I see this asked a lot.
It's a no-brainer. As long as you can fish 3 rods effectively in a given swim, you should use 3. It's not an extra chance imo - it's an extra fish, or more, if used correctly when on the fish.
I carry 3, if a swim is too small to use 3 effectively I'll use 2. Sometime I'll use just one in a diddy little corner under a bush. But the fact of the matter is if I can fish 3 effectively I will do - it catches more fish. Simple fact buddy!