Ok, so it wasn't a 1v1 fight, but it was because of one unit that I won the battle.

I was carthage, and my line was made out of libyan spearmen and iberian infantry (crappy stuff). But I had one unit of Armoured Elephants. For some reason, the romans charged my line, even though I was the attacker. In this case, my army had not yet reached it's position, save for the elephants. So basicly, the elephants stood there, watching as the romans charged by it and into my line. Of course, I took the oppertunity, and charged it right into the rear of a group of principes and NEVER EVER have I seen units fly like that! Man, a couple of them must have easily flown a couple of hundred yards. It was hilarious. Anyway, then I just plowed through the ranks of the romans with my elephant from one side to the other in a linear fashion, making every roman unit rout as they got trampled by the elephants.

Don't think I've ever seen an elephant unit get as many casualties as that one got in that battle. Quite funny.