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[Star Wars] What made it so hard for Obiwan to defeat Dooku?

Was it the skills or simply that Anakin tapped into the dark side and had far more potential to defeat Dooku in Episode 3?  But then, how was Obiwan able to defeat Anakin, was it purely because "he knew all his moves" and Anakin's mind was messed up?
gpt
Sidious and Dooku had a plan beforehand: kill Kenobi, and turn Skywalker to the Dark Side.  For some reason, Dooku had no inkling that his master intended to *replace* him as an apprentice with Anakin.  We can speculate as to why Dooku didn't realize this; for example, Sidious may have been affecting Dooku's mind with the Force.  Alternatively, Sidious may have told Dooku that Sidious intends to abandon the Rule of Two (which was true), which meant that he could have multiple Sith apprentices.  In any case, the plan was always for Dooku to kill or disable Obi-Wan, and then beat down Anakin until he gives in to the Dark Side.  

Dooku's uniquely suited for this task, because he's one of the finest lightsaber duelists of that era.  His lightsaber style, Makashi, was specifically designed for lightsaber dueling, and he was the undisputed master of Makashi at the time.  He was also exceedingly powerful in the Force.  This meant there were few Jedi who could stand against him toe-to-toe, as Obi-Wan found.  Dooku had no hesitation to unleash his full abilities against Obi-Wan, but he held back against Anakin, at least at first, because he didn't want to kill Anakin.  

After Dooku disabled Obi-Wan, he focused his efforts on Anakin, and actually encouraged him to give in to his anger and hatred, so that he'd have a taste of the Dark Side.  However, he hadn't realized how powerful Anakin was, or that Anakin's Djem So form was capable of overpowering his Makashi.  By the time Dooku realized he was outmatched, he was on his knees with a pair of lightsabers criss-crossed at his neck, and was missing one right hand and one left hand.  

As for why Obi-Wan won against Anakin, basically it either came down to luck, or Obi-Wan fully leveraged the greatest strength of his Soresu form, depending on who you ask.  Soresu is the most defensive form among the codified lightsaber forms, and a master of Soresu is virtually unhittable.  Obi-Wan was known as *the master* of Soresu at the time, as demonstrated by his ability to block all four of General Grievous's lightsabers at the same time.  However, Anakin was so good, he was still able to land hits on Obi-Wan during their duel, while Obi-Wan's lightsaber never came close to touching Anakin until the final blow.  In other words, had the high ground situation not occurred, eventually Anakin would probably have broken through Obi-Wan's defenses and killed him.  So, was it a stroke of luck on Obi-Wan's part that he was able to gain the high ground?  Or was this a demonstration of Soresu's strength, allowing Obi-Wan to keep himself alive until he could find an advantageous situation?  Opinions are divided.