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Does it make any sense to specifically hide the results of a player's dice roll from the said player?

This method is based on my assumption that many actions do not immediately reveal themselves as failed or succeeded. For example, jumping over a destroyed bridge is fairly obvious, while trying to get information from an NPC is not. I figured it would be useful in a situation like this:

A player uses Sense Motive to determine if an NPC is lying to him. If he rolls a 20, the GM is obliged to disclose the NPC's intentions. But if the player rolls a 1, the GM would (in my experience, at least) twist the facts and state that the NPC is 100% sincere and still raise immense suspicion. Now the player knows something is wrong, since he obviously failed the roll, but there's nothing to be done about it.

In this case, players could toss the dice behind the GM's paper wall instead of rolling it on the table/floor. A bit of poker practice would perfect this technique and let the GM handle such situations without any trouble whatsoever.

Is this already implemented by some players? If not, is this a sensible technique applicable in some cases? If yes, what are its limitations and general considerations to be mindful of as a player/GM?

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This is absolutely a common approach. For all rolls where the results aren't immediately visible, then I just roll the dice for my players. Sometimes I don't even tell them. Example, a wolf is stalking the players through the woods, and they need a Perception 20 to detect it. If you ask them to roll it and they all fail, then they will know something is afoot. Your fighter will probably draw his sword 'just because'. This type of thing can be averted by throwing fake perception checks at them (this is always fun for keeping folks on their toes). But I prefer to just not alert them to the fact that a check was ever made. Make sure you get the relevant modifiers at the start of the session, since asking for a perception bonus is the same as saying "Hey, I'm rolling perception for you."

That mostly applies for passive checks. For active checks, just roll it behind the screen and give them the results. This works great for sense motive checks and the like. I've had PCs roll a 1 to sense motive an honest man, and ended up CONVINCED that he was lying.

You can let them roll it themselves for simple perception checks, or ones in which the results will be immediately obvious or won't have any repercussions beyond the immediate moment. An example would be a trapdoor in a dungeon. Maybe someone can see it before the fighter falls down it. While this IS a break in the general rule, it makes things go a bit faster, since you don't have to roll for everyone personally.

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The way we do it at our table is simple:

Have the players roll 20 d20 ahead of the game session. Place the numbers in order with the characters spot, listen, perception, disable, and other "Adventure" skills that are normally hidden rolls a DM uses on the sheet next to their rolls.

This gives the players a feeling they did the rolls that effect them and they have no idea which roll is going to be for which RP encounter (Spot traps, hidden doors, and such).

Use regular rolling when they ask to "detect" something or for attacks, saves, ect. The rolls that let them feel they are playing the game.

What this does is allows the players to not hear you roll and stop everything they are doing to go through the whole:

"Everyone... DM rolled... search everything and take 20 also lets move in 5 foot increments then do it again".

Even fake rolling will lead to this or makes them feel you dont trust them to RP correctly and not use the "DM is rolling" meta-game.

We found also this speeds up the game play quite a bit, since you have the modify numbers there in front of you and have the rolls from the players and not from you rolling. This allows you to know if you need to describe the wall looks odd ahead of time... then they discover the hidden door. When they walk over to look closer, the ones who failed the rolls see nothing till the one "Spotter" pushes it open..... Well until the Rogue stops him/her just short of setting the trap off the spotter didnt see.

In the back drop you scratch out all the rolls used to make that happen. So Spots Disables and Searches in this case BUT can be any mixture for your game.

If your game goes long:

When you take a break or run out of numbers, just have them roll a second set of numbers. Even if you have more numbers for the other players left, get rid of those numbers so they don't know the one class that is burning through numbers. This also hides to all players what they need to be more aware of (Basically what the class that is running through the numbers is aware of).

Most the time the Rogues burn the most rolls and you can always have them roll more to begin with. Just if a player runs out have everyone re-roll but don't say who. More often this rolling becomes a bonding experience for the players.

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The way I'm used to doing this is for the DM/GM to make all dice rolls for the players, if the results would be hidden from the character. If you get a roll to notice a hidden item, the GM rolls, and only tells you if you actually did notice something. To keep from telegraphing, one might also roll meaningless dice at random times, so the players don't become conditioned to expect something to happen every time the narrator rolls some dice.

Of course, any roll resulting from player actions ("I'm looking for secret doors.") they'll know what you're rolling for, but they still won't know if they failed to find what was there, or if there was just nothing to find.

I've done it this way, and played in games where this was the rule, for almost forty years. I never found any problems with it, and it helps reign in the almost reflexive tendency for some player to meta-game.

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Yes, it makes perfect sense. My taxonomy is:

Die rolls with immediate, unambiguous knowledge of success or failure

Let the players make these. I am thinking about rolls to lift things, rolls to hit things, rolls to catch things. My examples are physical, but they need not always be. The key idea is that the player wants his character to do something, and the results-- the success or failure of it-- are obvious to player and PC.

Die rolls without immediate knowledge of success or failure

Let the player ask for these, or let the player know he has invoked one, but roll them privately. These are situations where the results, especially the success/failure criteria, are not known. Often one knows if one succeeded ("Is there a secret door?" "Yes!") but not if one failed ("Is there a secret door?" "Newp!")

Die rolls without even knowledge of die roll

Just make the roll unannounced. In some cases it may be appropriate to announce the results (without necessarily admitting the fact of a die roll.) In some cases, not even that. It helps to have a spreadsheet or such of all the PCs' various stats. These are situations where a die roll may be required, but it is not even appropriate for the player to know the die roll is taking place. These are often passive rolls: For instance, there might be a chance of noticing a secret door even if the player does not ask... but if the roll is failed, there is no reason to alert the player of anything.

That is my taxonomy. There is no requirement for doing things this way, but it is common in my experience. I have seen other GMs take that philosophy, and almost never have a player complain about unless we're haggling over a particular case.

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This is perfectly normal and used in many situations where the character would not know the result - did they not find a trap because there is no trap, or because they didn't find the one that is actually there? Making these sorts of rolls behind a screen has been going on since the 1970's. Indeed, it pre-dates RPGs and many three-player professional (ie, run by the military for the military) wargames for 2 players and a referee used the mechanism in the 60's; perhaps even earlier.

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