When a DM says make a skill check, how do they decide what value they need to beat?
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Skill checks are easy, medium and hard in difficulty. Take the level, compare it to the difficulty, you get a value.
See this article for the current guidelines: http://www.wizards.com/DnD/Article.aspx?x=dnd/drdd/2010september
Use your judgment.
This is a tough pill for a new Dungeon Master to swallow, I think. "My judgment?! I want the rules to tell me what to do!" That's understandable.
But part of the art of game mastering is learning how to make good judgments about play. D&D and similar games leave a lot of decisions about what happens to the DM. A good DM applies the following principles when deciding things:
The 4E rules do give guidelines for skill checks. These are supplemented by the discussion of skill difficulties in the article Design & Development: Skill DCs (Dragon #391). This article lists easy, moderate, and hard difficulty targets by level and describes the three categories as such (excerpted):
While these categories still leave the DM in a position where he or she must use judgment to determine what is easy, moderate, or hard, the categories and their definitions do simplify matters. Very easy and very hard tasks naturally fall into the outer categories. It's only the challenges of middling difficulty that you need to think about.
Do you want that task to be easy? Do you want that task to be hard? Generally, if you are wondering about it, it's a moderate task. The difference between categories is +4 at the lowest levels and +8 at the highest. It's significant, but not a deal-breaker. Apply the principles I listed above and make your best decision. Keep play moving.
The players will help, too. If you make a decision that is way off, most likely the other players will check you on it. Listen to them, consider their arguments, and then reconsider your decision.