I was really just trying to tie down the actual number of Waves...

[ Perchance you view all of the Waves as simply the original Emergence irrespective of the Year/s in which they arrive. I tend to view Groups which arrive in different ( non consecutive ) years as separate Hordes / Waves. ]
No, I'm counting the same way - IF I'd ever seen the Mongols doing what you describe, then I would regard it as separate waves - but I have never, ever, ever seen more than one wave in any game.... Perhaps I just kill them (or the Khan) off too quickly

I usually try to position myself for an early bridge defence battle, with lots of arbs and halbs, with the intention of killing the Khan, whether or not I can win the battle. My second line of defence is as many princesses as I can find.

@K9 - yes, they do seem hard-wired to go for the human player, if they can 'see' you on the map - even if you're a harder target than the AI faction on their opposite border. I've had at least one game when they've made it all the way to Ireland (can't remember who I was playing though, maybe Almos)