Chance is an important part of a tabletop game and the dice is our tool for introducing it. That little object can determine success or failure for our actions. However, one thing I've wrestled with for as long as I've been gaming is what the roll actually says. In some cases it is rather straight forward. You swung your sword and you hit. In others, such as rolling to determine if someone is lying, things get weirder. As a player, you can even ignore your roll in this case. And it is with the intent to explore this idea that I write today.
Regardless, I find things work best when the meaning of a roll and its result is understood by all at the table. It makes things work far smoother. That way a player knows what the roll failure means and can role-play accordingly. Restarting a scene is something I feel should not happen during play. It takes away one of the great strengths of tabletop gaming: the commitment to choices and progression of story. It is also a major thing that marks it to be different than most video games, though some try to do this as well (though some fiddling with your appdata folders is still possible).
So I roll my dice to see if the character was lying. Whether I succeed or fail, we are in a bit of an odd situation. If I failed, and they are in fact lying, do I think they are telling the truth? If they are telling the truth, do I think they are lying? This also adds an extra issue: if I do this consistently, the meta-game becomes obvious. If I failed I get the opposite result. If I rolled a 1 I know what is going on by process of elimination. I can obfuscate it and sometimes tell the truth and sometimes lie. I can also say they don't know when they fail and give the players an answer when they succeed. I'd say this last one is the most common and the simplest to implement. In general, it would be my suggestion for those things that involve recollection or mind related checks. Of course, introducing some exceptions into the mix can make for fun gameplay moments.
I don't mean ignoring them like when you don't bother to roll because a player role-played their character well and brought up an excellent point that doesn't need a charisma check. What I mean is that even if a player thinks a character isn't lying, they may still choose not to believe them. This is where things get a bit rough. Is a lie of omission a lie? Technically it is, and I'd argue that a roll should help you figure out that something is being hidden from you based on things you notice from the person who told the lie. However, even if that checks out, a player may still choose to ignore the result and not believe the character. This character broke their word thrice already. Why would I believe them again? Even if they don't lie, they are setting something up. There is a trick somewhere. These moments are great since it's the character the player created overpowering what the player knows or think they know. The roll gave them something, be it knowledge or a new position after climbing a wall. What they choose to do with what they gained is their business.
Did We Succeed?
Your character is trying to convince someone of something. Maybe they are lying, maybe they aren't. Still, how do you know if you succeeded? In this situation, it's hard to tell until the results come back to you. If a bad guy saw through your lie because they are better at reading your actions, or because they know something that directly contradicts what you said, you won't know until they spring their trap. Sometimes you will by a change in disposition. However, sometimes the result of the roll won't be known until farther along, because they'll use the chance to trap you. Again, it's fine and niche in application, but still important. Just make sure to note it for later use. It's easy to forget that your bad guy noticed if you don't.