Just-In-Time Compilation

Short Version:

If players would roll on something that yields a result of unknown resolution (knowledge, hide in shadows, demonic possession), don't roll when the event actually happens.  Roll when it actually matters.

Basically, you delay settling the fiction until it actually matters.  Up until that point, it exists in a quantum state, where both results are true until something forces that result to be observed, upon which it settles into one state or another.  

This is faster, prevents repetition, and neatly circumvents a bunch of metagaming.

Long Version:

I think I'll explain through examples.

Example 1: Cursed Sword

Traditional

Player: I want to pick up that mysterious sword.

DM: Okay.  Come with me into the next room.

(Player and DM leave the table, enter the bathroom, and lock the door.)

Player: Why are we in a bathroom?  Is this a sex thing?
DM: So that sword was cursed.  It's trying to take over your mind.  Make a save.

Player: (rolls) I failed it.

DM: Okay.  So the sword is controlling you.  When we go back to the table, pretend to be yourself.  But you're evil now, so you're going to betray the party the first time you get a chance.

(Player and DM return to the table.)
Everyone Else: Why were you guys in the bathroom?  Was it a sex thing?

DM: No.  Just a chat.  Player noticed some interesting runes on the side of the sword.

Everyone Else: Ah.  Cursed sword, then.

(Later on, the party fights some antipaladins.)

Player: I stab the wizard in the back!  I'm evil now!

Goblin Doctrine

Player: I want to pick up that mysterious sword.

DM: Okay.  It has some interesting runes on the side.  You can't read them.

(Later on, the party fights some antipaladins.)

DM: Player, make a save.

Player: What for?  (rolls dice)  I failed it.

DM: Okay, so that sword was cursed.  It's controlling you.  You need to betray the party now.

Player: I stab the wizard in the back!  I'm evil now!

Example 2: Hiding

Traditional (Secret)

Player: I want to hide in the shadows before the goblin enters the room.

DM: Alright.  What's your Stealth?

Player: 65%

DM: (rolls dice in secret, notes that player succeeded at the check) Okay.  You think you are hidden.

Player: Cool.

DM: The goblin walks into the room and doesn't seem to see you.  He begins taking a piss on the far wall, facing away from you.

Traditional (Open)

Player: I want to hide in the shadows before the goblin enters the room.

DM: Alright.  Make a Stealth check.

Player: (rolls dice) I succeeded!

DM: The goblin walks into the room and begins taking a piss on the far wall, facing away from you.

Goblin Doctrine

Player: I want to hide in the shadows before the goblin enters the room.

DM: Okay.  You hide.  The goblin enters the room.  Make a Stealth check.

Player: (rolls dice) I succeeded!

DM: The goblin doesn't seem to notice you.  He begins taking a piss on the far wall, facing away from you.

Example 3: Knowledge

Traditional (Secret)

Player: Can I make a check to see if the jelly bear has any weaknesses?

DM: Sure.  What's your Int?

Player: 13.

DM: (rolls dice in secret, notes that player fails the roll, rolls again to determine if the player remembers nothing or makes a dangerous mistake, notes that the player makes a dangerous mistake) You remember that jelly bears are weak to fire.

Player: I throw my torch on the jelly bear.

DM: The jelly bear happily swallows your torch.  It ignites its internal jelly glands.  It is now a napalm-breathing jelly bear.

Traditional (Open)

Player: Can I make a knowledge check to see if the jelly-bear has any weaknesses?

DM: Sure.  Make an Int check.

Player: (rolls dice) I failed it!

DM: Alright.  You don't remember anything about jelly bears.

Goblin Doctrine

Player: Can I make a knowledge check to see if the jelly-bear has any weaknesses?

DM: Alright.  You remember that jelly bears are weak to fire.

Player: I throw my torch at it!

DM: But is it really weak to fire?  Make an Int check.

Player: (rolls dice) I failed it!

DM: You were incorrect.  The jelly bear happily swallows your torch.  It ignites its internal jelly glands.  It is now a napalm-breathing jelly bear.

Discussion of Advantages

1. Prevents Player Metagaming

This old chestnut.  If the roll is open (i.e. the player knows whether they succeeded before the DM announces the results) it can taint their action.  If a player knows they fail their perception check to find traps and the DM tells them "you don't find any traps", they are still going to suspect a trap.

Even if the player doesn't want to metagame, it's hard not to.  If the other players suspect that one of the PCs is mind controlled by a cursed sword, it's very difficult for them to behave 100% naturally.

2. Players Roll More Dice

As a DM, I hate rolling dice.  I'm busy enough as it is.  If I have to roll in secret, then make a note of the results for later, it's a pain in the ass.  I'd much rather have the players roll the dice, as long as it make them metagame.

Additionally, players like rolling dice.  Let them roll their dice for their stats.  It makes it feel like they have more agency, and the dice are all out in the open where everyone can see them.  Speed, agency, and trust.

3. Prevents DM Metagaming

There's a reason that researchers like double-blind studies.  If the DM is aware of something that the players are not (e.g. that the hidden rogue isn't as hidden as they think they are), it affects the way that they DM.  When the PCs have fucked up but don't know that they've fucked up yet, there is a tendency to go gentler on them.  The inverse is also true.

4. Faster Explanation

In the Cursed Sword example, the DM only had to explain things once, to the entire table at once.  If he had taken a character aside for a private discussion, it requires everyone to wait while the DM and the Player talk.

5. Faster Resolution

In the Knowledge example, if the player had failed the Knowledge roll, the DM could have (a) said "You don't remember anything", which is boring, or (b) make the check in secret, then roll again to determine what result they would have gotten if they had failed.  This requires multiple die rolls and sometimes the consultation of a chart.

Additionally, sometimes players make a check that ends up not mattering.  If a player had wanted to set up a trap in a room and then hide in the shadows, that's potentially two rolls wasted if the goblin decides to walk past the room without even entering.  Instead, make the hide check when the goblin has a chance to see the player (not when the player hides) and make the trap check when the goblin steps on the trap (not when the player builds the trap).

Discussion of Disadvantages

1. Strains the Fiction 

I.e. "How can it be a narrative if things are happening out of order?  Isn't this just ret-conning?"  

It's not ret-conning because we aren't changing any established facts.  We are just finding out what those facts were at the moment when it becomes knowable/relevant.  In a way, it's more realistic to discover if a Knowledge check was true or not at the point where it is experimentally tested (hypothesis: jelly bears burn well) rather than at the point where one attempts to remember it.

If pushed too far, it can stretch the fiction.  In the cursed sword example, if the player had succeeded on their roll, the DM might have said "The sword tried to control your brain but you shook it off."  If that was said, the player would know that they were now in possession of a magic sword, and might have acted differently.

2. Knowledge Checks Change Facts Instead of Just Revealing Them

For example, once you establish that jelly bears are weak to fire, you'll have to keep that consistent from then on.  

I actually think this is a feature, not a bug.  I like playing to find out stuff about the world, I happily ignore published content (because it's not canon until its been established in-game), and I don't mind playing in a world where trolls are immune to fire but weak to brandy.  Also note that this criticism only applies to checks that establish some fact about the world (such as Knowledge checks, and maybe some Perception checks if you roll that way.)

3. Failed Knowledge Checks Require DM Invention

Sure.  It does require more quick-thinking on the part of the DM, but no one ever said it was an easy job.  And the reward is more interesting trolls.  Also note that this criticism only applies to non-binary resolutions (like Knowledge checks).  Stealth checks and cursed swords don't have this problem, because if it's not one, it's the other.

Broader Interpretations

You can even use this for wider ranges of things.  One of the players went to investigate the noise by themselves?  Make a check later to see if they were killed and impersonated by a changeling.  You can pause the game to run a 1v1 combat to see how the changeling's ambush panned out.

A dungeon where you don't find out if you died in the dungeon until you leave.  Man or ghost?

Villain jumping out of a window, and one of the PCs sends an arrow after them.  When they look out the window, will they see a corpse on the ground, or the villain fleeing for the woods?

A wizard learns a spell.  The first time they try to cast it, find out if they learned the spell correctly.  Did they learn a flawed version by accident?