Thinking about the inconsistencies of the saber duels, and re-viewing the film... I think it's possible that Palpatine might have been influencing the fight between Obi-Wan, Dooku and Anakin. This way he could move Obi-Wan out of the fight and Anakin could kill Dooku and then they could leave Obi-Wan to die.
It's just a theory.
