My own answer to the question is the GM calls for a dice roll when:
- Either the player or the GM asks a question about the setting for which there is no predetermined answer
- the answer will make a difference to a decision a character (PC or NPC) is faced with
- the GM wants the answer to be unbiased
1. A Question with no predetermined answer.
This is the main thing. In my game, rolls are almost always triggered by asking a question, although the question might be implicit in an action that appears to be a declaration: I swing my sword at the monster (did I hit?). Sometimes the GM is asking the question (do they notice the ambush? does anything noteworthy happen as they travel down the road?), sometimes the players (do the guards try to stop us from entering the town? Is the princess impressed with my singing?), but if there’s no question, there’s no reason to roll.
But there’s also no reason to roll if the GM already knows the answer. If the players come to a gate and want to know if it’s guarded and the GM has either noted specifically in the description of the gate that there are two guards or has established as a general rule of the setting that gates into town are always guarded, then there’s no reason to roll.
2. The Answer will make a difference.
Lots of questions, implicit and explicit, get asked in the course of a game session, and rolling slows things down–particularly if there’s a chart involved. If it’s not important, and I define important as being information for a decision the characters are making (or I anticipate they might make), then the time-honored technique of “making stuff up” is the way to go.
If the player wants to know what color clothes the guards are wearing, or anything else that has no particular bearing on something the player has to decide…perhaps just to help flesh out the picture of the setting in the player’s mind, there’s no reason to roll anything unless as a GM you just have trouble improvising.
3. An Unbiased Answer
If you don’t need an unbiased answer, then even if there are charts and skills that would be appropriate to the situation…you still don’t need to roll. Making stuff up is faster and just as good.
The reason for dice in the first place is to pick a random answer out of a list of possibilities. You want a random answer when there’s some reason that a biased answer (even if only possibly unconsciously biased) is unsatisfactory. It might be unsatisfactory because it’ll give players the wrong idea about how common certain things are in the setting. E.g. bandits are supposed to be rare enough that commerce is possible without every caravan needing a host of armed guards, but in order to keep things interesting it seems like every time the players pass a caravan it’s under attack by bandits. It might be unsatisfactory because you’re risking taking something significant away from the players (such as one of their characters) and you want it to be clear you’re not just doing it for plot reasons or to demonstrate that your setting is deadly.
Times not to roll
Note, though, that there are many reasons that you might want a biased answer. In that case, it’s a mistake to roll the dice. If failing to notice a secret door will stop the adventure cold, then having the play session end with a 5 in 6 chance is unacceptable. If a character is supposed to be an expert with lock-picks but keeps failing the rolls, you should probably make him stop rolling for a while and just have him open the damn locks. It’s true that if the skill and difficulty are set correctly, by the law of large numbers if he just keeps trying to open locks, eventually his record of success will match how good he’s supposed to be…but by Rule 2 where you’re only rolling if it’ll make a difference (or even if you roll every single time), the character may not have enough tries for that to work out. It can be very disheartening for a character to always fail at his signature talent. My home-brew actually borrows a concept from CORPS where you don’t even roll if the difficulty of the attempt is equal to the character’s skill; D&D 3 introduced the concept of Taking 10 and Taking 20 for pretty much this reason.
Don’t. Seriously, if the characters can always reroll for a success, then eventually they will succeed. Contrariwise, if the GM can keep asking for yet another roll to confirm the success (e.g. asking for a stealth roll for every 5′ covered) you can guarantee a failure. If it’s a task that the character can eventually succeed at with enough tries, then don’t roll for success, roll to see how long success will take (or how much money it’ll take, or how much damage they’ll take, or whatever resource they’re expending on each attempt). If it’s a task that the character could in theory simply not be skilled enough perform successfully, then treat a failed roll as indicating they just can’t do it unless they can bring something more to bear to increase their chances, e.g. coming back with better tools, having another character aid them, going away and training the skill some more.
The middle ground, and the only place (IMO) where you could consider allowing rerolls is where failures make success harder to achieve or can be addressed by the player choosing to spend resources (either meta-game resources like bennies in Savage Worlds, or in-game resources like potions in D&D), so the failure or degree of failure is an input to further decisions by the character. A typical case is trying to page through a book to find a specific passage while combat is swirling around the character; without the time pressure the character could certainly do it, but as GM you might not want to roll and say it will take 2 minutes–by which point the combat will be long over. In that case you could allow a roll each turn, so that the player could decide after a couple turns to try something else (or you could roll secretly to see how long it’ll take on the first roll and then let them know when they find it if they keep electing to spend their turns looking). In either case, the way that events continue to unfold around the character means that each decision about whether to spend the turn searching is a new one, and it’s worth giving the player the opportunity to make it.