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[Star Wars] If the Sith go by the Rule of Two, why does every Sith Lord (from Sidious to Dooku to Vader) have multiple appretences?

Vader alone must have had 5 at least (according to EU and the video games).
gpt
The main thing is that these Sith never had more than one apprentice at a time. 

Sidious started off with Maul, then when Maul "died" he was replaced with Dooku. Sidious never planned on Dooku's long-term apprentice ship. Dooku was a tool to be used while Sidious groomed Anakin for later apprenticeship. When the time was right and Anakin was ready, Sidious had Anakin kill Dooku to make room for himself. Mara Jade was given rudimentary Force training to better server as the Emperor's Hand, but she was never a full apprentice.

Dooku never had an actual Sith apprentice. The closest he got was Asajj Ventress. Ventress was a Dark Jedi, not a Sith. The difference is a Dark Jedi is just a Force sensitive who have fallen to/were taught the Dark Side, while the Sith are an ideological order with a definite heirarchy and many hidden techniques and rituals. Sith will often use the promise of these techniques to secure the services of Dark Jedi, and then never actually give them out. 

Vader's only known apprentice was Starkiller, and that turned out to be a sham anyway. Starkiller never reached the level of a true Sith, and he was thrown out and subsequently killed as soon as his use (finding the Emperor's enemies) was fulfilled. The process of cloning Starkiller was Vader's attempt to create a perfect Dark Side user to have as his own personal weapon. Obviously it didn't turn out very well. He trained a few other people for a position for himself similar to the Emperor's Hand, which he called the Shadow Hand. The original Shadow Hand, Lumiya, killed the competition. Lumiya was titled "Dark Lady of the Sith", but it was just a title. She was no more Sith than Mara Jade or Asajj Ventress until after Vader's death when she spent the following decades scouring the Galaxy for everything Sith related she could find and met up with Vergere, a Jedi-turned-Sith who had been in hiding since before the Clone Wars. She then founded a new Sith order and corrupted Jacen Solo and made him her apprentice.

Darth Bane created the Rule of Two so that when the time came for Apprentice to become Master, the apprentice would either be stronger than the master or end up dead. This ensured that the Sith would constantly grow in strength rather than stagnate and falter because a bunch of weaklings ganged up on a master and killed him in his sleep. Over the millennia this concept was slightly corrupted, where Sith who could not wait to rule would often kill their master with the help of an apprentice of their own or by guile rather than a full-on fight to the death, which resulted in a slow decline of power. However, centuries of the Rule of Two being followed relatively faithfully led to the Sith growing immensely in power, so even with the slight decline Sidious was still one of the most powerful force users in the Galaxy at his time, if not the *most* powerful.

**Tl;dr:** They do to a point, but it was very slowly being withdrawn due to the impatience and arrogance of various apprentices. Up until they were wiped out at Endor, that is.