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human
[Star Wars] What would have happened if Luke joined Vader?

Personally, I think he would certainly have been justified in doing so. He's been lied to, kept in the dark and stashed away on planet desert shit hole for most of his life.

Here's his opportunity to get to know what's left of his father, learn about his gifts and have a better life.

Anyway, assuming Luke says yes, rather than throwing himself to his death. How do things play out from there?
gpt
The Han Solo rescue op doesn't go as well.  It's either a colossal failure or has to be postponed until after the assault on the Death Star. (Han wasn't going anywhere, but there was a *very* narrow window for the rebels to pull off the Death Star attack)

Without General Solo on the ground, the shield generator remains up, which causes some issues for the rebels during the fighting over Endor.  Depending on how confident in victory Palpatine is feeling, he may even send Luke and Vader into combat either in the space battle (both Skywalkers being among the best pilots in the Empire), or on the forest moon, leading the force that traps the Rebels.  (IMO, he'd have Luke in space just in case being face-to-face with the Rebels might shake his new loyalty)

Although without the moon strike team being led by General Solo, perhaps Calrissian and Ackbar are quicker to bail on the attack and withdraw before the trap is *fully* sprung.

In either case, Luke's insider knowledge of the rebellion probably makes it easy for the Empire to roll them back following the defeat at Endor.

As for Luke, he probably becomes Vader's apprentice and, as Luke is still pretty raw in terms of Force use and lightsaber ability and Vader is a shadow of his former self in both of those respects, it's a toss-up as to whether they kill Palpatine, or he sees them coming and kills them first.  There is the *slight* chance that Palpatine gets Luke to kill Vader and become *his* apprentice, but if the whole father-son bond was what got Luke to turn at Bespin, it'll probably keep him from betraying Vader (at least until he's older and brings Kyle Katarn or Mara Jade on as *his* new apprentice).