Science Fiction & Fantasy Stack Exchange is a question and answer site for science fiction and fantasy enthusiasts. It only takes a minute to sign up.
Sign up to join this community
During the first battle of Geonosis, Mace Windu joins the clones on the ground with Kit Fisto, Aayla Secura, and others. The other Republic gunship, with Anakin, Obi-Wan and Padme on board, follows Dooku's speeder to his secret hangar.
Why didn't Mace Windu go with Yoda to confront Tyranus? Surely it would have been wiser for Master Windu and Yoda to tackle Dooku at the same time. Dooku couldn't possibly their combined attack.
The film's official novelisation mentions not once, but twice that Mace is utterly exhausted from his fight with the droids. In addition to needing someone else to coordinate the troops, I think we can reasonably assume that Yoda decided to leave Windu at the Command Centre because in a fight with Dooku he would have been a positive liability and one more Jedi for Yoda to have to worry about.
More Jedi went down under the sheer weight of the laser barrage. Less than half of them were still standing.
“Limited choices,” Ki-Adi-Mundi said to the exhausted and bloody Mace Windu.
and
Over at the command center, an exhausted and dirty Mace Windu joined Master Yoda, the two sharing looks that combined hope for the present and fear for the future.
Beside having limited Jedi forces with him (Windu was exausted as mentioned in earlier answers, many Jedi were dead) Yoda was not sure of Dooku's intentions. Only when he finally confronted him, he sensed Dark Side (the Dark Side I sense in you). Of course, there was the telltale sign of Sith - Force Lightning.
Dooku didn't confront Jedi directly up to that point (fight vs Obi-Wan and Anakin, and right after that vs Yoda). Therefore, Yoda perhaps wanted to resolve matters peacefully with hid old Padawan, but realized it is impossible.
I doubt this game is canon anymore, but I'm sure at one time it was. Anyway, in Star Wars: The Clone Wars you got to play as Mace Windu pursuing some other objectives while the whole Yoda/Anakin/Obi-Wan/Dooku thing was going on. I don't remember exactly what, but I think he was taking out a shield generator or coordinating troops to prevent some escaping Trade Federation ships or something of the sort. Obviously this answer only applies to Legends (assuming the game was considered canon at one time), and doesn't apply to Disney canon.
