3 Hatch Spire (vs. Protoss)
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This build opens very similarly to a ZvT 3 Hatch Mutalisk build. It looks to get Scourge and/or Mutalisks out very quickly to control Protoss' early midgame Tech, allowing Zerg the freedom to power Drones through the midgame. It can sometimes be used as an aggressive strategy by catching the Protoss main off guard while it has very few Cannons and minimal air defense.
|"3 Hatchery Spire"|
12 - Zerglings (6)
If you have scouted your opponent by this time, it may be possible to skip these Zerglings and spawn Drones instead. If you go this route, you should still make 2 Zerglings to kill the scouting Probe.
@100 Gas - Natural Extractor (optional)
By getting a natural geyser, you focus some midgame economy for more early game options; you allow yourself more Scourge against Stargate openings and Mutalisks against +1 openings. If you are planning on transitioning straight into Lurker/Ling, you should get the natural Extractor. You should also get it on a map where Stargate openings are popular and powerful (namely Andromeda). If you will transition into Hydralisks before Lurkers, you may forgo the natural Extractor.
@150 Gas - Overlord Speed (optional)
Against Stargate openings, Overlord Speed is usually recommended. If you feel confident in your Overlord placement, you can skip it, although doing so does limit your midgame options and may offer great benefit. Against +1 builds you can delay it as you see fit.
33 - 2 to 4 Overlords
If your opponent did a Stargate opening, you will lose at least one Overlord to the first Corsair; you want enough Overlords to cover those losses when your Spire finishes. Not being able to make Scourge right as the Spire finishes is disastrous. If your opponent opened +1 Zealot speed, you need enough supply to make 9 Mutalisks as the Spire finishes (Either 33/51 or 35/59).
@100% Spire - Scourge OR Mutalisks
Against Corsair openings, make enough Scourge (typically 4-8 depending on the map and Gateway count) to completely negate your opponents Corsairs. Send an initial pair of Scourge into your opponent's base to check his/her Tech (Robotics? Many Gateways? Continual Corsair production? Third base expansion attempt?) so you may counter accordingly.
Against +1 openings, make 9-11 Mutalisks to deal the damage, and enough Sunken Colonies and Zerglings to absorb the attack while stopping a potential run by.
Either way, this is not a Scourge / Mutalisk timing attack looking to finish your opponent. That build order is slightly modified and is a very high level build which should not really be attempted by lower level players. You should still use your Mutalisks to harass your opponent's main base and Mineral Lines whenever possible, but use the Mutalisks more so to gain map control while you power economy through the midgame.
After your Scourge or Mutalisks are out, immediately add a Hydralisk Den and Evolution Chamber (or two), research Zergling Speed, and place another Hatchery (at your third base or a fourth base). Once Overlord Speed completes, take another look at your opponent's base while spreading Overlords across the map at all choke points and potential expansions. Follow up with either Lurkers or Hydralisk Speed / Range. With no Corsairs to kill Overlords and with Overlord Speed complete, Protoss should not be able to take a third base quickly without being run over by Lurker/Ling or Hydra/Ling. Take this time to continue powering Drones while you move towards Hive.