You can build 4 banks with the normal build limit
The Bank of Amsterdam (a HC card, level 0, sent in age 1), can be sent to add 1 to your build limit, raising you to 5.
The Bank of Rotterdam (a HC card, level 0, sent in age 1), can be sent to add 1 to your bank build limit, raising you to a total limit of 6
Unique Church Techs (a HC card, level 10, send in age 2), can be sent. Researching the coffee trade (it's free) tech there adds another 2 build limit to your banks, letting you have a total of 8 . However, the coffee trade card is not usually one I send. I find that 6 is plenty. Plus, taking coffee trade lowers ALL infantry speed by 10%. Thats pretty rubbish. Speed = yummy. However, the 'Drummers' upgrade (from the 'Advanced Arsenal' (a HC card, level 10, sent in age 2)), costing 150 wood and 150 coin, will raise infantry speed by 10%.
So, in short, you can have 8 banks and normal infantry speed, but it will cost you:
4 HC shipments (Bank of Amserdam, Bank of Rotterdam, Unique Church, Advanced Arsenal
150 Wood, 150 Coin (from the drummers upgrade)
Due to this, most players would not consider it worthwhile.I certainly don't think 8 banks is necessary unless you are in a long game. If you find yourself in a long game and needing 8 banks, then simply build a church, research Mercantalism (gives you 2000XP (it ironically costs 1000 gold...)). Then, using the shipments you get from that (about 2, or possibly 3), you should be able to ship the Unique Church, and Advanced Arsenal Enjoy (sorry for writing so much)
-=» ESO2 name = Liquify «=-
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