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Although my question is based on the comic mini-series Infinity Gauntlet issues #1 through 6, I'm open to any and all answers (i.e Movies, other comic books etc. etc.) across the Marvel multi-verse.

It was elegantly presented in the Infinity Gauntlet series how Thanos, after collecting all the soul gems snaps his fingers and destroys half the universe.

Additionally, in the recent movie Avengers: Infinity War,

Thanos does it again! He snaps his fingers and destroys half the universe.

However, one thing is unclear to me. In both cases,

Half the universe is destroyed (or obliterated, or erased from existence).

But who decides which half of the universe should not exist anymore? Does the wielder of the Gauntlet choose, or is the Gauntlet (along with the stones) sentient enough to make the decision?

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    living_thing.is_destroyed = (Math.rand() > .5)? Yes:No. The infinity stones just run a program for everyone. – CBredlow May 3 '18 at 17:25
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    Note - in the comics referenced, half of the universe being destroyed is represented as us seeing the starfield behind Thanos, and post-snap, the left half (from our perspective) of that starfield is gone. One should also note that, in the comics, the death of half the universe is Thanos' gift to his beloved, Death (not normally seen as a specific individual with a personality, but as a female figure in a robe (based on shape) whose body appears to be skeletal). In the movie, they ennobled things, so the act is an evil means to a theoretically good end, not an alternative to roses.. – RDFozz Aug 9 '18 at 16:46
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It appears to be determined by the wielder

On Titan when Thanos uses the Reality Stone to flashback, he says that his solution to the over population of Titan was a random culling of half the population. A truly random one that would effect rich and poor alike without bias malice.

Later, after his fight with Iron Man, he promises Doctor Strange that:

He would not kill Tony Stark in exchange for Doctor Strange giving up the Time Stone

Obviously,

Once he snaps his fingers, Stark is only one of two survivors on Titan.

The important part being that he survived.

Additionally, Thanos wanted to kill half of any given planet (as seen on Gamora's planet, and again when talking to Stark), not simply half of the universe. This requires a degree of control since not all planets will have the same population count.

So in short, the randomness appears to be true randomness, but this is by conscious design (after accounting for the various other desires of Thanos of course).

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    I don’t think we have enough evidence to warrant that claim. It may seem like it, but Thanos also says that a random selection of class, race, whatever is the only way it works. – Edlothiad May 3 '18 at 20:50
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    We also have no evidence that Thanos has studied applied mathematics and statistics at his local university /s He might well be making one of the many errors that anyone who doesn't understand statistics correctly makes... – JK. May 7 '18 at 4:14
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    Killing half the population of each planet is evidence against randomness. If it were true randomness, some planets wouldn't be culled in half. Maybe Thanos is lying or more likely, like @JK suggests, he just doesn't understand probability and statistics :) – Andres F. May 9 '18 at 17:42
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    So what you're saying is that it's partially random.... Meaning that Thanos has an effort to allow people to live or die but for people whom he never has met, they have a random chance of living? – KingDuken May 18 '18 at 0:36
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    @AndresF. That's not accurate... assumint the 10T souls Heimdall sees are actually spread quite thin, on worlds that are only typically 1M dense, that is only 10M worlds, which is covered easily by 6 standard deviations from the mean. Each world would post-snap (with 50/50 culling) be 500,000 ± 500 people, with the most outstanding worlds being only ± 3,000 or so. So it's "culled by 50.0% ± 0.3% in the worst case," hardly worth being like "haha, I got you Thanos!" – CR Drost Apr 15 at 21:09
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Thanos himself says his selection process is passionless and (IIRC) random. Not based on wealth, power, or any subjective parameter. So presumably it's the same during the Snap as it was when he was doing it manually.

He may have made the one choice about saving Tony at that point, but he could just as easily have decided he only meant that he would spare Stark from dying at his hand, at that moment, on Titan, and only Fate left him alive after the Snap.

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    “Thanos himself says his selection process is passionless and (IIRC) random. Not based on wealth, power, or any subjective parameter.” Not quite — he says that that’s what he proposed on Titan. Although it’s reasonable to assume that’s also what he’d do if he had the power (which, by the end of the movie, he does), other considerations (including absolute power corrupting him) may have come into play. – Paul D. Waite May 4 '18 at 9:13
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This is mostly a headcanon answer but I find it satisfying.
We can't know much that was not said from the MCU universe but we have a lot of comic book history to fall back to.

In the marvel universe the whole universe is conscious. This consciousness is tied to the elemental forces such as life and death as well as the infinity gems. One of the main ways we see this power manifest is cosmic awareness. This is kind of like spider sense times a billion. Beings that posses it understand how every atom in the universe fits into the great puzzle, and while they may not be able to predict the future, they have this nebulous understanding especially when it comes to threats to their well being.
On top of just being able to judge threats, they also have luck when it comes to these things. The character that we are most used to having this power is Captain Marvel. Whoever holds the mantle will get randomly flung through the universe and know it was not random, they were brought to a place do do something because the universe wills it.
This is why Nick Fury calls her. He knows for a fact she is not dead. Captain Marvel can't loose a universal coin-flip, the universe would never allow it.

So now we are back to Thanos. If Thanos is not already cosmically aware being an avatar of death a fundamental power, I think it is safe to assume that he is cosmically aware holding the stones. Even if we ignore that, we know that the universe is smart enough to not kill the wielder of the gauntlet if he does not wish to participate in the coin flip.

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