Celebrim said:
1, 2, and 3) Should the DM ignore the narrative with respect to skill checks if the checks used to not entirely fit the situation at hand? If not, are these rules even needed in the first place?
4) Should the DM ignore spectacular stupidity or implausibility, such as answering a Diplomacy check with an attack roll?
Please keep in mind that I'm not saying that the DM can't successfully invent explanations, nor am I saying that it is impossible to adhere to the rules and also provide a logical framework.
There are a few ways to look at this. One is that in addition to spinning the narrative relative to the checks for a skill challenge, the DM can also decide which skill check successes are applicable to the challenge. Following the intent of the rules is generally better than following the rules as written in some cases, and this is one of them. No one would say that a successful Craft (Basket Weaving) check should count as a success in a chase scene. If the PC's are just going for a bunch of Knowledge checks, you could consider some of the checks to be extraneous to the challenge.
As for handling a spectacular failure due to the choice of a course of action, it comes down to a DM judgement call. Some things do not work, and should not be allowed to have even a hint of success. My own reccomendation is to allow a 'Failure with consequences'. The players get 1 failure towards screwing up the challenge, and the guy who commited the stupid act probably incurs some real damage.
Now, given those views, should we even have the codified system in place at all? How is it better than a DM pulling things entirely out of his arse?
Rules that do not interact with combat in the D&D game tend to fill the same role as Military doctrine, in my view. Doctrine is what amounts to 'given this set of circumstances, these responses are typically optimal'. Not all situations are typical, but having a default fall back plan in place allows you to respond much more fluidly to otherwise unanticipated situations. On top of that, the system does have quite a few things going for it.
1) It is widely applicable. The X success before Y failures mechanic can be adapted to face to face negotiations, chase scenes, traps, physical obstacles, and library research. Learn one rule, and you know how to run a huge number of in game situations.
2) It is simple. Consider these sentences. "Decide on a number of successes and a number of failures. To win a challenge, the players need to attain the number of successes before they reach the number of failures. Pick a DC for Easy, Medium and Hard. Succeed an hard check, and the players get an extra benefit on success. Fail an easy check, and the players suffer an extra penalty". Do you really think you will need to flip through the rule book to use these rules in play?
3) It allows for multiple right answers. There was an example of a pursuit challenge where one player chose Bluff for his check based on the notion of lying his way out of trouble. Another player chose Endurance / Athletics and just tried to out run the pursuers. This approach is a great deal better than having the DM or the adventure determine which skill check would be used. It increases player choice at the game table in how a situation will be handled. It also increases player involvement.
The last thing I will comment on is that it breaks immersion at the table to announce a skill challenge. I will answer that with a question.
Is player immersion in the game more important than player involvement?
As a DM, I would prefer to have my players having out of character meta game conversations about the matter at hand to having them involved in out of game conversations about the movie they watched last weekend. Having the players fully immersed in the narrative of the game is great, but it is pretty damn hard to pull off. But having everyone at the table involved in the game at hand makes achieving immersion a great deal easier.
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