Why would you assume the math needs to be different for skill challenges as opposed to single checks?
It's likely different to serve it's purpose within the skill challenge and have the math work.
On purpose-- The way I run skill challanges is in "cinematic mode". Different than combat enounter mode or general exploration mode. Skill checks represent "strategy actions" that get you closer to your goal and we don't worry about the details of exactly how many feet you can jump, etc. as long as the decription fits within our shared understanding of what somone can do in that "Tier of play". A successful skill check means you get closer to the goal, a failure means no progress and possibility a complication (which might change the nature of what skills are useful). So if we are 5th level and chasing someone through a crowded city, a player could say "I climb up to the roof tops and jump from roof to roof to try to get ahead of him" (Tier appropriate, yes). "I try to convince the 2 city guards near us that the man just stole a valuble gem from a nearby merchant and they should join us in the pursuit" (Tier appropriate, yes). The check represents the success of that strategic action and movement toward the goal but not each individual jump or balance or change in whatever. The fiction changes as we go along perhaps opening up and closing down some skills that are appropriate.
X successful strategy actions before Y failures or X successful before 3 rounds (different math/system) results in reaching the goal (capture the person they were chasing in this case).
The structure is there to provide closure to the scene that doesn't rely on DM fiat and to provide math structure that ensures a challenge that is neither trivially easy nor impossible over multiple checks (there are of course situations that are both easy and impossible -- but don't use skill challenges for them).
As a DM, I need to set some baseline DCs where you know that say a 5th level party that is likely to have +7 mods has say a 65%-70% of success IN TOTAL over the X checks. Or perhaps assume out of a party of 4, 2 have +7 mods for a physical challenge like this and 2 have +3 mods (either proficiency or high ability but not both). You can use creative uses of non physical skills in a physical challenge but perhaps only once a skill per skill challenge per party to let the physical skill people shine a little (wheras in a social skill challenge you might be able to cleverly use Athetics but again only once a skill challenge per party).
Then I can modify up and down that baseline depending on whether I think the challenge is above or below level so to speak. And characters with skill resources can handle above level challenges as well.
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On math -- Because it involves evaluating the results after a set of multiple checks, this likely requires different DCs.
It's like those DMs when I was a kid that made us make 5 consecutive successful stealth checks to sneak around. Let's say you have a 70% chance of succeeding at a single check. If you have to make 5 in a row your probability goes down to 17%
Anyway IMO it's fine to have different DCs because they represent different things. You can even call them something different, Skill Challenge Checks -- SCCs, so as not to confuse people. The checks simply represent ability to move closer to the goal using that "Skill mode" as means to the end.
I'm trying to set the SCCs at the right level so I can run these cinematic skill challenges and know that I'm not making it impossibly hard or trivially easy.
It's a very gamist structure but I find that it creates interesting non combat "scenes" and if the math is fair you can attach fairly meaningful story consequences to the skill challenges. For instance, you could have a wilderness skill challenge where you are trying to push your party to get through the wilds before an orc raiding party reaches a town. As a DM I set the DCs where I know there is ~65% chance of them getting through as I think getting though this wilderness fast is an on level challenge. Over 12 skill checks over 3 days and some memorable obstacles, they fail. They arrive too late and the town has been razed, one of their friends was killed ,and there are indications the orcs took prisoners. It's an easy way to abtract this non combat challenge AND put some non arbitrary resolution to pursuit of the goal.
See Stalker's Obsidian system for 4e for a more indepth look at one kind of skill challenge and the math for 4e.
Stalker0’s Obsidian Skill Challenge System VERSION 1.1 UPDATE!! The system has now moved to Version 1.1. The changes are small, here you go. Changes from Version 1.0 1) Critical Success now gives 2 successes, instead of providing rerolls. 2) Table 2’s victory and partial victory numbers have...
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