A barb camp will appear (whether it does this check for every time, or just the first, I don't know) when the total number of cities>=2*number of players (don't know if that counts dead players) and every living player has at least one city, (I'll go ahead and copy some stuff I learned earlier) and given sufficient space (in a spot no unit with attack or defense or borders can see, I assume) and if there are fewer camps than number of players (haven't tested what happens if a player is eliminated). A new barb unit (this may change when they start producing new stuff, i.e. horses or galleys) may appear (in one test it took four turns) when there are less than 2, 3, or 4 (for roaming, restless, raging respectively) barbs per camp (or perhaps number of players). The distinction between will and may is intentional.