my experience has so far shown that the number of family members is determined by game situation and at least not entirely by random factors. For example, if you expand quickly, a whole slew of children will be born. Likewise, if you are stagnant, no children will be born.
If these heirs were all adopted I could understand because that makes logical sense. If these heirs are not adopted then yes, the computer is cheating. Unfortunately, the only way to tell would be to see the nme AI's family tree so you could see how many kids were about to come of age.
And while I kind of like the adoption mechanism when the situation is desperate, I really don't like it when you're doing fine because the AI only seems to provide you with enough males to govern your cities and does not provide you with a surplus number to command your armies.
The fertility of my family should be completely independent of game factors, save for the Fertile/Infertile v/v. The number of cities I own should have no affect whatsoever on how many kids are being born.
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