Yes, barracks boost the infantry production, as well as moral.
Posts by Bagif
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There are also tutorial maps where beginners get 200 infantries (20 each province) and an artillery unit.
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There are something called a “Double Production Provinces” which produce double as much resources as the rest of the provinces, they have a shorter production time than other (22hours compared to 1day 2hours). However it’s a small difference so your enemy shouldn’t have that much of advantage (at least the first day).
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Percentage only increases the chance of AI to declare war on you, like for example an AI that has 30% relation with you will have 15% to declare war on you, while the one that has 10% has 80% chance to attack you.
(Note: this is just an example, not an actual thing)