When developing a tabletop RPG rule-set, one of the most important decisions one has to make is how to handle success tests. Those playing your game will be making success tests on a frequent basis, so a poor method for handling them can seriously disrupt the roleplaying experience. A good method, on the other hand, will be nearly seamless and transparent while still providing for plausible or believable odds of success. The ideal die-rolling method for success tests is one that the gamemaster and players will barely have to think about. This isn't necessarily the easiest goal to achieve, though, as the limitations of dice make them less than ideal for determining the success or failure of actions. This guide discusses the traits of a good die rolling method and the implications of certain choices.
Characteristics of a Good Die Rolling Method
The following is a list of traits that a good die rolling method will have.
Provides a wide enough range of results to allow reasonable odds for success and failure, and which does not make critical successes or failures too likely or unlikely. It keeps a +1 modifier (or other minimum modifier) from having too significant an effect on the chance of success.
Provides for always having a chance of success or failure on any roll except for those where success or failure would be impossible. (Of course, generally any time a success test is allowed, there should be some chance of success or failure.)
Can be applied to a wide range of situations, thus not requiring different types of success tests for different types of actions. In other words, every action relies on a core rolling method with minimal variation or adaptation; instead, each action is merely an expansion of the core method.
Uses rules simple enough and produces numbers small enough to allow any necessary math to be completed quickly and easily in one's head.
Has rules flexible enough to allow them to be easily used, or at least quickly adapted, for unexpected or unusual situations.
Rolling One Die versus Rolling Multiple
One mistake made in some tabletop RPGs is to mix the rolling of single and multiple dice without considering how this effects the probability of results. Designers should be careful to avoid mixing the different probabilities these methods can create unless they seek to deliberately exploit these differences to good advantage. It may be better to simply remain consistent, however.
Single Die: The use of a single die provides for simple, flat probability. Each possible result is equally probable. Note that when one rolls two dice where the ranges have no overlap (except for zero) and totals the result, this is essentially the same as rolling a single die. This is commonly seen with percentile dice, where one d10 is marked off from zero to nine by ones and the other is marked off from zero to ninety by tens. Since every combination produces a unique result, this can be essentially considered the same as rolling a single die.
Totalling Multiple Dice: One commonly seen approach is to roll more than one die with the same range of numbers and total the results. This does not produce a flat probability. Instead, if you graph the probabilities of each result, it will look like an upside-down V. Results in the middle of the range are far more likely that the results at the extremes. For example, with the common roll of 2d6, there is a one in six chance of rolling a seven, but only a one in thirty-six chance of rolling a two, with the same odds for rolling a twelve. The farther a result is from the middle of the range, the less likely it is to be rolled.
Independent Multiple Dice: Many approaches rely on rolling mutliple dice, but instead of adding the rolls together, each die is evaluated independently, usually by comparing each die to a target number and counting the number of dice that match or exceed it. In essence, the result of this type of rolling is the number of dice meeting or exceeding the target. This produces a binomial distribution in statistical terms. Essentially, higher target numbers make lower results more likely and vice versa. For example, assuming a roll of dice, lower target numbers make higher results like 4 or 5 more likely than the rest. Middle target numbers make a result of 2 or 3 more likely than the rest, and high target numbers make results of 1 and 0 more likely.
As each method described above produces different probability patterns that are affected in different ways by modifiers, it is wise to be careful about mixing them. It is recommended that one uses methods that produces probability patterns one understands. It is also easier to work with die rolling methods that have the same probability pattern.
Choosing the Number of Sides
Generally when using rolls with only a single die, d10s, d20s, and dice in between are the best choices. They provide enough of a range that +1 or -1 modifiers don't have extreme effects, as they would with d6s and dice with fewer sides, and it is easier not to make critical successes and failures too likely. Percentile dice may seem like an attractive option because of the common usage of percentages, but the smaller numbers produced by d10s and d20s are easier to work with. Percentile dice provide an unnecessarily wide range, which makes their use less seamless and transparent.
When totalling multiple dice, it's generally better to stay with a smaller number of sides. This is one of the places that d6s actually work well, as with rolls of 2d6 or 3d6. Using rolls of 4d6 or higher is not recommended, as adding that many dice together with several modifiers is not very transparent or quick. In general, 2d6 is probably a better choice than 3d6 as well.
When rolling multiple dice and evaluating them independently, d10s and d20s are still a better choice, but d6s are typically used in these cases due to the fact that they are more commonly available. It is better than using d6s in single die roll systems, but still, the limited range of a d6 means that even a +1 modifier has a fairly significant effect. (I personally recommend avoiding the use of any combination of die or method where a +1 modifier can have more than a 10 to 12 percent increase in the chance of success. For some numbers of d6s, this method can influence the probability of success by more than 15 percent on a +1 modifier.)
Additional Rolling Rules
One problem with using dice is that they produce a limited range of results, making it difficult to ensure that there always is a chance of success or failure. For example, extremely high or low skill values may ensure that even the lowest result will be a success or the highest result will be a failure. Thus, some additional rules are often added on to provide for some chance of success or failure in any case.
A "wild die" rule: When rolling multiple dice, many systems employ a "wild die," though they often use a different name. The highest possible roll on this die usually allows the die, and perhaps others, to be rerolled and those results to be added to the result already achieved, expanding the possible range. The lowest possible roll on this die sometimes calls for an automatic failure, and sometimes even a critical failure, though some systems just call for the highest die roll to be subtracted out from the result. The problem with this system is that it is usually used with d6s, which can allow for these special conditions to happen very frequently. Even if they don't make automatic or critical successes or failures too frequent, they will frequently increase the amount of math involved in a single roll, making the system less transparent.
Automatic success or failure: This method works well when the minimum and maximum results have no more than a five percent chance of being rolled. With this system, generally the highest possible result is an automatic success, and often a critical success, regardless of whether or not it beats the necessary difficulty or target number. Likewise, the lowest possible result is usually an automatic failure or even a critical failure. This method has the advantage of being extremely quick, but one might view even a five percent chance as being too high for a minimum chance of success or failure.
Bonus or penalty rolls: This method, used in single die roll systems, allows bonus rolls or enforces penalty rolls when the highest or lowest value is rolled, respectively. (In my system, which uses d10s and treats a roll of 10 as 0, a roll of 9 allows for bonus rolls. The player can continue to roll on every 9, getting to add +3 on each. A roll of 0 requires penalty rolls, where they must roll again on every roll of 0, imposing a -3 on each.)
This important choice is somewhat more complicated than many realize, and since this is such a critically central part of any roleplaying system, it is vital to take the time to think things out thoroughly. Having a poor die rolling scheme might just be enough to break a tabletop RPG, even if the setting and other rules are well designed. It is important to make sure that the rolling of the dice is simple and not obtrusive to the roleplaying experience, as well as being quick and smooth enough to keep the game moving along. It is also important to maintain consistency, which allows the system to be more easily understood and minimizes the time spent looking for specific rules. A careful choice here early in the design process can save a lot of headaches and potential time-consuming redesigns down the road.