" ...I may be thinking about this wrong, but let's go with this - DC 30 with 6 rolls required before 2 failures. Assuming a +15, you have a 50% chance of a success per roll and a 50% chance of failure. So what's the chance you'll fail before you make it? Let's just go with the stats of what it would be if you got to roll all 6 no matter what, which is approx. 25%. The SAME thing could be accomplished by having someone with a +15 roll against a DC35..." Anonymous Friend.I just couldn't help myself from chiming in when I read this. Skill challenges in 4th Edition Dungeons & Dragons are not easily reduced to equivalent single-roll "skill checks". They are more aptly represented by a collection of negative binomial distributions. This is likely technobabble to many of you, but suffice it to say that skill challenges represent a slight modification of well known type of probability distribution. Negative binomial distributions are usually those that describe a situation where you want to measure the probability of X number of successes before you reach Y number of failures given a probability of success P. The "slight modification" comes in because you are also considering that you might get all your successes before having any, or only some, of your failures.
I used Google Spreadsheet's bionomial normal distribution function to make these calculations by summing three distributions together that each had a different threshold for failure (0, 1, or 2 failures) like this:
=NEGBINOMDIST(X,N,P)+NEGBINOMDIST(Y,N,P)+NEGBINOMDIST(Z,N,P)where N is the number of successes needed, X, Y, or Z are the number of failures observed (0, 1 or 2), and P is the probability of success for the skill checks.
So, in the table below I have outlined the probability of success for a skill challenge that requires N number of successes before 3 failures. Across the top of the table you can see the actual d20 die roll needed for the success, and along the left you can see the total number of successes needed for the entire skill challenge to be a success. I'm also assuming that three-failures always represents failure of the skill challenge as a whole. Of course, this is still a simplification because I'm also assuming that the all the rolls would have the same DC - which of course is rarely the case. The table is also incomplete, but it gives you the general idea: skill challenges quickly become very hard as the complexity increases.
UPDATED -- 1/9/09 -- UPDATED
Use the above table to give yourself a rule of thumb when designing skill challenges. What's important to realize is that Complexity 5 skill challenges (i.e. 12 successes before 3 failures) are extremely hard even when needing very low rolls. I have no doubt that this is the reason why the DCs for skill challenges were made to be so low after the 4th Edition Errata was released for the Dungeon Masters Guide. I also believe this is a point many DMs miss.
Hopefully this post has shed some light on why the difficultly of skill challenges can be tricky to guage, and possibly helped a few folks in the meantime.