system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Wars] Why was Sidious supportive of Vader trying to persuade Luke to turn to the Dark Side when it obviously meant that Luke and Vader would team up against him?

Assuming the Rule of Two would be upheld, of course. Unless Sidious was so arrogant as to think Luke would kill Vader and Vader would be ok with that?
gpt
Afaik, Palp was hoping for Luke to defeat his father and become his new apprentice, not join his father. He wanted to fuel Luke's hatred for Vader so that the anger would overcome him and "complete his transformation to the dark side" or something like that. Either that, or Vader kills Luke, tightening Palps grip on him. 

TL;DR He was betting pretty hard against Luke overcoming his daddy issues.