system
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human
[Star wars] How was Palpatine so sure Vader wouldn't turn against him..??

Palpatine tells Anakin the tragedy of Darth Plagueis and how he got screwed over by his own apprentice and then he offers to teach Anakin the things in the dark side. How was he so sure the same  thing wouldn't happen to him. 

When Vader fights Luke he asks him to join his side so he could overthrow the Emperor and rule the galaxy... Meaning Vader already had the idea of killing the Emperor and taking his place. If Luke joined Vader or  never existed... In time Vader would have turned against the Emperor. So what was Palpatine's contingency plan in case something like that happened..
gpt
He did expect it. That is how the Sith work. The apprentice must eventually overthrow the master - if they are strong enough. Only through that can the strength and continuity of the Sith be ensured.

Sideous would rule until either Vader could overthrow him, or he found another to replace Vader would be stronger and so could.