Sith went into politics to beat the Jedi, knowing their enemies were politically naïve and disinterested. Palpatine maneuvered himself into becoming Chancellor of the Republic, and for over a decade he worked side by side with the Jedi, holding countless meetings with of the Jedi Council - including Master Yoda.
Yoda was undoubtedly the greatest threat to the Sith. The aged Star Wars: Episode III - Revenge of the Sith, he and Yoda engaged in a phenomenal duel - one Darth Sidious clearly took great pleasure in.
Curiously, though, there are striking parallels between Palpatine and Yoda. The comparison was recently highlighted in Star Wars: Crimson Reign #3, which revealed how Yoda hid himself on Dagobah during the Dark Times; he took advantage of the fact Dagobah is a powerful light side vergence in the Force, one that could conceal even his luminous being. The technique is an inversion of Palpatine's own, for there have been hints Darth Sidious took advantage of the darkness of an ancient Sith shrine buried beneath the Jedi Temple on Coruscant to conceal himself on the ecumenopolis.
This revelation only reinforces the curious narrative symmetry between Palpatine and Yoda; what one was to the Sith, the other was to the Jedi. Palpatine concealed himself from the Jedi, and through his plans the Sith ascended to power and overthrew them. But Yoda hid himself from the Sith, and because he mentored Luke Skywalker, the Jedi ultimately overthrew the Sith once again. There is, of course, a crucial difference: Palpatine's plans were focused on his own ascension, but Yoda understood he had to the torch on to someone else. In the end, Luke didn't defeat the Sith because he acted in accordance with Yoda's plan, as the Grand Master didn't believe Darth Vader could be redeemed, and simply thought Luke would be the one to kill the two Sith. Instead, Luke acted completely outside Yoda's philosophy of the Force, and his act of redemptive love was what truly thwarted Palpatine's plans.
Tie-ins have created yet more parallels between Yoda and Palpatine. Star Wars: The Rise of Skywalker, he left no successor, and the line of the Sith was destroyed.
Both Yoda and Palpatine were, in their own ways, responsible for the downfall of their respective Orders - a fascinating twist in the Star Wars saga.
