Thanks for the welcome Fisherking!
I also think that friendship doesn't mean, let's say enough, to the AI. But although it's not enough, it does haveeffect on diplomacy.Spoiler Alert, click show to read:
They definitely are more likely to deal with you the friendlier they are towards you. Sending some porcelain to somebody who refused to become my trade partner quite often made them think twice about my trade proposal. Sometimes of course with some additional cash during the trade proposal (which wouldn't have been sufficient before I sent the porcelain).
And when parts of the expensive porcelain get broken after time, causing our relationship to get worse again, some of those intellectual masterminds get the brilliant ideas that the best solution for everybody is to cancel their trade agreement with me. Well, I still own the by far richest nation in the world (GB in that sample), and they get closer to bankrupt for not trading with me (Sweden in that sample).
On the other hand, the AI's decision between war and peace usually does not sufficiently consider friendship. There is some part of randomness in the process, as some other people already posted in the forum. But I think there are also some territorial decisions.
Quite often I got declarations of war from small nations, e.g. some native American tribes, after expanding my territory close to theirs - even though the relationship between us wasn't bad. The stupid part of it is, that I didn't want to expand further ever. I didn't want their territories. I just wanted (as GB once again) to get rid of the French in between our two nations, and establish a trade route to the natives. That part usually works, but not for long. A few turns after I became their neighbor they canceled the trade agreement and declared war. I think I don't need to mention that they were history a few turns later.
I hope with one of the next patches the AI will be able to vague the risks of declaring war to an extremely mighty country in their neighborhood who want to be friends and trade partners.
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