They are best used where the decisive action will take place, either to force their way through enemy infantry, or to repulse the heavy cavalry of the other Greek states.
Hail Arche! Your finest warriors, the true elite of the polis, stand here before you. They are drawn from the bravest and wealthiest men. They eschew the horse, preferring to allow their brothers who are too cowardly to fight on foot the role of cavalry. They are armored in the finest bronze armor, with shields made from only the best and stoutest wood. These shields are faced with fine leather or bronze, and in the skilled hands of your greatest soldiers, they can stop all but the most determined blows. The spears of these fine soldiers are made from the best cornel wood and iron. All of them are battle tested veterans. None will shirk from the shield wall and the killing, for each regards it with the cold dispassion of an elite soldier that belies their name: the Epilektoi, or picked ones.
Historically, the Greek poleis fielded small numbers of extremely hardened and well armed warriors. These soldiers were every bit the match of the elite units of other nations, as proven in engagement after engagement. They are best used where the decisive action will take place, either to force their way through enemy infantry, or to repulse the heavy cavalry of the other Greek states.