3

Simple as that - is there any reason to build upgrades on tiles that are more than 3 away from the city? Normal ones, not the ones with luxury/strategic.

5

The only reason to build upgrades there is to secure strategic or luxery resources, to build forts to better defend a particular set of tiles or a citadel to expand your border to get a certain set of tiles within your control. Other than that, you can always build upgrades for a future city.

8

One additional case where it's worth building improvements more than 3 tiles away is when you're playing as Polynesia.

You get +1 Culture per Moai, plus +1 Culture for each directly neighboring Moai. Moai outside your workable area still count as neighboring Moai.

So if you're building a lot of Moai, it's worth building Moai 4 tiles away, so that they'll add the neighbor bonus to the ones 3 tiles away that you can work.

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