It's like this.
Heroes stream into your dungeon. They want stuff, like gold or to fight. They'll wander on their own, but you can guide them with building visual improvements that catch their attention. Then you create pentagrams which spawn monsters for them to fight, treasure chests for them to loot, and a few other buildings.
Once they're satisfied, they try to leave, and you chase them down with your Dungeon Lord character. Beating them and imprisoning them gets you soul energy, which you use to buy more prestige objects. You take the captured gold from heroes and use it refill your chests.
If heroes aren't finding what they're looking for, they get annoyed and start heading for your dungeon heart to destroy it and you. I guess only when they're not getting filthy rich do they decide to save the world.
Your dungeon prestige (which is the value of all the prestige objects you built) gives your dungeon lord stat bonuses, which he needs to stay competitive with the heroes, who get stronger and stronger. As you imprison more heroes, you eventually get a champion, which is a boss-hero that can kill your DL.
On top of that you have stat points to spend, a skill tree to work your way through, and several gradients of prestige objects, treasure chests, ect... that hold more entertainment for heroes, give it out faster, replenish faster...
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The big thing about the game vs. DKII is this. DKII was a sim. This is not so much a sim, even though it looks and acts like it a lot of time. Where monsters had feelings and motivations, heroes just have motivations. There's not a lot of fun in simply kicking back and watching things work.
In the campaign, you're challenged by different scenarios like escorts, non-hero baddies that march into your dungeon, and needing to explore different corners of the map. You get scrolls or bonus points to spend for beating the side missions, even the time limits are kind of abusive.
In the sand box, it's just about different map designs, which vary how many hero gates there are, and stuff like that.
I'm pretty vocal on their forums about where Dungeons falls short. There's NOT enough sim goodness going on, and there are too many restrictions placed on the player intended to balance out their design system. (This whole tangled web of soul energy, prestige and hero difficulty.) A couple other areas like the skill trees really, really need some post-release attention.
In general, Dungeons is about throwing a lot of activity the player's way, and the challenge of building your dungeon while you're constantly under threat from something. Not ALL levels are like that, but when Dungeons wants to challenge you, that's what it does.
I'm enjoying the visuals, some parts of the design and some of the humor. I appreciated the whole ethos behind the game, sort of like being an evil DM from a D&D game. I'm hoping the game does well enough that Realmforge gets the opportunity to make some changes, and inject some more sim fun and life into the game.