Originally Posted by Quirinus
placenik, you forgot to mention skirmishers and archers. In a medium- to large-sized army, archers will be protected behind flanks, from which they will decimate your HAs. Even if they're not that well-protected by other troops, you will still lose in an arrow duel, due to your lower numbers. Charge them and you might rout them, but you will lose quite a lot of your own HAs. So IMO, pitting one HA against a full-stack is not a very viable strategy, as there's a good chance that a full-stack will have a few skirmishers/archers.
A mass of HAs, that's a different kettle of fish.