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For a comprehensive summary of the mechanics behind all rolls and modifiers, see Die Rolls.
Difficulty Class (or DC) is a number that must be matched or exceeded to achieve success when rolling for Ability Checks, Attack Rolls, or Saving Throws.
When attempting to beat a Difficulty Class, the die rolled is a 
d20. The modifiers applied to this roll vary, depending on the circumstances and the type of check.
- Rolling a 1 on a d20 always fails.
- Rolling a 20 on a d20 always succeeds (except Ability Checks).