By the way, don't keep the game paused or you won't get any events at all. I'd suggest putting it on half speed and opening the game once every 24 hours to check what event you get. In addition to the 'old friends' event you might get the 'barrel o' babies', as you say. In that case any girl babies would have to grow up before they could have babies of their own, of course.
Nil Desperandum!
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To err is human; to arr is pirate.