Dealing with extreme luck

As a DM for 4th edition, I have a rather interesting bunch of players, but 4 of them that show up at my table tend to have extreme luck. 'W' and 'J' both have bad luck--there are nights where they cannot roll above a 6 on a d20, no matter how many times they try. On the other hand, 'K' and 'S' have extremely good luck. 'S', in particular, plays strikers with high damage, nearly always rolls above 15 for initiative, and has a habit of critting once or twice in a short combat. With his characters, (a monk with a vicious staff, or a slayer with a greataxe), he gets absurd amounts of damage on his crits, and often one-shots normal enemies this way.

What should I do to keep things fun and interesting for the table, when such extreme luck is going on? I don't want the high luck characters to be unchallenged, but anything that would threaten them, would destroy the low luck characters. Likewise, I don't want people upset at the high luck players--but even I get a bit frustrated by it. Help! ;)

• You could try and change their luck! – yhw42 Sep 30 '10 at 12:40
• Did you think about changing the dies between the groups, i.e. give the dies of W&J to K&S and those of K&S to W&J? – Stephen Nov 26 '11 at 20:43
• Extremely related question: rpg.stackexchange.com/questions/12254/… Tl;dr: If you really think your players' luck is predictable, take them to Las Vegas. – GMJoe Apr 24 '13 at 7:32
• A less related question: rpg.stackexchange.com/questions/8857/… – GMJoe Apr 24 '13 at 7:35
• Have to agree with @Stephen, maybe buy and supply dice for the group which you can test out ahead of time if this is really a bugaboo. – Joshua Aslan Smith Apr 24 '13 at 12:10

Embrace it!

Player-driven games are the ultimate success. Sometimes as GM you have to jettison your designs (or premade adventures) to accommodate this, but it's well worth the effort. It can be challenging, but the better GMs can and do seize these delightful opportunities.

Don't go negative, though. It's better to tolerate an over-lucky player (who will probably be reined in by peer pressure eventually) than to cause strife in your gaming group. If a player is actively causing problems, that's a different matter... but this issue is passive and not confrontational.

In this case, the die rolls -- whether truly random or somehow skewed -- are sending the game in a new and unexpected direction. Revel in it, extrapolate from it, and be ready to maximize it, either with prepared 'just-in-case' encounters or simply by winging it.

Game on!

Well, I have enough math background to know that extreme consistant high rolls can be due to more than "luck".

If you can, track their d20 rolls through the night and confirm what you think is going on. Our minds play tricks on us, and we tend to only remember the rolls that stand out (whether good or bad), it's called confirmation bias.

Is your party in the Paragon tier (or highter). If so, the rolls are more easily explained as their are several ways to get a larger crit range. Also, the feat "Danger Sense" allows the character to roll twice for initiative. That could explain the seeming consitant 15+ on initiative rolls.

• ACtually, I believe that the Rolling Twice has been equated to about a +5 bonus on the roll if you accept it no matter what, which mean the average dice roll would be around 15. But yeah, another vote for Confirmation Bias and character influences. The Dice have no memory per say. – Logos7 Sep 30 '10 at 13:35
• And you should track all rolls. With a random distribution of results crossed with a random order of rolls (init, attacks, saves, checks) you might have a night where the high rolls line up with the attack rolls. They still roll low as often as high, but in our minds those are different categories, which leads to the perception that "they can't miss!". – yhw42 Sep 30 '10 at 14:10
• @yhw42 Dice don't really work that way. All attack rolls should be just as random as all rolls overall, given a large enough sample size. – AceCalhoon Sep 30 '10 at 14:32
• @AceCalhoon - what you're saying is true, however I think with the small sample sizes that @yhw42's suggestion is valid. If you're only looking at one night, you want to get as much data as you can. – Pat Ludwig Sep 30 '10 at 14:37
• @PatLudwig Fair enough :) I think what I was trying to say was that if a player is always rolling well in combat over time, that's still wonky... Even if they sometimes roll poorly elsewhere. – AceCalhoon Sep 30 '10 at 14:41

If you're really seeing this much deviation, test their dice for fairness. I suggest using the Chi-Square goodness of fit test (How to at Statistics SE) for their rolls . You'll need to roll each die at least a hundred times. If the dice really aren't fair, get new ones! If the dice are fair, but the rolls at the table are that extreme (especially on the high side), look for signs of fudging.

I have noticed that skill, especially character creation, can make players seem lucky. Look at the average to hit of the players. Work with the lower end characters to raise their to hit, and otherwise improve their abilities.

Finally, don't be afraid to fudge. Modify your rolls to hit the players who roll high more often. Pick adversaries with high defenses for the high rolling players attacks, and lower defenses for the low rolling players attacks.

• one thing that I noticed seems to make good and bad dice days evaporate like spring rain, is a dice tray. Take a shallow dish (say like a shallow wooden box or biggish dogfood dish). Line bottom with thin felt to help keep the noise in check. Player wants to roll the dice? In the tray or it doesn't count. As for Chi-Aquare fit tests, I honestly think its more trouble then its worth. Have your players roll with several different dice. – Logos7 Sep 30 '10 at 13:37
• @Logos7 the dish is a good idea, you should post that as an answer. Chi-Square may be overkill, but I have found unfair dice before (the ones that come with D&D minis were often unfair if I recall correctly). – C. Ross Sep 30 '10 at 13:56
• Its just that to my understanding, even logging hundreds of dice rolls may not be a large enough sample for a meaningful chi-square test (feel free to correct me). There is also the fact that dice are labeled oppositely (on any particular dice the numbers on opposite faces should add up to the number of sides on the dice +1) to help minimize any effects of unequal dice. (which do happen). I think that between the numbering, and using a couple of dice any significant trends are really more the matter of selective dicing than problems with the dice being random enough – Logos7 Sep 30 '10 at 20:30
• You're assuming there's no way to cheat at rolling. Back in college there was a RISK game where I realized my opponent was definitely cheating (I had had suspicions before and worked out the math--he was several standard deviations out.) I started rolling where everyone else but him could see--and he refused to play. Admittedly that's d6s rather than d20s but I've seen people who seem to roll high too much even with a d20. – Loren Pechtel Apr 25 '13 at 2:03
• @LorenPechtel "If the dice are fair, but the rolls at the table are that extreme (especially on the high side), look for signs of fudging." ? – C. Ross Apr 25 '13 at 7:31

Track the rolls over a couple sessions. Write down every roll by which die is used. If one seems to be rolling more than 10% of a given number, then it's time to do a chi-square test on it, or get a new die.

I'm not dice-superstitious, myself; it's not luck, it's uneven dice and or mishandling.

I'd also suggest using a dice tower or dice cup. That massively reduces the amount of semi-conscious control people put on their rolls. (It also makes it easier for people to check rolls.)

Also, it's possible that people are in fact misreading the dice and skewing the results. I've seen players do this in both directions. One guy, the group bought him some oversized d20's (2" across) due to his misreading... He'd fudge for a crit in either direction: crit fail instead of fail, crit success instead of success. He wasn't really aware of it, either, until called upon it.

Treat it as a scientific experiment.

1. Check that you are actually experiencing what you think you are. If S. has a power that allows him to score a critical on a 15, normal rolls will produce your results (or even if he hasn't, but thinks he has, so announces more crits than he should.

2. Eliminate human interference. It may seem harsh to believe that players may actually cheat, so take steps to reduce subconscious eagerness instead. Insist everyone rolls dice in the same place at the same time (one way to get good results is to roll out of turn, pick them up if a bad result, but say "I've already rolled: look." if good), with a proper throw-length. This alone will eliminate 'lucky/unlucky players' 90% of the time.

3. Isolate the actual unusual factor. Make players swap dice for one session; if dice are (provably) good no matter who throws them, they may well be uneven, and you can go to more rigorous testing, or just ban those dice, as you prefer. If the player continues to have unusual luck when you record every roll and use different dice, you may have a phenomenon in which physicists would be interested. But I suspect he won't.

However much effort you wish to put into investigation, it is dangerous to 'compensate for bad luck' unless you specify for example "If you roll 3 1s without a 20 between, you can reroll the third" (though even that is open to selective recollection). Giving out rewards for something outside a player's control is always a bit iffy, and I seriously doubt whether all the players share your perception of 'how the dice always fall'.

There is nothing you cannot incorporate into your game with enough work.

Sidestepping the whole luck/statistics issue entirely, consider what you want out of your game. In a truly random set of any number of values there is always going to be the (small) chance that they will be dominated by low or high rolls.

It sounds like what you want is to even the playing field a bit, or ensure a "minimum" threshold of luck. This would allow you to challenge the high rollers more (allowing them to bask in their success) without completely leaving behind those who are rolling poorly. Consider giving benefits to characters who roll poorly enough to be considered statistically improbable. After all, the only reason rolling improbably high is good is because in D&D higher numbers are better.

I have a player myself who frequently complains of poor luck in combat where after a bad start I offered a +10 on any roll that combat if it persisted through a given period of time. It did, and I gave it to him, allowing his poor luck to be actually a boon in the next round. If he had not rolled poorly enough to get it, the not getting the bonus would be covered by the fact that the player was actually hitting. It didn't make it impossible to fail, or make rolling low better than rolling high, but it kept the combat from being something the player couldn't meaningfully participate in, regardless of outcome.

You might even be able to incorporate it into the plot, perhaps there are beings that are drawn to extremely good/bad luck in game. The effect would have to be such that you can safely allow whether or not they factor in to literally be decided by chance, but such measures don't need to be cheesy fourth wall breaking affairs.

Whether or not the numbers will eventually balance out, feel free to play with the results.

Remember, in real life there is no such thing as luck.

From a mathematical point of view you haven't really got a problem at all and this is only a coincidence. There is no problem to solve. He has as much luck as everyone else.

If he does get really "lucky" across several sessions, there must be something wrong with his dice. I'm not usually a very suspicious person, but you need to check the likelihood of such "luck" and then perhaps intervene. If he really gets two crits during a short battle, and this happens often, then there must be something wrong. This is highly unlikely.