probability model: “each life-bearing node independently dies with probability p = 0.5”.

Now, how do we all survive this massive shock to our ecosystems, economies, governments, technology base, communications, militaries, everything?



Do we all survive with equal probability, after the “snap”?

In ensuring that half will die instantly, independently on the individual level, Thanos’ claim of ultimate fairness-in-life-or-death falls into a common modern American political fallacy: the confusion of, or lack of concern in the distinction between, equality (“fair” treatment means all get the “same” access) with equity (“fair” means allocating resources to level out opportunities). For example, “the poor,” by definition, have a much greater probability of collateral loss than “the rich,” regardless of the Mad Titan’s expected full bellies. Thanos’ notion of fairness is reductive at best.

We could try another parameter dichotomy: how about “good health” against “weak health” as vague, but opposed terms, like “rich” and “poor”? It’s not going to work: “rich”, on average, yields better health outcomes than “poor”. (Please, check other parameters; I challenge you to find allegedly-opposing pairings under which the “poor” fare better than the “rich” under this extreme scenario.)

Let’s consider rebuilding. This… Snapture5 would very likely be considered (at least by American insurance agencies) an “act of God” (haha yeah, literally), and so not payable on most accounts without specific coverage. This sort of “black swan” event6 is so low-probability, yet so completely devastating, as to not register as a thing necessary to build into standard insurance models (although we might expect that some of the ultra-rich MCU inhabitants by now hold some kind of “Marvels coverage”… that’s not built into the usual plan). So, most people that lose property are likely not going to recover it, since the insurance companies won’t, or won’t be able to, pay out. On top of that, the reduction of the economy itself wouldn’t sustain those payouts.

Speaking of insurance payouts, one of the MCU’s primary recurring motifs is dealing with the aftermath of an unexpected, devastating attack7. Considering the disparate nature of wealth in surviving a sudden dire financial situation8, how will the remaining less-than-50% fare? It is required that someone legally, and fiscally, define “fair” for these events, and this definition does not always mean “equal”. For example, settlement payouts to survivors of 9/11 depended on the career of the deceased.9


A Very Mean-Variance Optimization

Thanos appears to suffer from what I’ll call “expectation reductionism”: the thought that probabilistic expectation (or mean, a probability-weighted average of possible values) is the most meaningful statistic of a random variable, to the dismissal of all others. (See, for example, the usual “don’t play the lottery” argument, which only considers the average economic value of a game in terms of repeated numerical wins/losses (negative mean winnings), and not less measurable effects such as potential short-term emotional benefits that are long-term healthier and cheaper than smoking, alcohol, or other drugs.10)

In addition, eliminating half the universe’s population will vastly reduce the variance of living beings. If adaptation to a cataclysmic change is important in recovering, the basic genetic ability to recover of any given species has been severely hampered, but mental ingenuity may win out over sheer variance. (Let’s call this concern a wash.)

Posing the “problem of life in the universe” in purely financial terms, Thanos’ gambit might work as a form of “mean-variance optimization”: for a random individual, if they survive, increase the mean level of resources and reduce the variance of overall disparity. (If they die, it’s probably painless and nearly-instant, and maybe they get to hang out in the Soul Gem?) It makes sense in a toy model in basic finance, but with the large multivariable nature of the interconnected systems involved, the potential individual infinite loss of life versus a possible finite gain in survival against not changing the system (Pascal11 much, T?), and not taking into account the real probability of system collapse, it is a grave miscalculation.

If, say, “the rich” have the same probability of snap-dying as “the poor”, then presumably wealth distribution just gets much more consolidated, not less, if “the rich” leave their wealth mostly to their families (and are more likely to have written wills). Post-snap, due to the “equality” of distribution, there are roughly half the people holding the top 50% of all wealth than there were days earlier. Perhaps the remaining double-ultra-rich will find themselves more charitable in the ensuing panic; perhaps their current notion of wealth will collapse with the nations. More than likely, the ultra-rich will remain ultra-rich.

What form will the wealth of the double-ultra-rich hold, though? If half of the economy just vanished, demand for most goods and services just instantly plummeted (except crisis management, demand there is through the roof). Likewise, supply just as instantly skyrocketed. How does a global economy survive such shocks? (I don’t know; not an economist. I doubt they know either.)


Punching Up

Could Thanos supply unlimited power instead of killing half the universe?

Could Thanos expand space to allow much more room for life instead of killing half the universe?

Could Thanos manipulate reality Matrix-style to provide for all life instead of killing half the universe?

Could Thanos share the notion and emotion of soul with all life, so that they may live in harmony with each other, sharing resources eternally, instead of killing half the universe?

Could Thanos unwind the timing of wars and inequitable policies instead of killing half the universe?

Could Thanos expand the minds of all life to understand the interconnectedness of collective resource allocation and cooperation instead of killing half the universe?

So why does he kill half the universe?

To efficiently do away with the “surplus population.” He claims individual planetary resources are scarce, but he literally controls all of existence’s resources. Also, in time, exponential growth models would imply that this culling of the universal herd will all need to happen again at a later date, and again, and again… until the heat death of the universe.

Thanos might think he’s Genocide Marx, but he’s really Scrooge McDoom.

You can’t retire, Thanos, you’ve got Infinite Work to do now.



  1. Flip Decision (1952)
  2. Donald in Mathmagic Land (1959) (watch here)
  3. Snowpiercer (watch clip here)
  4. There is plenty of Rapture-based fiction—you can run the gamut from the Left Behind series up to The Leftovers, and everything before and in between. The expected psychological distress has been explored.
  5. Snapture.
  6. I honestly don’t know if Nassim Taleb would hang out with Thanos.
  7. Tor.com’s own Leah Schnelbach has written extensively on this topic.
  8. This 2016 WaPo article explores the question “Do you have $400 immediately available to recover from an emergency?”
  9. In 2008, Kenneth Feinberg spoke to NPR about managing the compensation funds for 9/11 victims, and how the disparity in allocations influenced his management of the compensation funds for the 2007 Virginia Tech shooting.
  10. All that said, I don’t condone playing the lottery. This TED talk by Dan Gilbert has a bit of the usual lottery interpretation, with a dissenting voice from an audience member during Q&A.
  11. I couldn’t pass up the opportunity to throw in one of my favorite divisive philosophical topics: Pascal’s wager.

“Did Thanos Kill You?” image from the source code of didthanoskill.me, which I am sad I did not write. “Axiom” image courtesy @MichaelSLaufer.

Suppose Michael Carlisle (@drintangible) is a mathematician and writer living in New York.


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