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I'm a Dungeon Master, and I can't figure out how passive wisdom works. In the Player's Handbook it says:
A passive check is a special type of check that dose not use any dice rolls.
That is good to know, but it does not say how you determine if something is a failure or a success!
Let's say an enemy is hiding with a Stealth check of 15. Your players with 16 (or more) Passive Perception automatically detect the creature, they are aware enough to hear its breathing or notice its disguise. Same thing for a hidden trap.
Passive Insight against NPC Deception checks is also common in many tables. Basically, the passive check has to beat the DC of whatever it is against.
Specifically, the rules which define passive checks (PHB p. 176) don't specify how success or failure works because they are the same. Or, the success/failure condition is the same, because the rules don't change them.
Either way, you succeed on a passive ability check if your result is equal or higher than the DC you are making it against. The only difference is that instead of your result being the result of a d20 roll plus your modifier, it equals your static score (which is 10 + said modifier).
Obviously replace DC with the appropriate check result if you are using it in a contest, such as a creatures Dexterity (Stealth) check against other creatures passive Wisdom (Perception) checks when hiding.
