@A Voice in the Dark
Oh yes that's also a great one I like to use sometimes. The roll isn't if you succeed or fail but easy or hard success comes to you. A really bad roll could mean it takes far longer to succeed at something which could mean the bad guy gets further along in their plans or maybe the group draw the ire of someone in the process. A really good roll could mean they do it very quickly and they also accomplish something else by pure luck maybe they don't just find the info they're looking for but also some other important stuff they should know.
@Centauri
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My questions are: if the players know they rolled badly, do they have to believe what they rolled? Do others who know they rolled well have an opportunity to convince them, or are they certain they're right? Some GMs will hide the rolls, so the players can't be swayed by the rolls, but in that case why should the character ever believe anything they think, without the game turning into an effort to prove every fact the party is told?
I do not hide my rolls but I trust my players to not meta-game, but the reason this does not fall apart is because of wording and tone of how the dis-information is delivered. Let's take 2 examples that actually happen quite frequently and how they will normally go. The first example is one where I am ok with or it makes sense for the high and low roller having clashing opinions:
Insight checks on someone who the party suspect to be lying:
1 rolls well - you can tell there's something off about the way he's speaking, he's doing his best to divert the conversation away from the subject
2 roll bad - you can't get a good read on him
1 rolls really bad - you don't see anything to suggest this guy might be lying, he's either got a really good poker face or he seems to be legit
The resulting in-character interaction will usually go one of 3 ways:
>bad roller will give good roller the benefit of the doubt because it's better to be suspicious than not
>bad roller will call out good roller and there may be a disagreement between the two of them on the way to go forward
>the group will excuse themselves from the person they're talking to for a moment if they can, step away from the character they're talking to, and discuss how they feel about it which will generally lead to them being able to analyse both view points and when pointed out they'll recognise - yeah he was kind of avoiding talking about the subject (which isn't meta-gaming it's a case of not noticing a thing until someone else points it out, it happens all the time)
None of these are unfavourable results since the story will move forward regardless and it's completely in line with how a group of people would interact.
The second example is when this is done more for flavour and it gives the character a way to rp their bad roll:
Say it's a knowledge check on a monster, same results 1 good, 2 bad, 1 really bad.
good roll - here's some relevant info like something they're weak to/resistant to, some cool trick they can do.
bad roll - no info
really bad roll - "Oh yeah this thing actually sounds familiar, you remember your mother reading you an old fairy tale about this monster when you were a kid. Well the way the story goes the brave knight was able to form a barrier from the love of his dearly beloved anxiously waiting for his return which protected him from the beast's dread gaze."
Is anyone going to take that seriously? Absolutely not but it will give everyone a chuckle and if they're in top form the player might put that into their character's words before the fight begins 'hey don't suppose anyone's got a true love back home to protect them?'.
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Not everyone finds that kind of thing amusing after the first few times.
Due to statistics it won't happen enough times for the amusement to drop. If the barbarian needs to be rolling say 16+ every time to succeed at those checks and the wizard needs only an 8+ then the chances of both results occurring are low enough that the amusement will not fade. Or if somehow there is an unusual luck streak then there may be some frustration at the wizard's inability to roll well but if you have a player who is upset that someone else rolled well when they failed that is a seperate issue which needs to be addressed.
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Yes, and here's the thing: the roll itself can change the circumstances. In my view, it should, for every kind of skill checks. As your example demonstrates, knowledge rolls are problematic, because they don't inherently involve actually doing anything, just standing around and thinking about, or, at best, researching.
The roll has not changed the circumstances, only the players' understanding of the circumstances. You might say this is knit-picking but that is just how I apply my reasoning to the situation. For example if the players are facing a locked door and the rogue fails to pick the lock the circumstances haven't changed i.e. there is still a locked door there. The understanding is the only thing that has changed i.e. this lock is too hard for the rogue to pick.
As for knowledge rolls I'm not sure I understand how what I explained demonstrated a problem?
Circumstance 1: You think about a thing. You either have an answer or you don't (the roll).
Circumstance 2: You go to a library to reasearch the thing. You either find the answer or you don't (the roll, or as Voice said just now, if the library contains such a book you do find it eventually it's just a matter of how long it takes).
Circumstance 3: The library was no help so you make a pilgrimage to the old sage who lives up in the mountains to see if he knows (now either the sage does or does not know, if it gets to this point he probably would know unless it makes no sense for him to know since it was probably a mini-adventure for the party to get to him).
Do you see how the circumstances change each step?
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It allows it, but doesn't directly cause it. The players still have to change things. Some will, but as you point out you might have to block them from trying the most obvious thing, because nothing obvious and inherent has changed.
If GMs have an approach they like, and characters in their games can actually fail and the players still have fun when it happens, then that's all I can hope.
This does also have the benefit of encouraging the players to try other things when plan A fails. Sure plan A made the most sense but that doesn't mean it will always work. And if they are not willing to try something else or are unable to think of something else to try then they can accept the failure and move on, a failure in this regard will never cause the party to fail at the campaign. It might make things difficult later on but there are always alternatives or other things they could be doing which will help them out.
They didn't get the door open and they don't want to try something else like breaking it down. Ok they leave the door and go explore somewhere else. As a result they never get the evidence they can use to prove the evil senator's plan so they will have a hard time convincing people and will have to find another way to stop him.