What to do When Your Dice Often Misbehave

So you’ll often read online or hear during RPG discussions that someone’s dice were “misbehaving”, by which they usually mean they had a long string of low (usually, but sometimes high) numbers. It’s also regularly used as a reason why GMs fudge rolls as in: “I don’t usually fudge rolls, but the dice were misbehaving and we were close to a TPK…”. I personally have a love/hate relationship with dice. I enjoy crunching the math on die systems and figuring out optimal choices based on the probabilities involved, but when it comes time to belly up to the table, my dice very often run cold.

But of course, the dirty secret is that there is no such thing as misbehaving dice. There are only a hand-full of causes for so called “dice misbehavior” and they are all completely in the hands of the gamer. That said, let’s look into the causes and how you can counteract them.

• Faulty dice: While dice don’t misbehave per se, it’s entirely possible to have dice that don’t produce numbers according to the proper distribution. These dice aren’t misbehaving, but they’re not the dice you think they are either.  Here’s the results of an experiment on cubes of GW and Chessex d6s that showed they rolled 1 about 29% of the time ^[1]. Those dice aren’t misbehaving, they’re rolling according to the distribution they’re made for, it’s just that that distribution isn’t the uniform distribution they were supposed to have. Oops!
  So if you suspect that your dice simply aren’t generating the right set of numbers, what can you do? First, test them. The easiest way to do so is with a good old fashioned Chi-square goodness of fit test ^[2].* If they fail that test badly**, then it may well be time to follow Martin’s example ^[3]and bury them in your back yard.
• Strange runs: This is what most often convinces people their dice are misbehaving. They roll a bunch of 1s in a row or some other improbable feat. There are two things going on here, neither of which are your dice misbehaving. First, we tend to remember extreme results moreso than mediocre ones, so when you look back over your rolling for the night you may see runs of results that simply weren’t there. It’s just that you forgot all the boring results in between.  Second, don’t forget that runs are rare, but they’re not all that rare and on a night where you roll your dice a hundred times, you have a decent shot at getting a short run or two. Software companies, who generate many more random numbers then we do over the course of a night, are well aware of this and often intentionally doctor their results if, for example, your ipad randomly selects 5 Sting songs in a row or your WoW character crits over and over.
  So what do you do if you see too many runs, but you’ve already tested your dice and they seem to be rolling the correct distribution? There are two potential solutions here. The one I recommend is that you do nothing. Let the runs stand. They’re part of the normal flow of random numbers. However, you can do what the software companies sometimes do and save them for later. When you roll a particularly high or low roll, place your die on a marker of some sort. If next time you roll the same extreme, put down another marker. If you roll something else, remove all the markers.  At some houseruled number of accumulated markers, instead of placing one, you remove all the markers and nudge that roll toward more average results. Your run is broken. Either you or the GM gets a bennie (if your system has some sort of bennie system) or a token you can spend to nudge dice rolls later.
• Too many extreme results: This is another common complaint. Dice roll willy-nilly with 1s and 20s all over the place. The level of random nonsense is just too damn high! Unfortunately, these dice aren’t really misbehaving either, providing they test fair. Instead you’re playing a system with too much variance in it’s results. Single dice generate numbers on a uniform distribution and uniform distributions tend to have a fair amount of variance compared to other types. Success/fail die pools for example follow the binomial distribution instead and have a much greater central tendency. Likewise rolling dice and adding the results tends to produce average results more often due to their central tendency. You can go to anydice.com ^[4] and punch in some of the more common rolls in your system and get a histogram. The more the results look like a flat line the more variance is in your system. The more the results look like a normal curve, the less likely you are to see extreme numbers. Here are a few examples (1d20, 2d10, 3d6,5d4) that all produce more or less the same range of numbers:

You can see that by adding more dice, the chance of getting the most extreme results is reduced from 5% to ~.1% and the chance of getting the more average results go from 5% to ~15%.
So to fix this type of misbehavior, you could revamp your whole system to use sums or pools over single die rolls, but the impact of that to a system is likely to be fatal. Instead, it’s a better solution to simply switch to a new system that uses a die type that you like better.

So there you are: several common types of “die misbehavior” and how you can fix them. Did I miss any? Have you tried these or similar solutions in the past? How did they work out for you?

* As a fun side note: The chi-square goodness of fit isn’t really a test of randomness, it’s a test of distribution, so the following d4 rolls would pass just fine – 1111222233334444 or 1234123412341234. We don’t worry too much about patterns or runs with dice though because results are independent.

** Keep in mind that NO die is perfectly fair, and the more rolls you test with ANY test for fairness, the smaller deviation from the theoretically perfect distribution you’ll be able to catch. Don’t roll every die you own 10,000 times, bury them all in the backyard and be unable to game this weekend.