I've seen a combat run as a skill challenge before, and it worked quite well. I'm wondering, though, if anyone has made more formal rules for a combat skill challenge, beyond "pick main skills and set DCs", particularly when it comes to incorporating powers, HP, and healing surges.
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I've seen combat skill challenges for things like riots and obligatory thug attacks. Any skill was usable as long as we could come up with a description of how we might use it.
For example, a riot breaks out in the marketplace the players must put down the riot and keep the innocents safe. Heal was used to tend the wounded, insight to gauge the intent or morale of the rioters, subduing the rioters called for athletics, endurance, or intimidate rolls. Etc... A failed roll usually cost a healing surge from being beaten by the rioters.
Sometimes, a well timed or very suitable power could gain a automatic success. But it had to be a really creative and effective application of said power. Usually powers would provide a circumstance bonus to a skill check.
I've never seen anyone track hp or healing powers in a skill challenge. I guess because you might as well run a full combat then. The healing surge penalties for failed checks usually seems to be sufficient to capture the consequences of a fight.
Failing the skill challenge sometimes has additional consequences, such as capture, etc. But death seems too severe a penalty. If it's a tough enough fight to kill a PC then I think it would be better run as a combat.
I recommend looking at the "Dungeon Reality Show" adventure from ChattyDM and his other writings for skill challenges. The rough change is that failures should cost the party surges and 3 failures gets them into a (probably quite nasty) combat.