The important thing in defending the homeworld is to not let any enemies orbit. If they are foolish enough to orbit uncloaked, you can tractor or pressor them out of orbit. If they are coming in cloaked it's a little tougher because you can't see them on your tactical. Use your galactic map (the TAB key will toggle to a higher-resolution scan) to detect cloakers. The position is inaccurate, but gives you a rough idea. Fire your weapons till you start hitting and then pound the enemy to bits.
If everyone is clustered around the homeworld defending it, it will be hard to see cloakers. Bases usually can defend the homeworld by themselves, but won't mind one helper. Remember to pick a ship with good fuel regeneration. If you find yourself running out of fuel, you're probably flying the wrong ship for homeworld defense.
The enemy will try to take over your planets. To do this they need armies, and to carry armies, they need kills. Don't worry about bases, they either can't carry armies or can't orbit enemy worlds. Look for enemy ships who have kills. They might carry armies. Hunt down these carriers and kill them. You don't usually have to kill them right away. They will run to their teammates for protection. This is OK, because they can't take your planets when hiding in their own space. Whenever they come out into your space, harrass them. To take your planet they should have to get past you, which puts them at a disadvantage. You can often doosh an impatient carrier this way.
Protect yours by ferrying armies to your starbase or homeworld. Any planet that has more than 4 armies can have armies bombed off it. If you have kills, pick the armies up off that planet and carry them to your starbase or homeworld. Avoid dying while carrying armies. Your teammates will be angry with you if you do.
Destroy the enemy's armies. Get in a scout ship and fly around in enemy space. Your scout will scan nearby planets and if you find any with more than 4 armies, go in and bomb. If any other ships see you they will try to kill you. It is usually best to run from them. You can sometimes kill them if they chase you. It's usually a good thing not to die because if you die, it will take you a long time to drive back to where you were, and the enemy will have a kill.
If you have kills, you can carry armies, usually 2 armies for every kill. If you think you can carry armies safely to an enemy planet, do it. When you pick up armies, send a carrier notification with the F key and then send a message to your team telling them where you plan to take them. Hopefully you can get a wingman who will help protect you from enemies. Remember, the important thing is to get the armies to the planet.
You should scout these planets because the enemy may have secret facilities hidden in faraway corners. Destroying these hidden facilities gets you points and helps your team.
Protect your armies, on planets or in friendly ships.
Destroy enemy armies, on planets or in enemy ships.
Get information on all enemy and neutral planets.
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