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Reading through the basic set there is a DC Check difficulty table found on page. 58, but aside from the basic description of what a check is and the basic mechanics (d20 + mod/skill + any situational modifiers vs. DC) there are no guidelines for how a DM should assign DC levels to various tasks. Are there any guidelines outside of the Basic set that could inform 5e DMs?

DC Table

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up vote 7 down vote accepted

Yes, in the starter kit

In the introduction section of the Lost Mines of Phandelver there is a primer section for new DMs which includes descriptions of what type of activities would make up the Easy, Moderate, and Hard DC check levels.

  • Easy (DC10). An easy task requires minimal level of competence or a modicum of luck to accomplish.
  • Moderate (DC 15). A moderate task requires a slightly higher level of competence to accomplish. A character with a combination of natural aptitude and specialized training can accomplish a moderate task more often than not.
  • Hard (DC 20). Hard tasks include any effort that is beyond the capabilities of most people without aid or exceptional ability. Even with aptitude and training, a character needs some amount of luck -- or a lot of specialized training -- to pull of a hard task.
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It's also worth mentioning its advice for easier and harder tasks is to just say yes/no. – SevenSidedDie Jul 15 '14 at 16:15

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