[RPG] the technical name for “cylinder” shaped dice

So, I am a freelance game designer and I’ve worked on a couple of systems and with a couple of design teams, but I am a “professional” only in the strictest sense (I have been paid for my game design work). I still have a day job; I do not spend all day, day in and day out, working on game design, and that matters.

But this isn’t the concern that game designers I have worked with have had. Players will, particularly in the right moment, be perfectly willing to add up large numbers of dice (some players even especially like doing so). The real concern is what sorts of mental mathematics you can rely on players to perform reliably, quickly, and accurately. You are quite constrained in what you can do before one or more of these starts to suffer, and they are all important to keeping the game moving and ensuring your game functions as you intended it to. If you ever do reach some limit where people just don’t want to sum that many numbers, then you are way, way past the point where speed, accuracy, and reliability are all solid, so that’s what you should be concerned about.

The other advantage here is that people’s ability to perform mental math quickly, reliably, and accurately is 1. quite objective, and 2. of considerable interest outside the RPG scope. This means that there is research you can leverage to answer this question. A study of what RPG players are, on average, comfortable with, would have to be very large to be valid, and would be of minimal interest outside the RPG industry. I am not aware of any such study, and truly doubt it exists or ever will. (And if it ever does, that kind of market research is often not made public, but rather produced specifically for the publisher that funded it and kept as a trade secret.)

The rules of thumb that I have kept to include:

• Not doing any math is always much, much better than doing math, no matter how trivial. Reading a number off a die is much faster than any arithmetic, and can be assumed to be perfectly reliable and accurate. This could be a reason, for example, to prefer a d20 over a 3d6: the more-normal distribution of the 3d6 may be nice, but the speed at which a d20 can be used over 3d6 could be a big advantage.

  There is actually an inverse relationship between these: if you are going to be rolling very often, the speed benefit of the d20 is bigger. At the same time, the normality of the 3d6 is also less significant, because the more-frequent rolling implies that any individual roll is less important and it is the accumulation of rolls over the course of the encounter that are more important (see goblin dice). That means that rolls will “normalize” over the course of several separate rolls, so that benefit of the 3d6 over the d20 is reduced.

  The flip side is also true: if you roll less often, that implies that any single roll is more important. The more-normal distribution of a 3d6 may be very desirable, and the small-but-significant speed, reliability, and accuracy losses for using them instead of a d20 will be mitigated by the fact that you don’t need to do it as often.

• There is a big, big difference between a pre-calculated value written down on a character sheet, and a value that has to be calculated in the middle of the game. The former has drastically reduced need for speed, which results in much, much higher accuracy as people take the time to get the number right, and those are not what we are talking about. Ultimately, the following rules of thumb are extremely restrictive because we are talking about calculations that have to be performed often and quickly. Even low rates of error become badly exacerbated under these conditions, which means we need to stick to things that are almost impossible to get wrong.

• It probably goes without saying, but stick to whole numbers. Decimal values cause some trouble, and fractions can cause a lot of trouble.

• As much as possible, stick to single-digit numbers. Human brains actually process basic arithmetic on small numbers differently than they do large numbers, because we actually have parts of brain dedicated to small numbers and can manipulate them “intuitively” whereas larger numbers forces us to track them symbolically. Moving past these throws a significant delay into things, and drops accuracy rates some.

• If a large number comes up in an exceptional circumstance, or is accumulated over time, pen and paper are useful tools that drastically improve accuracy and reliability. They come at a heavy cost for speed, however, and thus tend to not be used—even when they should be, for accuracy’s sake—if these sorts of calculations have to be performed frequently.

• Addition is pretty much the only really safe operation. Even subtraction has significant reductions in accuracy rates. Multiplication is worse than that, and division is just right out.

• Doubling and halving, rather than arbitrary multiplication and division, are fairly safe, though. Again, doubling much more so than halving—doubling is actually just addition anyway, add the number to itself. Quadrupling and quartering (doubling or halving twice) are probably safe—but slow. Tripling can be OK, but I would not use “thirding” (which, tellingly, isn’t even a word).

• Multiplying and dividing by ten are entirely safe, because you don’t perform any multiplication or division at all, you just pad with zeroes or remove digits off the end, respectively. They tend not to come up terribly often because they result in larger numbers (undesirable) or decimals (undesirable), but the operations themselves are probably safer even than addition.

• Division by multi-digit divisors, as well as any form of exponentiation or roots, are “safe” only because players will tend to just give up and use a calculator. Most players would prefer to avoid them, however, and will not use them unless they “have to”—which is why these operations that force them to do so are actually “safer” than those that they can do in their heads (because even though they can, errors tend to creep in when you have to do it fast and frequently).

You can do a lot more research into this, though. These rules of thumb are just things I have picked up from working on things with game developers I respect, as well as some things I remember from my undergraduate psychology courses. That’s good enough for me, and I suggest that these are issues you want to stay well inside the lines, rather than toeing them on, but ultimately, you can definitely find more information out there about what sorts of things do and don’t work.

The default set of dice used by Pathfinder (or D&D, as you mentioned in the question body, they use the same) would be:

• a 4 sided die
• a 6 sided die
• an 8 sided die
• a 10 sided die
• a 12 sided die
• a 20 sided die
• a 10 sided die numbered 00, 10, 20, 30, 40, 50, 60, 70, 80, 90

A basic set (as you could buy in a store) includes one of each, although most players prefer to have some extra 6 and 20 sided dice because they tend to be used a bit more.