star wars - Why did Palpatine order Anakin to kill Count Dooku when Anakin was not yet turned to the Dark Side?

This follows from this question: Does the Rule of Two Serve any Actual Purpose? , Darth Bane came up with the “Rule of Two” to ensure the survival of the Sith. The answer to that question says:

The Rule of Two perservered because it worked. Those Sith Lords who violated it by trying for >1 apprentice, seemed to have ended up worse off than if they only had one.

Meaning, being alone was the worst condition & violating the Rule of Two was a proven thumbs-down thing. But Palpatine still ordered Anakin to kill Dooku. Why? It was clearly breaking the Rule of Two and Anakin wasn't his apprentice at that time. It was also possible that --despite his future vision-- he would fail to seduce Anakin.

Answer

The Rule of Two doesn't mean there can't be only one - this has frequently happened, usually because the Master has killed an Apprentice (or he has died in some other fashion) or when the Apprentice has become the Master.

In Palpatine's opinion, killing Dooku in cold blood was an important step in turning Anakin to the dark side. He lost an Apprentice, true, but Dooku was never going to become a Sith Master - his Force abilities were not insignificant, but he was not in the same league as Windu, Yoda, or Sidious.

Palpatine has always shown himself as willing to sacrifice an apprentice to gain a better one, so when he judged the time was right, he had his handpicked potential apprentice execute his current apprentice, hoping it would help steer him down the path towards the Dark Side.

It worked.