When the GH first emerge they can appear in 1, 2 or 3 different provinces, depending on the current strategic situation.
Khazar - usually the bulk of their forces, typically 15 stacks
Georgia - smaller, but still pretty big
Armenia or possibly Edessa - again a smaller army
This is all basically the one emergence. Like any other faction though, if you kill off the royals*, the rest will turn rebel, but there is always a danger of re-emergences. If the faction re-emerges, you'll get a NEW army somewhere, plus the old rebels will revert to GH faction.
How many times this happens is all down to your individual game. It's always interesting to have the whole map revealed (.matteosartori. cheat code) at emergence time, just to keep an eye on them - or flood the area with agents so you can see without having to use the cheat....
* on the first emergence there is only ONE royal - the Khan - so if you can kill him in the first year, the faction goes rebel straight away. I think there are a couple of immature heirs, but theyb take a couple of years before coming of age. It's a narrow window, but there IS a window when you can knock them out. It's worth having some emissaries in the neighbourhood, as Mongol troops are very cheap to bribe, and have low upkeep costs, and it's always nice to have a few Mongols in your army![]()
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