39

According to Thanos's plan in Avengers: Infinity War, which of the two statements is true:

Thanos intends to kill half the population from the whole universe, randomly.

or

Thanos intends to kill half the population from every planet, randomly.

Population varies from planet to planet, so the number of people killed on each planet will be different in each statement.

  • 2
    This would be a good exercise on the math exchange. My belief is there wouldn't be near as much deviation as you're thinking. A planet with a billion people, for example, probably would end up in the 400-600 million range as opposed to an even 500 million. – sirjonsnow May 9 '18 at 12:27
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    @sirjonsnow Yes, but not even as large a range as 400-600 million. Take Earth (~7 bill. pop.) as an example. If Thanos kills half the universe randomly, about 3.5 billion Earthlings die, with a standard deviation of sqrt(3.5 bill.)=59,000, which is less than a thousandth of a percent of 7 billion. So there is a 99.999% chance that between 49.9% and 50.1% of Earthlings are destroyed. With the inaccuracies of the global census, we'd never know the difference between the two hypotheticals. – Sam May 9 '18 at 13:29
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    An important thing to note is that he explicitly tells Tony Stark that because he's impressed with him, he'll leave half of Earth's population alive. The way he delivers the line leaves some ambiguity as to whether that was always what was going to happen, or if he's promising Tony he'll ensure that's the case - implying it's not NECESSARILY the case elsewhere. Just to muddy the waters some more! – CGriffin May 9 '18 at 18:40
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    I don't think Thanos would understand the difference. If he understood statistics at all he would have noticed it only took us 40 years to double the population to 7 billion so he's not going to be able to, as he says, 'rest'. – Julian May 9 '18 at 19:18
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    @CGriffin I don't think that's what he said. He did say that he was impressed with Stark and that he hopes that the people will remember him. He also said he'll kill half the population. I don't think these two statements were connected in the film. – Cubic May 13 '18 at 14:15
43

Based upon how Thanos explains it, planet by planet is most plausible

Thanos explicitly explains his motivations in the film. He's trying to to spare other populated worlds from the fate that befell his. Which is to say, collapse due to overpopulation and competition for/exhaustion of finite resources.

Prior to acquiring the infinity stones, his method for accomplishing that goal was to visit every planet and then use conventional measures to eliminate half of its population. Whether 50% is some ideal number for reducing resource contention doesn't matter, what matters is that Thanos seems to have considered it to be. He could have just as easily killed 20% of the population, or 70%, or anything else, but he settled on 50% as the "correct" proportion for his goal.

So the 50% per planet seems significant, and although killing 50% of all the people on each planet will produce the same bodycount as killing 50% of all people in the universe, there are statistical differences between the approaches.

A demonstration probably works best, so here's a Thanos Murder Simulator (or an alternate blue/orange version).

Notably, killing 50% of the people in the entire universe produces a result like this (each box is a person; green is alive, red is dead, groupings of boxes are planets):

enter image description here

Notably, one unlucky planet has only 6 survivors (nearly a 75% kill rate). A couple of others have lost only ~25% of their populations. If you need to kill 50% to curtail overpopulation on a planet, then killing everyone in the universe at random is a bad way to do it. You'll get some planets emerging relatively unscathed, and others catastrophically depopulated (I mean, even more catastrophically than 50% would be).

You get a much more uniform result by killing 50% of the population on each planet:

enter image description here

Considering Thanos's stated goals/motivations and the way he went about culling planets before completing the Infinity Gauntlet, the latter scenario seems like what he would go for.

Other characters say 'half the universe'

However, these other characters are not Thanos, and may be paraphrasing for expediency.

The only character who knows what Thanos intends is Thanos, and he gets to deliver a fairly lengthy explanation in the film. His explanation leans more towards randomly killing 50% of the population of each planet than it does towards 50% of everyone in the universe.

The bodycount is the same either way, but to Thanos it's the distribution of the bodies that's most important.

  • Comments are not for extended discussion; this conversation has been moved to chat. – Napoleon Wilson May 10 '18 at 18:26
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    I think it's also worth noting that 50% planet-by-planet leads to 50% of the universe, but 50% of the universe doesn't lead to 50% planet-by-planet -- so you could perfectly accurately say he's going to destroy 50% of the population of the universe either way. – Nic Hartley May 10 '18 at 20:14
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    This answer is pretty but mathematically misleading. The variance of 50% probability applied to 7 billion people is tiny compared to the variance when applied to 25 people. – RBarryYoung May 11 '18 at 14:25
  • @RBarryYoung - That depends on a number of assumptions. The first is that the infinity stones create 'perfect' randomness, which is actually very hard to do. The second is that there aren't many planets (or planetoids, or space stations, or colony ships) with low carrying capacities. The third is that Thanos, with the power to wish for either outcome equally easily, would choose to wish for the outcome that admits the greater capacity for variance. – aroth May 11 '18 at 23:01
  • @aroth: Can you switch to a different color scheme for your (lovely) Thanos Murder Simulator? Red-green color blindness is actually very frequent (about 8 percent of males are affected), and for these, distinguishing the survivors from the victims is more difficult than necessary. Other color combinations work much better, e.g. blue and orange. As a quick note on creating "perfect" randomness: C'mon, these stones twist reality and time and things. There's surely also some built-in mechanism that harnesses quantum stuff to create real random numbers. :) – Schmuddi May 12 '18 at 7:37
28

Using a Binomial distribution with number 7.5 billion and probability 0.50, the chances of Earth's death count from a universal unbiased killing resulting outside of 49.99%-50.01% of the total population is 1.7*10^-132, which is less likely than flipping 438 heads in a row with a fair coin.

Updated: I was first using a Poisson distribution which is a limiting case of a Binomial distribution (old claim: The chance of >50.01% (or <49.99%) of Earth's population being killed universally randomly is 3*10^-32! This is less likely than flipping 100 heads in a row with a fair coin). I found this site now which can handle the very small numbers involved in the use of the error function.

So, it doesn't really matter which interpretation is the true case: Planets with realistic populations and even very accurate census won't notice the difference.

Full disclosure: I haven't seen the movie, nor have I ever read a comic book or know who any of these characters are. But I'm familiar with statistics and probabilities and have a habit of browsing the network Hot Questions, so...

Explanation: The Binomial distribution is useful to see the results here. It gives the probability of observing integer random outcomes (like number of people killed) from any expected average (like half of a population). My use depends on the following assumptions.

  • The gauntlet will kill exactly half of the universe's (sentient?) lives (rounded if total is odd).

  • The gauntlet will take absolutely nothing into account -- the chosen to die are chosen randomly to meet this quota. This means the gantlet does not travel planet-to-planet, or choose those to die one at a time, or kill the oldest, the smallest, the smelliest, etc.

  • The population of any planet is a small fraction of the universe's population. If Earth comprised all of the universe, obviously exactly half of us would die. But if 10 googolplex exist, and thus 5 googolplex must die, each of our deaths makes a negligible impact on the quota and our chances of living are unchanged -- 50%.

  • The Marvel universe has no more than a trillion trillion trillion times as many galaxies as our own universe, and each of its stars has no more than a trillion populated planets each. These very large (and very small) numbers can be hard to wrap your head around, but no scientific estimate of the number of galaxies/stars/planets in this universe comes close to legitimizing the chances of the asymmetric planet-wise killings proposed in the comments/answers.

The Math: From the binomial wiki page linked, the standard deviation is $\sqrt{np(1-p)}$, with p=0.50. For the Earth (n=7.5 billion), this is 43,301 people. In terms of sigma, 0.01% of our population (7.5 billion) is 17.32 sigma. As a rule of thumb for statisticians, there is a 99.7% chance of drawing a number from within three sigma from the mean. Likewise, there is a 99.999999...% chance of drawing from within 17.32 sigma from the mean. Put another way, with the error function tool linked above, the chance of drawing outside of 17.32 sigma from the mean is less than 1 in 10^100!

The range of likely death counts from this event is much smaller than Earth's census would even notice. Moreover, as others have explained, the "kill randomly universally" method also avoids the complication of identifying to which planet (or ship, or rock, or floating naked in space...) each person belongs.

  • 1
    @ArturoTorresSánchez I've actually been meaning to ask that exact thing as a question, but there are so many questions about this already and I don't know how answerable that is. – F1Krazy May 9 '18 at 16:01
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    This is a binomial distribution: mean = $pn$, std = $\sqrt{p(1-p)n}$. A Poisson distribution is an approximation of binomial for small p, in which case the square root of the mean is a reasonable approximation of the std (note that with small $p$, the $1-p$ factor can be ignored). Since $n$ is so large, the binomial distribution can be approximated by the Normal distribution. Here, $p$ is not small, and you're off by a factor of $\sqrt 2$, although it doesn't have much effect on the ultimate answer. – Acccumulation May 9 '18 at 16:11
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    Are you assuming that each person dies with a 50% probability or that out of the total population of the universe exactly 50% will die? Lets assume that the galaxy has 7 billion planets of 3.5 billion people. I think what you are saying is that the mean will be ~1*10^19 and the standard deviation will be 3.5*10^9. That means from your link that by the time you get to the last planet there is ~30% chance that your current kill count is more than 3.5 billion people from the average which means that to ensure that you kill exactly 50% you will need to kill all or none of them... – Chris May 10 '18 at 11:48
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    @Chris No, I am assuming that exactly half of all people are killed. The caveat I state is that if each planet's population makes up a negligible fraction of the total, this is equivalent to each person having a 50% chance of dying. If you are familiar with probability, this is like drawing colored balls from an urn without replacement; but if there are trillions of blue balls and trillions of red balls, drawing a red ball negligibly changes the odds of the next ball being red. I'm also assuming that this gauntlet is killing everyone all at once, so there is no quota later to be met as you say – Sam May 10 '18 at 13:24
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    I am talking about it as an ordered thing purely as a way of looking at the problem. Your assumption that it is like each person having a 50% chance of dying is wrong though. For the first people it is but towards the end one you have drawn all but say 10 of the balls then you have a reasonable chance that those balls might be all the same colour. This is what I was getting at. The last 3.5million balls out of 10^19 have a reasonably high chance of all being the same colour I think (since 3.5millon is the standard deviation). – Chris May 10 '18 at 13:30
15

It was mentioned that Thanos wants to kill half the population of the universe.

From transcript of Avengers: Infinity War,

Gamora: He won't stop. Until he destroys half the universe. Everything you know. Everything you love. It will all be gone.

However, before acquiring the Infinity Stones, he actually went to each planet and kill half the population there. This part might have created the confusion.

From transcript,

Gamora: No, no, we were happy on my home planet.

Thanos: Going to bed hungry, scrounging for scraps? Your planet was on the brink of collapse. I was the one who stopped that. You know what's happened since then? The children born have known nothing but full bellies and clear skies. It's a paradise.

Gamora: Because you murdered half the planet!

and

Thor: There's six stones out there. Thanos already has the Power Stone because he stole it last week, when he decimated Xandar. He stole the Space Stone from me, when he destroyed my ship and slaughtered half my people. The Time and Mind Stones are safe on Earth. They're with the Avengers.

Also, different sources like this and this mention that he wants to kill half the universe.

Killing half population of the universe and half population from each planet seem similar if we do the math. If he kills half population from each planet, he's still killing the half population of the universe.

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    Killing half the population of the universe at random would still leave a lot of overcrowded planets. I think we should assume that he wanted to kill half the population of each planet randomly thus killing half the population of the universe. Thanos is a smart guy, he would have thought this through. – Yates May 9 '18 at 10:14
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    This is exactly what he is doing as mentioned in the transcripts I linked. – A J May 9 '18 at 10:24
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    @Thomas Yates But a lot of people don't even live on planets (take "Knowhere" for example). – Muschkopp May 9 '18 at 11:11
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    @Muschkopp then "Knowhere" is counted as a planet. I think the point is that if you wipe out half the universe at random then you're going to end up with overpopulated planets (and/or planet-like space-stations) still. Thanos pretty much explicitly explains that he's killing half of everybody specifically to counter overpopulation. It follows that the 50% is on a planet(oid) by planet(oid) basis. It's randomly ineffective otherwise. – aroth May 9 '18 at 11:37
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    @ThomasYates Some overcrowded planet - possibly, a lot - what is a lot? For a planet with a population of a couple billion you have 99.7% chance of not missing the target by more than about a hundred thousand people (and really a lot of nines after the 99. for even a million). – Michał Politowski May 9 '18 at 12:20
12

Thanos tells Tony that when he has accomplished his goal, half of humanity will remain. This is important, because he we know that he intends to choose his victims randomly.

If Thanos intended to simply draw his victims from one big pool containing the entire universe, then he could not be certain ahead of time that half of humanity would remain. By random chance, he could very well draw more of Earth's population than that, or less. It's even possible, if unlikely, that he could wipe out Earth entirely, or leave it completely unscathed.

Let us suppose that Thanos got a big bag of marbles -one for each person in the universe, half of them red, half of them blue- shook it up, and forced everybody to draw. Everyone who draws a red marble disintegrates. This is guaranteed to kill exactly half the people in the universe, while still being random. However, with trillions if not quadrillions of marbles in the bag, there are going to be runs of the same color that last for thousands, millions, maybe even billions long. It's entirely possible that everyone on Earth might draw red marbles (i.e. Earth is wiped out) or blue ones (i.e. Earth is unscathed). Earth probably wouldn't even be the only world this happened to. The universe is a big place.

But that's not how Thanos acts. He knows that half of humanity will survive. The only way he can be sure of that, while still holding to his idea of "fairness through randomness", is if he has another method for choosing his victims. He would need to divide them up according to their worlds, and choose half the people on each: in other words, a bag of marbles for each planet, rather than one for the whole universe. This is similar to the method he used before he had the Stones, though faster and more efficient. More to the point, it's more closely in line with his idea that the resources on each world need to be distributed to half as many people: he needs to be sure that there are actually half as many people on each world, and this requires a finer-grained approach than throwing everyone into one large pool.

  • 1
    Citation needed for the earth could be completely wiped out or left unscathed – Kat May 9 '18 at 23:09
  • (Editing to incorporate the "bag of marbles" explanation into the main text) – The Spooniest May 10 '18 at 19:18
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    @Kat - "That'd be 86,602 sigma (!!!)" – Sam (Translated: 'No, but you can try.') – Mazura May 10 '18 at 20:33
  • I guess I should have been more clear: you need to check your math, because the chances of any planet in the universe with billions of inhabitants being left untouched or completely wiped out is pretty much zero. See Sam's answer. – Kat May 11 '18 at 2:46
  • The chances of being completely unscathed or wiped out are quite small, it's true, but it doesn't have to be complete either. The odds of the kill count for a given world being nonzero, but still rather far off from 50%, aren't that low. – The Spooniest May 14 '18 at 7:41
4

Thanos intends to kill half the population from the whole universe, randomly.

My impression while seeing the movie was that he meant planet by planet, although this was likely caused by seeing Thanos visit each planet and killing half the population manually before he had the gauntlet.

However, if we look into the scene where Thanos snaps his fingers we can see on Titan that this was not the case. At the time of the snap, Titan had 7 people. Iron Man, Spider-Man, Dr. Strange, Star Lord, Drax, Mantis, and Nebula. The snap killed 5 people. If his snap killed half of each planet, we would expect to see only 3-4 people dead.

My conclusion says this is done on a universal level, rather than a planetary one.

  • It could be done on the basis of home planet. Like the way King Herod required everyone to return to their birthplace for the census. – Gaius May 9 '18 at 20:57
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    @Gaius doubtfully, home planet basis or the planet of origin is an extremely subjective approach... Take the "rabbit" (rocket) as an example, would you consider where he was assembled his home/origin or where his parts came from? What about Starlord? He was born on Earth, spent most of his life in other planets and he has part of a living planet in himself (Ego)... – CPHPython May 10 '18 at 11:19
  • @Gaius that seems speculative at best. What of those without a home planet? Or those who had their home planet destroyed? It's a possibility for sure, but seems to be a reach. – Mat May 10 '18 at 15:57
2

I think both of your statements are false. Why? Let me 'splain...

We know that the 'snap' wasn't localized to Earth because characters on Titan also flaked away so he's not going planet to planet.

We also know that, on Titan, about half of the Human characters flaked away (Starlord, Dr. String and Spider-Man)... There were an odd number of humans so you couldn't get EXACTLY half. That would just be gross.

Therefore, this is a bit of a leap using available info from only the first IW but I believe the snap effected the Universe as a whole but NOT at random. I believe that half of all species on every planet were hit at the same time. Where there was only 1 of a specific species, (thor, rocket & groot on earth or drax & mantis on Titan), they could stay or could go based on whatever intent was behind the snap. Where there was an odd number, the "odd man out" could stay or go based on the same intent

I think the previous answers underestimate the power of the Infinity Stones and the ability to control intent across the universe when wielding them all.

1

Thanos WAS doing it on a planet by planet basis, manually and sequentially, since that was what was within his capabilities.

The whole point of gathering the Infinity Stones and wielding them with the Infinity Gauntlet was that he could take care of the whole universe, instantly ("snap of his fingers").

Since your question seems more focused on whether "randomly" translates to an entire population on a particular planet being untouched, potentially and an entire other planet getting wiped clean, using the entire universe as a random pool would kind of defeat his (to himself, at least) altruistic intentions. The idea is that the universe's resources are finite, but so are each planet's. In order to save populations from their own excesses, the "pruning" would have to happen both locally and universe-wide, to achieve his goals.

What's interesting is that on Titan people were taken out, but that appears to be within the pool of "Earth" population, in practice. It appears that he's going by each sentient species and planets they inhabit, not just visit.

Though I'm not sure that this is canon, because the movie makers might not have considered this at the process-design level.

0

Thanos intends to kill half the population from every planet, randomly.

Because the motive of killing was that the living beings will have more available resources and there will be less sharing. If he kills from every planet then the other half of the population will always have the resources. But if he kills randomly from universe, then, some planets will still have same number of beings and some might be wiped off clean with all the resources and nobody to use it.

  • "some planets will still have same number of beings" -- as we see in other answers, this claim is yet to substantiated with math and/or lore. Please elaborate. – Sam May 10 '18 at 14:44
  • You totally missed the important point! The whole idea of killing half population was to distribute the resources so that everyone had a fair share. So when half the population is being killed randomly, there is just one case- 1/nth probability (assuming 'n' is the different no of ways killings is done), the case in which all the planets have exactly the population eliminated, in which this motive will be achieved, which makes no sense. Here my friend, we don't need calculation but common sense to understand it. – Parul May 14 '18 at 11:10

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