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I understand how Insight and Perception can be used passively: for the DM to determine if an enemy Deception or Stealth attempt is successful without alerting the players that someone is deceiving or sneaking.

But the Observant feat in the Player's Handbook states:

[...] You have a +5 bonus to your passive Wisdom (Perception) and passive Intelligence (Investigation) scores.

So in what situation would a DM be rolling something against the player's Investigation without letting them know?

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Passive Investigation could be a way to determine whether to feed players information that their character might pick up on, but the player might not think to explicitly ask. Note that a passive check can be against a DC, rather than an opposed roll. Some examples:

  • From the angle of the body, it looks like the Mayor didn't fall... She was pushed!
  • That pouch looks awfully light to be containing 300 gp.
  • Isn't it odd that the Kobold only steps on every third white tile?

How are these things not Perception? Because what you are noticing isn't remarkable unless you compare it to your expectation of how things should be. It's a test of reasoning rather than of, well, perception. I keep wanting to say "think Sherlock Holmes", but he's also rocking Perception, so that's actually a terrible example. So... Rain Man, maybe?

PHB suggests passive checks (p 175) where the GM doesn't want the players to know they've succeeded or (more typically) failed at something.

A passive check is a special kind of ability check that doesn't involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster....

Hidden checks are fun:

  • Arcana to see whether you realize the mystic sigils on the amulet you're buying are all inverted
  • Animal Handling to determine whether the donkey will kick you as soon as it sees an opening
  • Deception for whether an unseen observer notices you slip out of your false identity when you think no one is noticing

A paranoid player might call for a check for all of these things, but if they don't think to, they won't know they failed until you start giggling.

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    \$\begingroup\$ @waxeagle That's why a canny GM will cultivate a habit of rolling dice for no reason at all (and, if such a thing sounds annoying, you just jot down the result to use later when you need that specific type of roll). \$\endgroup\$ – Stormhound Nov 1 '14 at 9:51
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    \$\begingroup\$ @Stormhound Alternately, roll that d20 about a dozen times before the game; write them down and use them in order. A-temporal die rolling! \$\endgroup\$ – Smithers Nov 1 '14 at 15:06
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What I also use Passive Investigation for, is for example recalling things. Maybe you visited a house of a suspect, you later can, when new clues come up, recall details from there.

For examples, I agree to the other comment that Sherlock Holmes is no good example because he also has a high passive perception..

So, think of someone like Adrian Monk (like in the TV series) when you think about it.

He could maybe been hit on the head by someone sneaking unto him from behind without noticing, because I consider him having a low perception. But on the other hand he could maybe even recall the name of the books that were on the desk of the suspect when they visited him. Or if they talk to him to tell the player "you recall very clearly that the ledger he said he worked on wasnt on the table" if he tells the player something different.

Because I disagree on the part on actively telling the player stuff he isn't looking for. If a player thinks that a room doesn't have to be searched, don't give them away stuff they only would get trough a investigation check.

But hey.. If they later think "damn, I should have searched the room!" they at least can count on their passive investigation, for remembering only very few basic details (DC 10) or quite a lot more (DC 15) and so on.

Also, maybe giving them some ready-to-go conclusions on a high amount, after having them actively rolled. Like, if they investigate the window and the glass shards are on the outside rather than the inside, and the player has high passive investigation, tell them what that means ("so you immediately reason it was crashed from the inside of the house!") instead of only ("you see a crashed window with a lot of shards on the outside"). Because its fair to tell players who have a low passive investigation in real life, but their characters have in-game, to use it for such hints.

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