There was always a deal between Sidious and Dooku in Lucas' mind. Sir Lee didn't want Dooku to beg ofor his life, so it was cut-off. For me Dooku just realized at that point, when Palpatine encourages Anakin to kill him, that Palpatine broke their deal and he's already done.
I also believe, that Dooku still had the upper hand against Anakin and Obi-Wan, and - unlike a a novel version - he was taunting Anakin to both - him and Sidious - could see his full power. Anakin became much stronger, Dooku couldn't keep up, he tried but lost.
It was very similar to what Vader did in his final fight with Luke after all.
Dooku was slightly above Anakin during their last duel in TCW, I believe it was a season 6. Very smilar version of Anakin stared the fight with Dooku in ROTS. And he was unable to find any advantage as long as Obi-Wan's hindering presence was there. After Kenobi lost and Dooku taunted Anakin to use his full power, use anger and hate, Anakin won.
Look at Anakin's body language in the the last seconds of their fight in S6 TCW. Perhaps two last seconds. And first half of their duel in ROTS.
He was following orders to be captured and realized right before Anakin was going to kill him that Sidious was going to betray him before the fight even started. Dooku I don't think was ever suppose to kill Anakin in any of their fights.
The price of fame is high and the Thing cant pay the way.
I don't think the plan necessarily was *for* Dooku to lose the fight, at least not as far as Dooku was aware. The plan was for Dooku to win, but if he lost, Palpatine would grant him clemency or whatever the ****. Palpatine just didn't honor that deal, because all Sith are just retarded enough to not understand that betrayal and the eternal climb for power is the center of Sith idealogy.
"The Daemon lied with every breath. It could not help itself but to deceive and dismay, to riddle and ruin. The more we conversed, the closer I drew to one singularly ineluctable fact: I would gain no wisdom here."
No, it was. Dooku has a whole scene in the RotS novel where he complains about it. He's so caught up in his whining that he completely overlooks it when Sidious comments that he thinks Dooku would lose even if he did try to kill Anakin.