Been away from the game for awhile (playing WOW), and figured I'd see if I still remembered how to do the ZYW thing. I figured I'd post a turn by turn account so that you could see how I do it. Keep in mind that I'm certainly not the best GCII player and don't really know how to score big, It's just an example of how you can pull off a ZYW from an average player. Here goes. (this is for Dark Avatar BTW)
SETUP - Tiny Galaxy, All rare except for anomalies (abundant), Very fast research, 0 minors
RACE - Custom, Super annihalator, 4 points research, 3 points range, 5 points speed, 1 point luck, 1 point creativity, 1 point weapons (couldn't think of where else to put it hehe)
Political party = technologist, 1 opponent (arcean)
TURN 1- Research Xeno Research - Home planet, rush build basic lab (107bc + 10 bc for 180 weeks) -Focus production on research -set production capacity to 100%, taxation to 100%, research spending to 100% - Set flagship to auto survey - Aim colony ship and space miner at center planet of enemies influence.
TURN 2- Research spore weapons - Rush buy Xeno Lab (140bc + 12 for 197 weeks) (300% bonus tile on my planet)
TURN 3- Rush buy Xeno lab (140 bc + 12 /197) (200% bonus tile on my planet)
TURN 4- Rush buy Xeno lab (140bc +12/197)
TURN 5- I can see Arcean home planet this turn. Park miner next to it.
TURN 6- Research space militarization
TURN 7- Spotted second Arcean planet, parked colony ship next to it. - Research beam weapon theory
TURN 8- Research basic logistics. - Design spore ship (S-1) (Cargo hull,spore module,laser,basic supportx4) -Upgrade miner (112bc +10/183) and colony ship (111bc +10/182) to spore ship (S-1)
TURN 9- Research general life support
TURN 10- Research new propulsion techniques
TURN 11- Research Impulse drive
TURN 12- Research impulse drive II - Attack Arcea with spore ship. Arcea falls -hold off attacking second Arcean planet because I think a victory this quick will flip cheat flag for MV games (can't remember exactly)
TURN 13- Research warp drive
TURN 14- Don't really pay attention to research anymore -Spot third arcean planet -Attack second arcean planet. It falls -Design another spore ship(S-2) (Cargo hull,spore module,laser,impulse III drive,extended life support) -Rush buy S-2 on Arcea (453bc +28/324)
TURN 15- Send spore ship to third Arcean planet
TURN 16- Spotted Arcean colony ship approaching fourth planet next to my home planet -Rush buy S-2 on my home planet (453bc +28/324)
TURN 17- Spore hip takes fourth (just colonized that turn), Arcean planet.
TURN 18- Spore ship conquers third Arcean planet. Arcean defeated. Score 22 400
I had a good position in this game in that the enemies home planet was pretty close to me. You may have to worry about the range of your spore ships if the enemy planet is located far on the other side of the tiny galaxy.
If you're interested in maximizing your score I don't really know any tricks. Kzintpat, nielo or some of the other heavy hitters on this site would know about that stuff alot more than me.
I've managed to do the ZYW thing on Gigantic galaxies a couple of times today but it's not a sure thing for me and I seem to need the enemy planet to be reasonably close to me in order for me to have a chance at winning. Not sure how the big boys do the gigantic ZYW thing and have no idea how they score so well hehe.
Follow this basic model and I think you'll get yer first ZYW 
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Good luck to ya.
