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My friends and I have been playing Heroes 3 since its release, and we play with slightly different rules than those offered on your portal. For example, we don't use Conflux or Necropolis at all (but if we happen to find a random resource or a Vidomina mine, we'll mine it until we're exhausted, which happens rarely but can solve problems).
So, the classic strategy has long been Castle against Sylvan (because Knights, as many have already pointed out, are fast and allow for quick scouting and breaking through small, and sometimes quite solid, blocks). It's also quite common to play Castle against Dungeon (for the same reasons: speed + quickly built bears and hippos). It's quite difficult to start against Castle playing as Tower or Swamp, as you have to stay in your starting area.