Fourth Circle demons only spawn when the Lord track has cycled back to 1. This takes anywhere from 9 to 4 turns, depending on how many players are in the game. Sometimes it takes slightly less or more time, depending on certain gifts or abilities that affect the Despair track. (For example, when a Texas Ranger dies, you get to lower Despair by 1.)
Fourth Circle Demons are particularly mean, because they roll 4 attack dice (the exact magnitude of which varies with the particular demon), and they have 4 hit points. Lesser demons are killed with a single hit, but you have to wear down the Fourth Circle over time.
In addition, they score no less than 4 Doom if they exit the map! On the other hand, if you manage to kill one, you score 4 courage. Sometimes this does lead to squabbles among the players, because damaging a 4th circle gives you nothing. Many’s the time I’ve hit a 4th circle demon 3 times, lowering it to 1 health, only to see some other player run in for a cheap shot, finishing it off and gathering all 4 courage for himself or herself. Ah well.
The Fourth Circle demons act like bosses in a sense. All of them affect the map in a major way, and while one is in play, it is definitely the center of attention, with the players either trying to avoid it, or gang up on it to kill it.
A lot of the 4th Circle demons boost the other demons, or have some other effect which the players decry. Really, they affect the ongoing part of the game even more than the Demon Lord itself. Though when the players finally come to grips with the Lord, he is far more brutal & important.
The core game features the Hellhound. It has an “average” attack of 4d10 – nothing you’ll want to endure. Its special power is dire. Basically, if no hero is in the Hellhound’s area, it attacks anyway, targeting ANY hero in ANY area, chosen by the team captain.
This means that hiding away from it won’t work. It’s going to keep attacking you no matter what. So you may as well try to kill it. Luckily, its fairly low defense of 4 means you have a good shot at killing it though it might take you 2-3 turns, depending on dice luck, hero advancement, and the like.