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I do not necessarily agree. I usually use the "Toys for Boys" one, because the benefits for a very happy empire are very strong. You get more food, dust, science and influence at the cost of some industry. If you can use the cram exam act without going below 70 or 85% approval then obviously it's a good idea, but with some factions it's not the *best* choice.
Would you rather have +10% FD, +15% SI and -10% industry, or +3 science per pop at the start of the game? The malus to industry sucks, but you can argue the bonus to food will get your pop faster and overcome the industry malus compared to if you did not have the food bonus. For this reason, I believe starting as a Republic is not bad.
Unless you are playing as the Riftborn, So long as you don't go below 30% approval, sacrificing early industry sounds awful. But they also start as a republic, rip. Vodyani wouldn't benefit as much either from the difference between early game Toys for Boys or Cram Exam Act.
-10% ind isn't as much as it sounds on faster speeds, since it probably won't change the number of turns needed, and you're probably building production improvements anyway
Federation is god late game.
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Republic adds major effects to some of the 'auto-laws' that each party has:
Religious: +1 Influence per person
Ecologists: +1 Food per person
Pacifist: +1 Dust per person
Scientists: -10% Tech costs
Indu just gets 15% dust instead of 10%, and war party gets bonus approval on war.
But those bonuses change the early game vastly depending what you're doing. +1 dust PP is enough to tilt early game economy well into your favor and make rushing easier. +1 influence means laws are basically free; +1 Food means your systems never starve early on.
But it's the tech bonus that's critical. On Sophons, it means all techs that get their 50% omni bonus cost 45% of maximum, on top of any other bonuses. It doesn't sound like much, but consider that with Oracle you're likely going to be researching T3 techs before turn 50. This changes it from a 'normal' 45 turn slog to an easier 15 turn. If that.
Without Omni, it's a 90% of maximum cost, which is still significant. That can be a whole 1~5 turn difference. It makes Science-Conversion easier to grab early on and rush the techs. Remember, turn 50 is mid game, turn 100 is end game.
Federation on the other hand is mean to compete with Democracy, which main draw is bonus approval, more laws and parties, and reduced law costs. While the bonus system cap is nice, by the time that Federation is relevent it's irrelevent. The critical thing is the -20% System Development cost. This is massive. This is a whole star system worth of difference. Especially if you're rolling with a custom faction or Vaulters. It means you can more quickly build up to Sys-lvl 4 and roll out Auto-admin improvements and raise the system cap. It also means you can reach a 180% fids bonus-- or a 505% bonus if you're using Material Experties and Quadrinix.
One you finish bumping up your systems to lvl4, switch to Democracy or back to Republic. There's no point to sticking with Fed after you've tooled up....And better or more laws is flat better, trust me. Especially when you can make some of your fleets esscencially free.