Iaosatae get my vote every time. They make mincemeat of anyone when experienced, and are versatile, and they have many more shots than the archers so it really all balances out, especially where I use them most; sieges. Usually I just stand my slingers in front of wooden walls, and fire at will until all the enemy has retreated to the town square, exposing their backs in the process (just taking a few Gallic towns brought my iaosatae as the Arverni to triple bronze, this way), then halting their fire and turning off fire at will. Then I advance my rams, stopping in front of the wall without ramming. Some units would begin running forward again to anticipate the ramming. My slingers drive them off again with directed fire. Further losses. Then I begin ramming, and as this goes on more units will come forward again, and I whittle them down even further. By now only the town square unit is left, and my iaosatae will have conserved their ammo (I always leave a last few salvos for the endgame).
Did I mention my slingers outrange the archers so before the archers defending the town can open fire, they're running and facing their backs to me because I struck first?
My assault troops storm the breach, sweep away whatever pathetic opposition remains, and surrounds the town square. Then I bring up my slingers, and put them behind the surrounders. Fire two salvos, and the enemy should nicely and obligingly rush out of the town square to engage. Once they rout, battle over.
Either that, or keep firing until they die. That, or (in rare occasions) my slingers run out of ammo, my assault troops storm in (they have overwhelming superiority now) and slaughter the whole bally lot of 'em.
It's a real force multiplier. Now you can trap whole fullstacks in a city and whittle them down. Run out of ammo before the killing is done? No problem. Withdraw, come back again, besiege, and kill some more. Only when the skirmishing has brought the enemy down to manageable numbers, then assault and slaughter.
Even accensi on double silver are a force to be reckoned with. Archers are only one-dimensional--they can only engage unarmoured units effectively. Slingers can do both, are longer ranged, and have more ammo, though admittedly their unit size is smaller. It's pretty balanced, but when you consider that many of the (civilised) faction enemies you will face are armoured in some way or other, it's really much more useful to have slingers.
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