Let's say you're the GM and the player attempts to do something, but you already know that given his current stats, it's impossible for him to succeed at it. Do you make him roll anyway, or do you just tell him he's unsuccessful? If you flat out tell him he fails, it might imply what he's trying to do is impossible even though it might be possible for him to succeed later.
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Here I’m echoing the advice of Angry GM in his Five Simple Rules for Dating My Teenaged Skill System. Please do note that Angry GM lives up to his name, and his articles are littered with strong (but self-censored) language. It’s all pretty tongue-in-cheek and harmless, in my opinion, but your mileage may vary.
Anyway, the second of the five rules addresses exactly this point:
In effect, rolling takes time. If the roll’s result is predetermined, just tell the PCs. In the case of failure, this sends a clear signal that they cannot just keep trying hoping for a better roll – they have to change something. If they cannot fail, then rolling the die is literally pointless, die-rolling for its own sake. (If you feel like your PCs are not getting to roll enough dice as a result of this approach, that would be a strong sign that something is off about the difficulty of challenges the PCs are facing relative to their ability.)
Whether or not the non-roll consumes the PCs’ time is fairly critical in some situations, and should be made clear, but this can be made clear much more quickly by simply saying one way or the other, rather than making a die roll stand in for such a statement. How much they should learn about why it was impossible may depend on the situation, but no matter what, knowing that is was impossible, even if slightly meta-gamey in some situations, often isn’t that much of a stretch (PCs tend to be experts in the things they’re trying to do), and even when it is, it speeds up the game, making it more fun and less frustrating for the players. These are good things.
Angry GM also goes on to describe how, in the case of possible success, rolling is still pointless unless there is some reason for them to not try over and over. Because they will try over and over until they get the right roll, barring some important reason for them not to. He goes on to describe how to make time limits “real” in conjunction with this approach, and I consider it quite good reading.
Does the player know the action will fail? Does the character know?
There are two kinds of actions that are guaranteed to fail - obvious ones and non-obvious ones. If a character tries to jump to the moon, in most games that is an obvious failure. If a character tries to punch the Flash in the face, that may be a non-obvious failure (since the character may not know the Flash can dodge practically any attack). Therefore, there are two cases for what you should do.
When failure is obvious, don't let the player roll
If a character in a medieval game wants to roll to invent modern chemistry, you don't need to make him roll to tell him no. The last thing you want is the player rolling a 20 and demanding that something ought to happen because a 20 is special. Saying "no" rather than letting him try is important because it does not use up the character's action. If a gnome wants to try and suplex Godzilla, he will not only fail, but waste valuable actions in combat.
When failure is not obvious, let the player roll
If two warriors square off, and one is warded by a mystical veil that makes him impossible to damage, you should let the player try to attack anyway. Failure in this case is simply the discovery that the desired task is impossible. The character didn't know that what he was trying to do was impossible, but now he does - describing the results, make sure to indicate to the player that he failed not just because of a bad roll, but because it's simply not something that will work without meeting some condition. Let's take a D&D example:
If you flat out say it is impossible without indicating why, the players may be discouraged and might accuse you of railroading. If you set up the problem as one that can be overcome, and roughly indicate how to do it, the players will take it on as yet another challenge instead of an arbitrary roadblock.
But why roll?
In the game rules, the roll represents a player's commitment to a particular goal his character takes. Once there is a roll, the action happened. If there was no roll, did the action happen, or did it not? Does the DM saying "no it's not possible" fall into camp A (forbidding the action because it would obviously fail) or camp B (allowing the action because the character could think it would succeed)? Keeping the die roll resolves the ambiguity. The character tried, the character failed, the character is certain that trying again will not change the result.
I think it's a bad practice to tell the player it's impossible, because...
World can't tell us that something is impossible. It's only our guess.
How can we understand that some task is impossible for us and with very high chance we will fail in real life? Our experience. Well, someone's experience. Our wise friend can see that we will fail and tell us about it. And so your players should do in the game. They may not know themselves as players what their characters can easily assess. Experienced adventurers can tell that something is unachievable for them. In order to "ask their experience" players should ask GM what their characters think about this attempt.
And I think it's a good practice to allow player give it a try, because...
Everything that player did or didn't has it's impact on the world. But, of course, activity leads to something interesting more often, rather inactivity.
So let them try!
Maybe player will get natural one(or any other result equivalent to serious fail) and you will come up with fun result which will have impact on subsequent events. Or it may be critical success(or something really extraordinary in the results of player's roll) and with proper description for his action(maybe with some cunning idea) you will see that allowing player to succeed now will be much more fun, rather than forbidding it at all. Again, due to difficulty of the task, you may let your player succeed, but with some drawbacks.
For example, possible situation with the system which has critical success rolls:
Now, because of overconfidence John will fight with injured arm and this may greatly affect what will happen next.
One exception that I find logical:
Sometimes if you don't know how - you can't try.
Well, I can try to throw a knife without any skill or knowledge, but if I'm a peasant who always lived in his village, I can't even try to assess some spell or do something not obvious, that can't be achieved by intuitive actions. In some games you can decide this based on character's proficiency.
First, I am assuming from your question that impossible is a concept in the game. Some games, through the use of hero points, fate points, or critical successes, don’t have impossible. In that case, of course, you always allow the roll.
But in games where impossible matters, I go by, does the character know it’s impossible? If so, I tell them it’s impossible, and potentially why, because if the character knows it’s impossible, they most likely also know why it’s impossible.
If the character has some knowledge, that knowledge should not be hidden from the player.
If the character does not know it’s impossible, then yes, ask them to roll. They may glean useful information from the roll about how difficult this task is, and then choose to either investigate further to find out why it is more difficult than it seems, or try to change the circumstances so that it is easier.
In general, there is information to be gleaned from the die roll, so err on the side of letting them roll.
The problem with your stated rationale for not telling them that failure is automatic—that it might be possible later—is a problem for both options. If they roll an 18, 19, or 20 (on a d20 roll where high is successful), they may make the same assumption. The solution is not roll or don’t roll, the solution is to pay attention to the choices the players make, and adjust the amount of information you’re giving them.
If they’re always trying impossible things as if they weren’t impossible, then either you aren’t giving them the information necessary to make the proper judgments or they think they’re in a different game.
You’ll want to find out which, and then either be less stingy with your descriptions, or find a game that matches the group’s desires more closely. For example, if the players are seriously asking to do things like “lasso the moon out of the sky”, they are probably expecting a game that enables the stories of early myth, possibly playing out the creation myths of the world.
The same would be true of wanting to play the A-Team but using a game of gritty, high-casualty rules. If people routinely die in hails of gunfire, an A-Team game is impossible—you need rules that support the genre you want to play.
If the character cannot know that it's impossible then let them try: if they roll max then tell them "your aim was perfect and power was great, yet the target seem absolutely not affected" and character should deduce that it is impossible. But what if player rolls minimal value? "Your hit barely touched the target, it isn't strange that you can't see any effects" So... Player may decide to try again, and waste more time, and that way affect the adventure increasing chance of guards noticing them or something like that!
If the character would know they have no chance of success, then don't make them roll.
If the character would not know then do make them roll.
Obvious example: find traps. If there's no traps to find, then the best the player can do is try a few times and then assume that it's safe. This is obviously analogous to the character's real perception in the gameworld - they can not ever be totally sure.
Other obvious example: trying to jump over a 10' wall. No need to roll, just say "it's too high".
In the general case, if something is impossible for a reason the character could not reasonably know, then you should make them roll and spend the time to work out that something unseen is going on.
No, you don’t ask for a roll
There is a good article, explaining why such a roll would be a waste of time made by AngryGM. To make a short point without the need to read the whole text:
Making a roll, in my experience, is not helping players to understand the reason for failure. In many cases the bad roll is interpreted as a reason to failure, not that the action was in fact impossible. The explanation by DM is what makes the thing clear. If, for instance, a dragon with high DR is hit by a attack that simply cannot harm it, the DM should just state "your weapon is not enough to break through his magical scales. You`ll need some magical help of your own", and not bother letting player roll his damage dice.
I'm going to go at this from a different angle, though I'll start by concurring with everyone here: do not make a player roll for something if you already know they cannot succeed.
This means that if you have a skill system/save system/any rolling system that has auto-success on a natural 20, and the circumstances aren't such that it is literally impossible to succeed, you can and should let them try (though I would exercise caution in doing this - most systems have auto-success at nat 20 as a house rule, and for a good reason - not everything has a chance to succeed).
Let the player act
If your player is being prompted to roll for an action that there is no chance at succeeding, you're already going about it the wrong way. A player attempting something should tell you what it is they are trying to do. You, as the DM, should explain the circumstances of what they're trying, and if there is any possibility in accomplishing what they do.
If the player decides they want to perform that action anyway, because their character is desperate enough to try something impossible in the hopes of having some effect, you can let them roll - in some systems (since this is system agnostic) there is a chance to have some impact on the game world despite not having a statistical advantage in a situation, and the act of trying to do something, even when impossible, can both be in-character and progress the story in a significant way.
You should talk this over with the player beforehand - let them know, before they roll, that there is no circumstance where what they try will succeed, but if they know that, and they want their character to try anyway just because it's what they'd do...then consider letting it play out. This is extremely circumstantial, and depends on what the player can conceive of doing outside of just rolling for success, but it is worth doing, if it leads to a good roleplaying experience.
Don't ask for a roll, but do allow a roll
Let's say that we are having a normal human trying to move a skyscraper by pushing it. I'll tell the player the building isn't on railroad tracks and that human strength isn't exactly enough to move a skyscraper. However, I'll also tell them that they are always free to try. Then, the player can respond in one of several ways:
This way, the player is never restricted in what he can do. The character is restricted in what he can do, but not what he can try. Only if the player and the DM agree, you won't roll and when you do roll, the roll will never be completely irrelevant.
Obviously, this strategy only makes sense when the player and the DM both know that this task is impossible. There are several other situations that may involve rolling on a task that can't be accomplished by some players.