Why didn't Dooku just betray Sidious? It seems like at some point during the Clone Wars, Dooku would say to himself, "I control an entire army, everyone except Palpatine thinks I control this army, why don't I just fight this war for real?"

In all seriousness, I just get frustrated with how "in control" Palps is during the prequels and TCW. It seems like nothing ever throws a chink into his plan, which seems really reliant on a) Nute Gunray not knowing who he is (and even Ahsoka was able to tell a computer to ID a hooded figure) and b) Dooku doing everything he tells him without question. If there is any Legends or canon material that says otherwise, let me know.
