On a strategical level, don`t bother to fight HA armies in the field. Take their cities instead. For this purpose thureophoroi are your friend. Spear armed, decently armoured and cheap, they can chew through anything, nomads will throw against you in melee. Just get to the town square and wait till the timer runs out. Thureophoroi are also much more flexible than phalanxes, when you need to react quickly to a flank charge and whatnot - in my anti-nomad armies they take the role of main infantry unit along with lots of foot archers.
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