You could fight other players or the AI. I think serial cables was waaay back, wasn't it? As in, pre-Internet? I recall some Atari games had that option. Playing the DK games against another player is done through an online thing - there's a lobby and stuff where you can go to see if anyone is up there looking for a game, I think.
You can do some form of Sneaky Bastard Tactics in the games - there's a spell called Sight of Evil, for example, which you can cast over an area of Fog of War and it'll reveal it for a short time so you can see what's beneath (if anything). In the first game, though (can't remember whether it worked in the second), you could mouse over areas on the map and hear any sounds emanating from there. As such, in levels with a rival Keeper it was easy to find their Dungeon Heart because you could just mouse over the map until you heard it beating - then you knew which direction you needed to head in order to find it. There was also a spell (only in the first game) called Disease. It used a lot of mana, I think, and could only be cast on creatures which were standing on tiles belonging to you (like most spells). But if you could just tag an enemy creature or two with it and then basically leave them to it, eventually the disease would spread amongst all the creatures in that dungeon, slowly killing them all. Then it was just a matter of heading in there and easily destroying what was left. You could cure diseased creatures by putting them into the Temple (not sacrificing them - just put them on the floor), but the AI never seemed to bother with this, that I recall. Oh well, their loss

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You could also use the Call to Arms spell (both games) which would place down a waving banner - all your creatures (except Imps) would head to that flag and basically mill around there. So what you'd do when ready to take on another Keeper (or a hero fort, or whatever), would be to place down a Call to Arms flag at the entrance of their territory (I think in the second game it only drained your mana if it wasn't on a tile you owned, so if you made sure your Imps were claiming land as fast as your creatures were moving forward, you could keep moving the flag and not worry about mana loss), and then chuck all your creatures as close to the flag as possible. If it was another Keeper you were attacking, he'd probably then also dump all
his creatures at that spot and there'd be a massive free-for-all. But eventually you'd get far enough that you could drop the flag beside their Dungeon Heart (not applicable in Hero forts, of course) and hopefully you'd have enough creatures left to just destroy it, at which point any surviving creatures in the enemy's dungeon would immediately head straight for the nearest Portal. I think Imps probably just automatically died or something.
Attacking an enemy Dungeon Heart was obviously made much easier and quicker if you broke into their dungeon at a spot as close to the Heart as possible, and preferably avoiding always-busy rooms like the Lair or Training Room.