I play EAP and have prepared my army to encounter HF-plenty armies (I only have played 10 games, and most of them agains such armies, though in the last tournament, shoot cav armies were more common, and thus I ended 17 th

)
Anyway, against a Republican roman, my last game, I could finally use my plan, and worked perfectly:
Sparabara in one flank, asisted by greek Cv. Immortals, persan cav and hoplites in the other flank. Hoplites more centered. My center was the rest of persian cav and skirmishers. The plan is to advance in the center and flanks. Then, fall back in your center with your cav, while you keep on pressing on both flanks. If the romand had tried to reinforce their flanks, my persian cav would have become menacing enough to stop him. In the moment of the clash, sparabara kill enemy cav, immortals envelope the end of infantry line, and central cav keeps on shooting-falling back. Hoplites clashed against some protected HF in the center and becomes a sweet for the rest of roman HF, which forgets about their flanks and go for the hoplites, giving me time to finish them on both wings.
So, the key is attacking the ends of the line while you fall back in the center with units strong enough to become dangerours if the enemy tries to redirect some troops to the center.
Other plan, I tried agains medieval knights, was immortals more centered in front of knights. I advanced them to the center of the table. When the enemy was near enought, I just turned them 180ยบ (while stationary, does not need CMT for drilled troops), and then fell back. Knights could not reach me, but pursued me till my long border, where I had a hill. When immortals reached the hill, I turned them againd and begun to shoot knights. Then, he could have only charged me or turning 180 to leave. In the first case, I was in rough hill, so I was uphill, and he would have fallen to several disordered. In the other, I could have charge their rear. (here the time run out, but it would have been very nice. The game endend with a draw).