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Many RPGs have random elements, such as dice rolling, which can determine success or failure of an action. In some of these games, failure basically means the player character does nothing or contributes nothing on that round.

For example, in D&D 4e, there are a great many encounter powers with cool effects when they hit and no effect at all if they miss. If the player misses, they may as well have said "I do nothing" on their turn. A player's entire contribution to the game is predicated on the dice "allowing" them to contribute.

However, the issue I want to discuss in this question isn't the mechanics of the game that leads to this "fail and do nothing" event, but how the players deal with it. Sometimes, players will roll a failure and will just walk away from the table. Sometimes it can become difficult to engage with the players who are failing roll-based checks because they are disengaging with the game.

(example: Player declares attack, rolls die, sighs in frustration and says "I miss" and turns away from the table or picks up their phone or whatever. All before anyone else can get a word in edgewise.)

In a previous question, edgerunner's answer to dealing with bad rolls themselves was to make an awesome story out of failure. I really like that answer and I'm going to pitch it to my group, but I realized it would still be difficult to overcome the psychological disengagement that happens with bad rolls. The players stop trying to do anything, role-play or otherwise, when they're overcome with dice frustration. How can I help them get back into the game and help them engage in the failure role-play?

This question is not asking how to avoid bad rolls. If you have that kind of answer, please post it to Balancing players' rolls, not characters instead.

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did you also follow the link to to Goblin Dice in the comments to that question? i read a few of the posts there and there is some really good insights on how to make 4e play more enjoyable and interesting. –  b33f3r Mar 5 '13 at 16:47
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The goblin dice article is interesting but deals with large issues rather than the relatively minor round-by-round outcomes of rolls. This isn't about one player, I'd say most in my group are this way. What if they reversed the roll and got a 20? They'd experience the same or even more frustration! –  Soulrift Mar 5 '13 at 20:43
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This question is not about how to avoid failure; it's about how to keep players engaged and happy during the failures that are inevitable in chance-influenced games. The OP has stated that he understands RP is a major component of this, and that he is very clear on the inevitability of failure in these games, and yet several answers are dedicated to those generalities rather than the specific strategies he's requesting. Maybe some judicious editing of the question is in order? –  BESW Mar 6 '13 at 11:17
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9 Answers

up vote 16 down vote accepted

If your players are easily frustrated by a few bad dice rolls, that's a problem with your game in general. Bad dice rolls happen. And they will happen a lot. If the laws of the universe don't change in the near future, I would even dare to say they will happen with the same frequency that applies to good dice rolls.

After all, your players don't get frustrated rolling too good, do they? Did they ever leave the table because the rolled 3 criticals in a row totally dominating the encounter? So the real problem probably is, that their only action and therefore their only fun producing aspect of the game is winning the dice roll. That is fine for a board game, but not exactly the goal of roleplaying games.

You can do a lot more in a turn of combat than stand there and hit the enemy. You can move to flank the enemy. You can taunt him (just in character, without any rules involved). You can be creative. You can have a lot of fun with failures. My most memorable moment in roleplaying was when my ninja character failed so miserably sneaking out of a bar that she ended up on the doorsteps with a broken ankle and screaming. Sure, that was a failure, the worst possible combination of dice I ever saw, but it was still fun and a happy memory meeting the people of this group even ten years later. But you need to encourage it and you need to allow it, even if (especially if!) it's not in the rules.

Example: Playing a specialized magic user, our party once met a monster that was completely immune to any of my magic. I could have taken the second (or third) row in combat shooting ordinary arrows at it. I would probably have missed 20 times in a row. It would have been incredibly boring. After 10 misses I would probably have left the table, too. Life is too short to be bored. Instead my character switched into light armour (no proficiency, but who cares), got a dark cape and a dagger and sneaked behind the monster. He failed the sneak roll, he was unable to cast magic due to the armor and he really sucked at hitting it with the dagger. BUT: the GM decided it would turn to me and leave it's back turned to the warrior leaving it open to his attacks, because even the dumbest monster knows that those sneaky dark dagger people hurt the most. I failed every single roll that combat and still contributed and had fun.

Remember, as a GM you need to encourage and allow it. No rule ever said that monsters need to turn to the sneaky git with a dagger. That was good GMing. We had fun. Much more fun than any fireball-damage-dice-rolling-spell could have brought. Build your encounters so that the players feel they can be creative. And allow them to be creative. If the players are creative, then no dice roll is needed to "allow" them to contribute. Contribution is measured in fun, not damage points.

--- Edit: ---

The first part was about what can be changed in the gaming group and playstyle to make failed rolls less frustrating. A commenter remarked that sometimes it has nothing to do with the game or group and that's absolutely right:

Some players simpy cannot lose. They can't. If they lose, they get frustrated. But losing is part of any game. I guess we all know people who are like that. It's also never them. It's the noob team. Or the dice. Or whatever. If the game was lost, somebody must have been a bad player. That you can play a game, be good at it, have fun and still lose doesn't fit in their world view. For them, it's about winning, not about having fun playing. If this is the case with your player, there is little that you can do to change that. For him to be the winner every time, the rest would have to lose. And you can't have that in a group. That's not fair to the others.

Some players are just bad at statistics. They don't have bad luck. They only feel like they had bad luck because they don't know better. Some people need a 18 to hit on a d20 and think missing 3 times in a row is incredibly bad luck. It's not. To the contrary, it would have been pretty lucky to hit just once in three tries. Make sure the players know at least basic statistics and can convert your systems dice rolling to percentages, so they have a number they can grasp.

Some people are building their characters with damage dealing as a priority. They can dish out huge amounts. Many dice. Large numbers. But most systems are quite balanced, so to achieve this, they sacrificed something. Most likely their chance to hit. So they sit there round after round waiting for their one moment of glory where they land a lucky hit to show off their uber damage. That's a decision. They could as well have build a character that attacks three times a round for little damage and in a good system it would have the same end result. As long as they look only at one number (damage) and not at the full picture (damage * chance to hit), they will frustrate themselves every time. Make sure they know that this is their own decision, because they can only change this situation themselves.

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While I feel this answer has some great insights and ideas, its tone (especially in the first two paragraphs) comes across as being kinda judgmental and condescending; that is, it's giving of a severe "Your players are doing it wrong," vibe. –  Lord_Gareth Mar 5 '13 at 20:46
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Well, if they don't have fun, then they are doing it wrong. They need to find their own way to happiness, but I don't think roleplaying is about being frustrated all evening. –  nvoigt Mar 5 '13 at 21:13
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As it is currently worded, this answer is "if you are sufficiently creative, then you will never suffer from frustration or disengagement," which is not true, and insulting to those who have been frustrated (since the immediate implication is that they are insufficiently creative). It's also useless to the question-asker, seeing as he explicitly said he'd already gotten quite a few ideas along these lines from another, linked-to question, and was looking for different sorts of ideas. –  KRyan Mar 6 '13 at 4:58
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Please avoid back and forth bickering in the comments. Additional comments of that sort will be result in the thread being purged, cats living with dogs, the release of the Clowns from the Hidden Fun Stuff, and general discomfort all around. –  C. Ross Mar 6 '13 at 23:30
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A few ideas that have worked for some groups of mine in the past:

  • In systems that care about tactical decisions (Legend, 3.X, 4e), see if there's other things that the player could be doing in their turn, like making useful skill checks, enabling tactical positioning, or even trying another gambit. If a player seems consistently frustrated with binary "yes/no" dice rolls, encourage them to seek concepts and/or mechanical builds that have more options per round available to them.

  • Show off some awesome failure yourself. Did your NPC whiff his mighty charge? Maybe the orc spins crazily, trying desperately to control his swinging axe. Describe the dripping spelltaint that runs through the fingers of an NPC spellcaster whose magic has been foiled, or hammer home the desperation of a "reliable" Hedge guide (Changeling: the Lost) who can't seem to succeed at his navigation rolls. Don't ham it up (unless your table likes that kind of thing!) but doing this sort of thing can serve as an olive branch and a demonstration that roleplaying failure doesn't mean you've done something wrong.

  • Offer roleplaying XP or minor mechanical rewards. In my opinion this option can be sorta like inscribing what you want on a brick and beating your players with it, but sometimes it works and it might get your players to have fun in these situations.

  • Try to work with your players when describing these sorts of events. If a player makes a tough, no-nonsense warrior of Summer, then maybe you shouldn't describe the failed roll as slapstick comedy; likewise, if you're playing Toon you probably should represent it as slapstick. Players will tell you what kinds of themes and moods they want to deal with when they make and personify their characters - working with those themes and moods can help take the sting out of the failed roll.

  • Make failure less likely by teaching your players to optimize. Feeling in control of their own fate can help ease back the feeling that the dice have more agency than the player does. Make sure you discuss with your group the level of optimization you want to fall under and approach this with maturity and respect - some groups are just fine with having the PCs construct their own fortress-demiplanes, but if yours isn't you should decide where the line rests as a group, not as a GM dictating it to the players.

  • Talking is a free action in almost all systems. Encourage players to plan tactically during combat; that way, even if the player who failed his roll doesn't feel like roleplaying they can still meaningfully contribute to the group as a whole.

Some additional ideas:

  • Some systems already have rules in place for "circumstance" bonuses and penalties that affect a roll based on factors like advantageous positioning, experience with the subject in question, slick ice, or poor library catalogs. Consider making use of (or inventing!) such rules in your game - it'll help alleviate some of the failed roll problems, but it'll also help your players feel creative.

  • White Wolf's Storytelling systems include a kind of "roll" (challenge, really) known as "Extended and Contested", which I've used to great effect in other systems with a bit of tweaking. Essentially, an Extended and Contested roll involves a conflict between two parties that takes some amount of time beyond a combat round (like a foot chase, a hot dog eating contest, a climbing competition, etc). Each party involved makes rolls as appropriate - maybe they're pinning down the vampire while one PC drives the stake, maybe it's a case of Drive vs. Athletics while a sprinting man tries to catch a taxi cab - and compare results. In Storyteller systems, there's usually some kind of threshold for total successes needed for one party to claim victory, but there's no reason yours needs to work that way. Extended and Contested rolls tend to be a lot better for non-combat scenes than they are for combat ones, and they have the advantage that a single roll doesn't necessarily put you out of the running. Chasing a dangerous necromancer, a paladin in Legend might roll Athletics (against the necromancer's athletics) only to find that the necromancer edged him out and is staying ahead. The paladin trips the necromancer up by cutting a clothesline that tangles into him (a successful engineering against the necromancer's failed acrobatics, maybe), then manage to grab the wily fiend and subdue him (opposed grapple checks). The downside, of course, is that it does involve more dice rolling at the table, which can sometimes take up time. I highly encourage the use of this system with the circumstance bonus/penalty system mentioned above.

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+1 for showing off your own failures. I will often play up my disappointment when my monsters have a round of whiffs, which usually results in the players feeling smug. Also, not enough for an answer on its own, but once when a friend didn't roll above an 8 the entire session (he tracked it), the DM offered him a bonus (I think it was an auto-hit or an auto-crit or something similar) that he would be able to use once. Doesn't help long-term, but it mitigates the immediate issue. –  thatgirldm Mar 5 '13 at 17:41
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First, realize that randomness is part of some of these games. The best approach may be to simply accept this fact. If the fact that randomness is a factor bothers the player, then perhaps this game is not the right one for them. Games have a spectrum of how much is luck and how much is random. Games like Go or chess have essentially no chance involved. But other games like Magic: The Gathering, Poker and many role playing games involve Luck alongside skill, and that is just a factor of the game.

Since randomness is part of some of these games, consider games that involve close to no chance if the random element really bothers some players. I haven't tried it, but I understand Amber involves no luck. Fate involves substantially less dice rolling.

The middle ground is to help them to see and take advantage of the secondary tactical effects. Perhaps Bob the Barbarian's attack missed and did nothing. He is still tying up that particular threat so that the threat isn't charging at Wally the Wizard. He is also distracting that target so Roger the Rogue can set up a backstab. This is similar to how you might need to line up your Rook in the right place so your Knight can capture the queen. In a more modern setting, Gary the Gunsman might have missed hitting the mook, but the mook might be ducking behind cover instead of firing the next round because of Gary's shot.

You can also help them find techniques that minimize their own rolls. A character built around buffing the teammates will have fewer rolls than one built around slicing the enemy. And, especially when talking about spells, many of them have only a reduced effect if the other party resists rather than no effect. So the turn isn't "wasted". Of course, there is often a trade off. Many techniques are high-risk, high-reward. They can do spectacular things, or nothing at all, or even make things worse (see Botch in shadowrun, etc.). Many of the techniques that have less risk also come with less payoff.

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Amber has luck built-in. They are attributes of the character (good and bad stuff). Generally, it is assumed you have one or the other. I like having both -- see the main character in Chinese Ghost Story for an example of how that works. –  Sardathrion Mar 6 '13 at 8:27
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Unfortunately I am not familiar with systems other than D&D 4e, and to a lesser degree 3.5 and Next.

A mechanical thing to consider is what is causing a miss against AC for example. If a fighter swings a big sword and even gets close to "hitting" his target is going to have some effect. This effect may not be damage but the sheer force of the swing is going to be transferred to something. Maybe knocking the target off balance on a near miss, or if it is a sprightly target using light armor his dodging maneuver means he is less capable to dodge the next attack.

Obviously using this too liberally means the game becomes as disinteresting as failing repeatedly, but if on a near miss of 1 (maybe 2 for an encounter or daily) there is a random effect dice roll to see how that near miss causes the target to struggle to avoid the blow.

This could also be applied to attacks against any defense stat in a different way like poison vs fortitude causes the target to get clammy hands and his weapon slips out on a swing or double vision. On reflex maybe the target has to move to a different square to avoid the attack. That would not be a shift because the attacker does not control the movement.

Edit: Adding non-combat near-misses

For Diplomacy checks a near miss could mean that the "target" takes a second to think and decides to help but for a price. The price could be anything from doing a task (potentially incompatible with the adventurers current task) or merely gold. The continued conversation would open the "target" up to further dialogue options like intimidate or "lets go to the bar and get some drinks while you tell us about your plan, then when you get drunk enough you will just tell us what we want to know."

On a near miss intimidate the DM describes the wavering but as of yet un-broken resolve to withstand the adventurers efforts. This would allow them to possibly resort to other tactics like free action scorn and mockery for the little bit of pee showing on the NPC's pantaloons.

Stealth checks that are near missed could cause a guard or two to become alert and investigate where they "saw" something but not out-right raise the alarm. Similar to mechanics in many stealth video games.

Perception could be handled similarly but in the opposite direction. The adventurers think they see a thing at a location but are not sure.

Acrobatics and Athletics you fall just short of the goal but are able to keep from hurting yourself and are now in a bit of a difficult situation.

History, Religion, Arcana, Streetwise, Insight, Nature, and Dungeoneering you get a sense of something but nothing more than a vague sense.

Heal could maybe only allow regain half of surge value or a plus 1 to their saving throw.

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This is more of a long term suggestion. It won't help during the combat but should help recover afterwards.

When I plan my sessions I try it include one segment for each PC. It could be an NPC contact who addresses that PC, an incoming message, etc. Personal plot is ideal but it could even be something generic that doesn't apply to that PC (ie a downed carrier pigeon, message intact) so long as you have at least one item per player.

Anyway I write the players name next to these notes. When someone looks bored, I queue up their plot to be the next part of the session. It almost always engages that player and pulls him back into the game.

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I've seen this reaction happen for a couple of differnt reasons:

  1. A player is having an off night with the dice. It's random, sometimes things just don't go your way all night. Some players handle this better than others do, and that comes down to personality and experience. If it's localized like this, there isn't much you can do. The good news is that they'll have another night where they can't fail and feel awesome. (One thing you can do is use a system like hero points that give the ability to reroll. That way if they fail an important roll, instead of feeling frustrated they can spend a point to try again.)
  2. The player isn't very engaged in what's going on in the game, and thus they're getting bored easily. There's a lot of potential causes for this, and thus several potential actions. From my experience, I've had players who really prefer one aspect of the game over the other. In this case it'd be someone who likes exploring, RP, and party interaction, but finds combat tedious. It's very easy for her to tune out of a battle if it's not something she feels like she's really needed for, and bad rolls definitely remove that feeling. For a player like that you'll need to try and include opportunities to do something they do like while in the situation they don't (such as fights you can talk your way past).
  3. The worst case scenario is when one party member is outclassed by the rest of the party, and as a result they need better rolls than others in order to be effective. That invariably means they'll fail to do so more often, and they start feeling useless and bored. I've seen this one happen a lot to newbies, or players that either don't know how or don't care to optimize in a group of players that seriously optimize.

In that case, depending on what the problem is you might need to step in and help them with their character, to ensure they have something they can excel at to boost their contribution to the group. It might also require you to tweak the adventure so they can be useful more often.

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Maybe you need a different RPG system. You might want to give Apocalypse World, and the powered by AW games a try (particularly Dungeon World if your players enjoy the fantasy setting). In these games interesting things happen regardless of whether they succeed or fail the roll, and this can help keep everyone engaged, even when their character might be having a string of bad luck.

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I tentatively agree that this could be the answer for this group, and yet… Games with pass/fail structures will still get played if one group somewhere switches to a *World game, and there will still be players frustrated and disengaged from that. How to handle that is still a useful GM skill we can help with. –  SevenSidedDie Mar 6 '13 at 16:11
    
While this answer does not solve the general case, I think it is a very valid point in the OP's specific case. –  Yianes the Sneak Mar 6 '13 at 22:15
    
All true, but you can take the lack of a binary resolution mechanic and apply it back to D&D. Maybe not all of the time, but certainly in social situations... Failed your bluff check? Maybe he believes you after all, but doesn't react exactly the way you hoped. –  aslum Mar 6 '13 at 22:27
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Savageworlds uses a system called Bennies to counter this. Every player starts with approx 3 poker chips. When redeemed, one chip allows a player to re-roll his/her last roll.

This forces every missed roll to be evaluated for a moment, and ultimately puts the decision in the players hand. It goes from "I missed, these dice are horrible" to "I missed but I only have one Benny left and I WANT TO SPEND IT BUT I MIGHT NEED IT TO STAY ALIVE".

As a GM, I also try to describe what happens when players miss. You blow struck but was deflected by his armor, you're character is momentarily blinded by the sun, you tripped over your ally (when both players miss), etc.

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I like the answers posted so far. I have had a number of experiences related to dice frustration. There's been the table of mostly engaged players except for that guy that gets mad whenever he doesn't cleave an orcs head in every time he tries. We don't play with that guy anymore. Then there's the engaging mid-level campaign where everyone is starting to get frustrated because they've invested time from level 0 in the campaign and like it but the dynamics of their characters don't make sense anymore and everyone wishes they go could go back and change something critical at level 1. That stands out especially related to dice rolls, but usually doesn't happen often since the players are already experienced and I take time especially with new players to make sure they create a balanced addition to the party. The most experience I have with this seems related to your experience, however. Most of the time when this happens, even if the players are trying to stay engaged and are not necessarily being immature or unreasonable and are just frustrated, it's due to what appears to be cursed math and nothing more (or a prankster Kilroy has defiled all our dice). A particular example that stands out was the straw that tried to break the party's back in the form of a displacer beast that magically enjoyed uncanny good fortune when trying to displace itself and avoid physical attacks and nearly destroyed the entire party. This was after several sessions where attacks that barely needed checks would result in the player rolling a 1 or the previous band of orcs getting multiple critical hits and avoiding attacks that they really shouldn't have had much chance to avoid.

I pulled a plot deus ex machina out of thin air to explain the mishap with the displacer beast. A trusted NPC that had been questing with the party was able to identify a curse on the party that had been negatively influencing the party's luck. With some non-combat effort, they were able to remove the curse. For the next few battles that occurred immediately after, I informed the players of depreciating bonuses to all their rolls. It started with +3 during the first encounter and went away at the rate of 1 each new encounter. This was explained as the characters feeling like they were suddenly extra lucky for a short time due to the psychological effects of the curse's immediate removal. By the time the bonuses wore off, everyone mostly rolled an expected balance of results except for a last couple straggling botches by this one guy that has since burnt those dies and purchased new dice. The players expressed this was a fun way of temporarily distracting from dice frustration without unbalancing the characters permanently or sending monsters that weren't any challenge.

Another thing that I have done in the past is keep a secret log of roleplaying that players do and use that to reward particularly unlucky rolls all without the players knowing I do that. I award a special type of experience for roleplaying that the players do not know about on a scale of 1-5. 1 means they at least tried but just not very well or in depth, 5 means they did homework and spent time researching topics in between sessions or sacrificed a great deal for the purpose of roleplay. One of my players intentionally had her character become problematic for her party to persuade her character to board a large seafaring vessel for the next leg of the quest. We hadn't discussed why her character didn't have any points in Swim in character creation, but over time she developed a fear of large bodies of water due to a tragic childhood accident. The quest was delayed nearly to disaster, and I secretly awarded her character 5 roleplaying points. I have different triggers for how the points are redeemed (again, without the players knowing about all this):

  • Start of a session. I roll for each player to determine how much of their built-up secret roleplay experience points they will spend this session. This depends on how long the campaign has been going, but is generally between 1 and 10 of their points but no more than half their remaining points. If they will be spending more than 5 points, I spend 5 of those points to throw in special magic items that will be in the loot of the session designed best for that character's body type and class (what the party does with it is a different story, though).

  • For dice rolls. I reserve the remaining points that will be spent by that player to distribute throughout the night to that character converted into secret bonuses, secret negative modifiers to targeted enemies, extra clues, and the occasional "I'm sorry, I didn't see that roll.. can you roll it again? hint hint, cough cough" for an exceptionally bad string of rolls. The players think the latter is done to save the storyline so we aren't rerolling new characters every week, but in fact it's due to a systematic approach of rewarding their roleplaying.

  • More notes on the deus ex machina. In addition, if everyone's having a rough time with dice rolls but everyone has a good bank built up of secret roleplaying experience points, I may elect to spend more of the players' points they have in reserve to activate the cavalry riding in at just the right time or the evil gnome tinkerer's weapon of moderately-massive destruction suddenly has a critical structural failure and starts collapsing which distracts the evil gnome's henchman and gives the party the upperhand again.

This is a pretty systematic approach that might work better for me than you, but ultimately I believe in ditching the rules for the sake of the storyline. If the players make reasonable decisions that just turn out bad due to unruly gambler's fallacy and the lack of infinite hit points and they are altogether great roleplayers, I try to assess how to relieve frustration without unbalancing the game. If the cavalry makes sense, send them in. If they can survive even though they'll end up losing ground in their quest and a few prized possessions and we can find meaning and a satisfying way to overcome the obstacles within a few sessions, I will make them roll with the punches of bad rolls.

Another approach that can work is to simply change gears. Give the players some shore leave, let them pursue some of their characters' bucket lists for new and strange places when there isn't an immediate crisis going on. Ultimately, I think dice frustration when there are a lot of uncanny bad rolls can be rooted in a loss of control. If overlooking bad rolls or sending in the reinforcements doesn't make sense, reroute the story for a couple days in-game time. Cut the dungeon crawl short, get them back into town or in a new place, and make sure the players know there is nothing to do but wait for a couple days. Give them enough time to prepare for the next leg of the quest, but give them way too much time to prepare. If they have a brief but unavoidable period of nothing to do but pace and twiddle thumbs for their characters, they'll likely go exploring to do unrelated shopping and pursue character development interactions with townfolk. The rogue may finally have time to try and create her first set of Masterwork lock picks with some good tools from a friendly or unsuspecting smith's shop. The cleric may take some time to explore the art of cooking by experimenting with strange local flavors in a foreign land. The barbarian may want to stand drop-jawed all day in the weapon surplus store engaged in battle story exchanges with the retired barbarian shopkeeper. Give them chances during this time to make skill checks that aren't quite so critical. So what if the cleric rolls a 1 cooking fish soup? OK, so that's a bad example. Maybe dissuade anyone from attempting advanced cooking that could result in poisoning the party if botched. But you get the idea.

It can be understandable for players to get frustrated. It really depends on you, your players, and your dice experience. It's inevitable that some RPG group somewhere in the world will eventually roll thirty or more 1's in one gaming session. In one game where I myself was a player with four other players, all five of us proceeded to get a critical hit each in succession of another. Initiative determined that the enemy went last, but the enemy didn't get to do that. Things would have been challenging as it turns out, we found from our DM who spent three minutes staring at the table in what could only be described as awe and disgust. Upon being attacked, the enemy would have activated a contingency of powerful magic effects and summoned cohorts for an epic battle. They didn't get the chance because we weren't supposed to do that much damage in the first round before the enemy could act. It turned a very powerful and nefarious "boss" fight into an anti-climax of curb-stomping the enemy immediately. It goes both ways, and that's reflective of real life. Sometimes, the final boss is a pushover. Sometimes, the peon manages to whack you in the back of the head just the right way to knock you out even though you were a blackbelt when the peon was in diapers. It happens.

If it's a reasonable crew, make accommodations that somehow make sense, don't unbalance the game, don't convey that the players can expect such whenever they are frustrated, but also restore satisfaction to the game. If it's a reasonable crew and there are not very unlucky dice rolls and only merely consistently unfortunate rolls in minor and moderate ways, try the solutions in other answers, too. If the players seem too quick to walk away when they fail rolls more than seems to be average, remind them of math and that they need to roll with the punches or consider a different game to relieve stress.

One last thought here is that I once DM'ed a dice-less version of Dungeons and Dragons for a group as a collaborative experiment. We created stats and continued to level up, but this was more to gauge and help give a mental assessment of each character. We based what happened on common sense rules. If a clumsy character tried to hit an enemy with a rock, it usually didn't happen as they would have liked. If a skilled paladin was trying to smash in a low-level mob's head, they usually did with no problem. I would occasionally make a random judgment call to mimic an expected and reasonable average of probability related to scores and who should be able to do what how many times out of a hundred. Generally, everything was using a modified "take 10" system. If it was reasonable to auto-pass, they usually would. If they were overextending themselves, I'd let them succeed part of the time and fail part of the time. I'd spit out random hit point values when needed, trying to not show favor to particular low or high ends. This approach was interesting for a simple and quick mini-game, but not something I would do for a whole campaign. However, this approach can be used temporarily in a standard game if everyone is getting bad rolls and they are becoming frustrated. Just switch the dice rolls off and play it by ear using common sense. They probably aren't going to critical much if at all and are going to get hit sometimes and only sometimes hit an even match. The rogue might be better at this than the wizard.

Best of luck, and whatever you do don't try microwaving everyone's dice so that 1's are avoided. It doesn't work well, makes the dice ugly, and ruins your burritos forever in that microwave.

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Wait, wouldn't rewarding players to playing in-character but not telling them make the reward almost useless, as players wouldn't actually be encouraged to do what you're rewarding them for? And wouldn't letting the players think you're fudging dice rolls for the sake of keeping to "the story" lead to players feeling disempowered and railroaded? How do you avoid these pitfalls? –  GMJoe Mar 8 '13 at 6:43
    
Both great questions, both which strike at the heart of the matter. What are they player types you are dealing with? Mine are responsible players that get a variety of benefit from playing. They like a good varied experience involving a little hack and slash, a little political thriller, a little dungeon crawling, some back story, the occasional annoying puzzle, etc. They just have incredibly bad luck rolling dice sometimes. I haven't noticed these pitfalls, but they are something to watch out for. I actively encourage roleplaying in other ways, and reserve this as less of a reward system. –  James Broyles Mar 8 '13 at 8:34
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