What are the mechanics behind tile acquisition?
If you go into the details of a city, it outlines one or more hexes with a purple border, which indicates possible tiles that will be acquired the next time the city generates enough culture.
However, it is not clear which tiles the game favors, except that it seems to prefer tiles with improvements (eg natural wonders, resources, etc). In some cases, as many as six or more tiles could be highlighted, and not knowing which one will be chosen ahead of time makes planning difficult.
I have also noticed that it can be cheaper to buy tiles from one city, rather than from another, but I can't figure out what determines the cost for buyouts. Highlighted tiles seem to be cheaper, but beyond that I can't figure out why one city would cost say, 65g, while another would cost 110g for a tile.
Finally, what determines the radius of the tiles that could be chosen? I noticed that very late into the game, cities could grow to a 4 or 5 tile radius (even if they can only work tiles with a radius of 3). It feels like it tries to grab land first, then water tiles once it has exhausted the options.
Best Answer
City border growth attempts to choose the best tile for that city. This is based on yield, so cities will prioritise hexes with resources, or tiles that provide what the city needs. Cities may also acquire tiles to gain access to another tile if that tile is particularly lucrative- usually strategic/luxury resources. Cities also tend to prefer tiles closer to them- tiles two hexes away are often taken before those 3 hexes away and tiles further away are almost never taken until all the workable ones are.
The cost of manually acquiring a tile is inversely proportional to how likely the city is to take it itself. Grasslands and resources, for example, are relatively cheap because the city wants them anyway. Useless looking deserts, on the other hand, are often expensive.