Based on what I saw on the movie, I realized how surprised Count Dooku and maybe even Palpatine were when they saw Anakin using the Dark Side of the force. In the book it actually shows how Dooku was feeling at the time, and the curious think about his account is his surprise in his strength. Meaning the original plan was to essentially lure Anakin into defeat and force him to kill his own master, as in many cases of Sith inauguration into the ranks. As such, Dooku used his full strength too late and essentially lost his ability to become an effective Sith and leader. There have been times where the Sith's rule of two have been broken due to what they would perceive the greater good, but many times because their is a rebellion in the Sith ranks. However, it is very feasible that Palpatines' original plan was to have two of the greatest members of the force underneath his guard. There is some hint to that Anakin was essentially a product of Sidious. Because of this, it is also probable that it was Sidious' plan all along to have his product by his side. If the theories are true.

After Dooku had failed and lost his hands (and his strongest ability as a Sith) it is no wonder Palpatine let Anakin kill him. I say "let" even though he was ordered too. There are two reasons for it. One, we all know that Anakin craved and longed for it, but also, Palpatine was able to absorb the guilt for him by not letting him make that decision. It brought the Dark Side a great ally, because, Anakin was seen has as a hero in front of the entire Republic, and as such, he knitted a stronger bond with Palpatine who actually let him express what was in his heart of hearts, instead of the restraints (at least what Anakin personally felt) of the Jedi Council.

Darth sidious kills Dooku for a reason. Because it is the Sith way to kill your master once you've learned enough of his teachings... and that's a problem for sidious since he wants to rule the galaxy, so he kills Dooku via Anakin to stay in power. And since Anakin was a powerful jedi. He had no need for teachings. Plus Anakin didn't know it was the Sith way to kill your master. Besides what did he have to lose even if Anakin said no he could call order 66 and kill Dooku himself... hope that helps.

I thought he might have been worried that the Dook-ster would betray him as the leader of the Sith. Under Jedi interrogation - or even just normal droid interrogation - or something.

I mean, nothing in the movie implies that at all - it seems to be more "Palpatine pushing Anakin along the dark path" in the movie, but presumably a captured Dooku was a big risk to the Emperor.

Of course, that theory throws the whole "Palpatine's plan to get captured" into disarray... did he just get captured to further Anakin? What if someone else had rescued him and taken Dooku prisoner, or what if Obi-wan hadn't fainted?

But that's a question, not an answer. I'd assumed that rule of two or not, Palpatine needed to keep his secret safe, and a captured Dooku was a big risk to that secret.

After reading the book of Star Wars III: Revenge of the Sith, during that part it is revealed that Darth Sidious never intended to keep Darth Tryranus as an apprentice, but he was merely an ends to a goal of gaining Anakin as his apprentice.

If I remember correctly, one of the main reasons was that Tyranus was old. Anakin was young, a thousand times more powerful and was prime for being an apprentice, whereas Tyranus was old and powerful-yes, but who would want a greasy taco when they could have a loaded plate of nachos with all of the fixens?

During the fight, Anakin was struggling to keep control of his anger after seeing Obi-Wan nearly get killed during the fight. If we all can remember Yoda's great teachings, "Fear is the path to the dark side. Fear leads to Anger. Anger leads to hate. Hate.....leads to suffering. I sense much fear in you..."

Having Anakin kill Tyranus served two purposes...

1. It would remove Darth Tyranus as his apprentice, giving him leave to find a newer and better one.
2. It pushes Anakin further towards the Dark Side... and towards being that apprentice.

Sidious has Dooku killed because he was a potential rival. He needed to kill Dooku to advance to the final stage of his plan. How could he end the Clone Wars if the separatist leader was still alive.

Also there was no place for Dooku in Sidious's schemes post CWs. He needed an enforcer/soldier (Vader), someone to punish his enemies and maintain order. Dooku was too smart and capable for Sidious to keep around, eventually Dooku would've found a way to kill him and take control of the new empire. Just like Sidious, Dooku was a schemer and plotter.

Even if Vader wasn't maimed in his battle with Kenobi, he would never gain the wisdom needed to be a rival to Sidious. Vader was always blinded by his own passion, which makes him a great warrior but not much of leader.

This is explained in J.W Rinzler's The Making of Star Wars Revenge Of The Sith.

Amongst the script notes is this quote from Lucas, which explains that the whole thing is a test to see if Anakin is ready to become Palpatine's new apprentice. Palpatine never planned on having two apprentices.

LUCAS: "Palpatine has told Dooku, 'I have somebody who I think will become a great Sith Lord and I think we can get him to join us. But we need to test him. So we're going to set up a situation where you fight him. If he gets the best of you, then I'll stop the fight and he'll have passed the test. If you get the best of him, then we'll let him go, and we'll let him stew for a few more years until he's ready.' But behind it, obviously, is Palpatine's real intention: If Anakin is good enough, Anakin can kill Dooku and become Palpatine's new apprentice. But he didn't tell Dooku that."

In most possible outcomes, Palpatine comes out ahead. If Dooku wins and kills Anakin, then will they have eliminated a powerful Jedi who may cause further problems down the line. If Anakin wins, he will have found a new apprentice, and gotten rid of his current apprentice.

Treachery is the way of the Sith

Because Palpatine wants Anakin to be his next Sith apprentice. Realizing that Dooku/Tyranus has been incapicated, he needs a more powerful apprentice than Darth Maul or Darth Tyranus.Palpaтιne ĸnowѕ тнaт anaĸιn ιѕ тнe cнoѕen one. He ĸnowѕ тнaт anaĸιn'ѕ ѕтrengтн ιn тнe ғorce ιѕ ѕтronger тнan ever вeғore. Notice that Palpatine is very watchful of Anakin. Anakin thinks that Palpatine takes care of him and trusts him, but in reality Palpatine was just manipulating Anakin (as we see in the movie). In Return of the Jedi, Palpatine does that to Luke. When he asks Luke to kill Darth Vader, Palpatine wants to take Luke on as his new apprentice. However, Luke rejected Sidious. That's what Darth Sidious does; he double-crosses his apprentices because he always wants a more powerful apprentice.

"Soon I will have a new Apprentice. One far younger and more powerful"

I believe that dooku is killed for two reasons, Both mentioned on here bot not together, In attack of the clones Dooku tells obi wan that "the republic is now under the control of the dark lord of the sith" Then obi wan is set free. Obi wan would have def told the council about that, and would have reached palpatine. Making him a liability. And then of course to affect anakin.

During the Clone Wars series it definitely seemed like Dooku was working his own angle, he may of said he needed bodyguards a few times but when he was training his new apprentice after being ordered to kill Ventress. He definitely seemed like he wanted more power and knew Sidious couldn’t be trusted.

In ROTS, Palpatine knew Anakin was a close equal to Dooku, but he also knew Dooku was more powerful than Anakin. Palpatine also knew that Anakin had the highest Force potential of all time and he wanted Anakin to be his successor in the rule of two not Dooku.

Palpatine knew that the only way for Anakin to defeat Dooku was by tapping into the dark side of the Force. If Anakin did this he would surpass Dooku and carry out the rule of two, also Dooku was much older than his master Palpatine and didn't have the potential to defeat him and become the Sith master but Anankin did.

Palpatine was the one giving Anankin Force visions of Padme’s death and he knew Anakin would do anything to save her including joining the Sith order. Palpatine was a master of deception and knew exactly what he was doing.

Just like Luke's situation he wasn't more powerful than Vader it’s just that Palpatine would do anything to get Vader replaced because Luke had potiental to be twice as powerful as Vader same with Anakin and Dooku Vader and Dooku were more powerful than their replacements it’s just that Palpatine gave the challengers a handicap against their oppenents AKA the dark side of the Force.

Both Vader and Dooku were victims of Palpatines foul play. If Vader and Dooku fought their replacements without their replacements having handicaps the favor of the two battles would fall into the Sith lords hands having them as the victors.