RE: "war of attrition" - Yea; a bunch of relatively cheap defenders (archers, feudal sergeants, and some light or medium cavalry to take out enemy missile troops once the heavy Mongol cav is committed and fighting from the woods really nails the only good troops (the heavy cav) that the Mongols have and they usually can't seem to rebuild them. I've also had success at destroying every building in the provinces and falling back.
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