I was watching Ep 3 and I was wondering if Sidious had planned Dooku's execution by Anakin.
It's possible that Sidious had instructed for Dooku to incapacitate Kenobi first during their fight, to leave him and Anakin in a 1v1, and in the likely event that Anakin disarmed Dooku, Kenobi would be out of the picture and leave Sidious open to order Dooku's execution.
There is no way that Dooku would have been executed had Kenobi still been conscious and in the fight.
Dooku was a place-holder for Anakin. Sid planned the death as another provocation for Anakin.