Horsemen won't win from Hoplites, so you'll need something stronger when facing the greek. However, when you play as the Iroquois, your horsemen will have attack 3, which is VERY nice for rushing
But then again, Persian Immortals are very strong as well, they may not have retreat, but their attack rating is the highest possible in that era, and they also have a defense rating of 2....
You should play on a challenging enough level that you can't just walk over the AI. As DD said, it's hard to blast through infantry with cavalry. Artillery is then your friend.
Samurai play just like any fast unit such as knights.
I tend to look at outdated units as partisans. They aren't good for much but trying to mess up the enemy's roads... and they can be a handicap when they get mowed down by more advanced units that go elite.
I use single unit rushes less often in Civ 3 than I did in Civ 2. In Civ 2 I would build all knights or all tanks or all howizters. In Civ 3 I have to build defensive units and bombard units to accompany my assault troops.
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Above all, avoid zeal. --Tallyrand.
This city was just captured and the enemy is putting on the pressure.
WARNING: Take special note of the lowly Spearmen. You may think they are not important, but they can cut your roads, your luxuries, your resources, prevent you from building advanced units, and send your city into disruption, and possibly cause a reversion. When fortified on mountains, they can be very difficult to dislodge, and can provide a haven for enemy artillery to bombard your city.