Byzantium has +3 ToTF, being the single nation in the game to have it in its ideas. All other ToTF ideas max out at 2, with some being 1. This means that your Orthodox provinces basically have -5 unrest, since being Orthodox already gives them -2 unrest.
-10% advisor cost is decent early on, but great in the mid-late game where you can stack level 5 advisors to overload yourself with MP.
-15% mercenary maintenance used to be good, but the merc rework made using mercenaries pretty bad, so it's kinda meh now.
+10% manpower is usually a standalone idea by itself, but the +5% goods produced on top of it makes it a very solid use of a idea slot.
+10% tax is filler.
So is -10% stab cost.
+10% global trade power is pretty useful, although it does come kinda late in the idea set.
+5% discipline is great.
Byzantium's +3 missionary strength, akin to its ToTF, is exclusive to it, with the only other way of getting +3% being from religious ideas. Stack Orthodox's +2 missionary strength on top of that, you get a flat +5% missionary strength, without even taking religious ideas. This, along with the ToTF, is what makes Byzantium's idea great. Late-game, you can stack missionary strength to convert non-cored heretic provinces in 3 months, while also maxing ToTF at around 16~18, which along with the unrest modifiers mean you have no unrest on freshly conquered provinces, even without humanist. Another note that Byzantium can get 7 (8? Not sure, it's been a while) missionaries.
+1 prestige is filler, but not useless.
So we have 4 great ideas, 2 decent ones, and 4 fillers. Are their ideas trash? Heck no. If you want to see some real trash ideas, look at Betsimisaraka, Navarra or Genoa.
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