Image courtesy freeimages.com / Uros Kotnik

If you need to save time or mental bandwidth, consider using dice roll averages for rolls of more than 4 dice.

Disclaimer: nothing in this article should be considered prescriptive. You know your game system, your players, and yourself best. Use what seems useful and put the rest in your back pocket for when you need it.

Dice statistics are commonly recognized as a relatively dry subject in tabletop games. However, the Game Master would do well to respect the power of chance over their games. Success, failure, and their magnitude are at the whim of the roll; understanding how randomness can affect game-play will give the GM some useful tools for controlling the table.

GMs are only human. This is both a boon and a bane to the game; the near infinite flexibility of having a mortal parse game-play competes with the limitations of the GM’s capacity to do so. Quality game design necessarily takes that into account, limiting game mechanics (and their interactions) so that the needs of running the game are within the GM’s bandwidth.

One tool to help do this is by using dice roll averages vice rolling large numbers of dice, but at what point is that a useful tool? Under what conditions are the GM’s bandwidth limited, increasing the value of this tool? What other tools are synergistic, and what tools invalidate the usefulness of average rolls?

Players have similar restrictions. In the absence of interesting game-play, they look to other sources of diversion (these days, it’s often the phone in their pocket). Player engagement is a concern of all GMs, and it’s rare for a player to hang on the edge of their seat for a large dice roll to tally. Opposite this effect is the excitement of the roll itself. A goodly portion of engagement-worthy game-play is the randomness of the roll, and taking that away from the players (either by enforcing roll averages on them or by not rolling yourself) can drive engagement down. Finally, calculating the average dice value takes some mental bandwidth, so economy of calculation vs. roll tallying should be considered.

Process

For reference, calculating the average is simple enough – for N dice of S sides with a modifier M (NdS+M), Avg=(N*S+N)/2+M. This often produces fractional values, so it’s important to understand how your game system deals with fractional numbers.

It should be clear to the GM that at some point, using the roll average will save time. In 5e D&D, the Meteor Swarm spell calls for two rolls of 20d6. Almost nobody has twenty 6-sided dice on hand, and if they do, digging through the rest of their dice to produce them can grind the game to a halt. Likewise, rolling 1d6 forty times can be time consuming (and mentally challenging – was that 18 rolls or 19?). So the GM should be able to understand the value of time saving techniques (and there are others that are discussed elsewhere ? see Mike?s article on using Random Results).

Less clear, perhaps, is there a tipping point between the fun of a roll and the savings of an average? Is it more than 10 dice? More than 5? Let’s look at the math.

I took the dice total probability distributions from anydice.com for 1 to 20 dice of 4, 6, 8, 10, 12, and 20 sides and copied them into a spreadsheet. Next, I looked at three scenarios: the probability of a roll being within 30%, within 15%, and within 10% of the average value. Multiple scenarios will hopefully give the GM the ability to decide for themselves where the break-over point for usefulness of this technique lays. Below you can see the distributions charted, by dice size.

Results & Analysis

Click on this thumbnail to download a zip file containing the spreadsheets and results graphs in a larger size.

Not surprisingly, the more precision demanded by the GM, the less likely it is that a roll will meet the requirement. Also, as the number of dice increases, the likelihood of rolling within the precision required increases (rolls become less random with many dice). Finally, as the number of sides on the dice increases, the likelihood of meeting the required precision increases.

These conclusions hardly warranted the effort of this analysis; the results should have been obvious even before the numbers were crunched. But it?s not this big picture that we really care about ? it?s the thresholds of precisely when randomness becomes too low to matter as much as the time savings.

It’s worth noting that at low number of dice or sides, the discrete nature of dice roll values produces irregular results (1d4, for example, cannot produce the required precision at ±15% and ±10%). If you take a look under the hood and examine the spreadsheets, you’ll also find that the processing of data provided by anydice.com produced some errors. I’m disregarding those errors, since they would not have impacted the results.

What IS worth noting, however, is that generally a roll is within 15% of the average more than 60% of the time when the number of dice is greater than 4. As a GM, I find this precision and frequency “good enough?, especially when you consider that mentally calculating the average requires the same number of operations as rolling when the number of dice is 4 (multiplying two numbers, adding a number, dividing by two, and adding a final number takes me roughly the same amount of time as throwing four dice and adding four values).

Rebuttal

There are circumstances where I would not recommend this technique.

  • When using digital tools. Digital tools make it very easy to produce a random result while requiring only the bandwidth to make the request.
  • When party size is small and other mental distractions are minimized. I still may recommend this technique for very large rolls, but in the narrow range where the number of dice is between 4 and 10, it’s probably worth the increased bandwidth for the fun of rolling the dice.
  • I would never recommend enforcing this technique for player rolls. It will reduce player agency and take a vital part of game-play from the player, and save the GM no bandwidth. For very large rolls (see Meteor Swarm above), I may give the player the option before the roll, but otherwise, I’d let it lie.
  • If you’re morally, philosophically, or otherwise opposed to the idea. See disclaimer above.

In conclusion, using average values for dice rolls can be a valuable tool for saving GMs time and mental bandwidth, but circumstances and personal preference can invalidate its usefulness.

About The Author:

Clint Hillman has been in love with Sci-Fi and Fantasy since he was very young. When 3rd Edition D&D was launched, he bought himself the core rulebooks and started GMing for his friends. After over a decade of military service, Clint looks to the gaming industry for his next challenge. He lives in Arizona with his wife Ashley and son John. This is his first published article, and he hopes to publish many more.


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