Making the Dice Work For You
Some small observations on rolling multiple dice, with emphasis on character creation and The Unnamed Three.
RPGDESIGN
7/10/20263 min read
When talking about lessons from The Unnamed Three, we mentioned how we're not very worried about players getting lucky with their stats. If we want to stack the odds in our favor, there are some tools to use instead. However, let's start with the core idea first:
The Law of Large Numbers
If you roll one die and get a result, it is anyone's guess. If, instead, you rolled a hundred and summed them up, it's around 60% likely that the result's between 335 and 365. In other words, a range of 30 out of 500 possible results account for more than half the actual results.
So, if you want greater control over your dice rolls, simply use more of them. Now, let's see how we can use this idea in a game:
Multiple Dice
In The Unnamed Three, I wanted stats clumped up near 9 (average of 2d8) to create tension in checks. To this end, I used 2 dice. Original Dungeons&Dragons (1974) uses 3d6 for each stat, with an average value of 10.5.
Personally, I'd recommend against using 4 or more dice in a setting where we sum up the results. At that point your results start to get too reliable and you lose the "random" element of rolling dice. Even 13th Age, where you roll damage dice equal to your level, up to 10, actually recommends taking average except a handful of dice.
There's also a second edge of this "multiple dice" blade: If you design your system with 4 or more dice in mind, then any result on the extremes can cause a crisis. This applies even more strongly to character defining values. While rolling 7 damage or less in 4d6 (which can occur roughly 1-in-40 times) is a quick laugh or groan at the table, a key ability being 7 in a game where design assumes abilities to be between 12 and 16 can be catastrophic.
Multiple Samples
For The Unnamed Three's three stats we roll a total of 6 dice. For Dungeons&Dragons' six abilities, players roll 18 dice. Keep in mind that The Law of Large Numbers, in essence, deal with averages. By rolling a lot of dice we don't necessarily increase the chance of all stats being near the mean, but rather decrease the chance of all stats being at one extreme or the other. In other words, by having multiple samples (abilities in our case) we more or less guarantee that your results won't be wholly terrible or wonderful.
(To increase the chance of all abilities being near the mean, we must use multiple dice to determine them as discussed above.)
A few points about this:
First, unlike using multiple dice for abilities there's nothing stopping us here. If your game needs 20 abilities, all randomly generated, go for it. At least mathematically there's no reason not to. (There may, on the other hand, be practical reasons not to.)
Second, if you roll multiple dice for each sampling, you reach the expected average faster. That is to say, D&D wit its 18 rolls is more reliable in not giving a character with all stats high than our The Unnamed Three. Recall that a player with exceptional stats in a session partly is the motivation behind this post.
Do We Need Random Abilities?
As a bonus, let's talk about random abilities specifically. Techniques we talked about make it likely, but not guarantee, that generated numbers gravitate towards the mean. However, since it is up to chance, there's always the possibility of an exceptional set of abilities in either direction. With that in mind, I think it's okay to generate them randomly under a few conditions:
Either your game, or the characters, lasts for a short while: if, after 4 or 5 sessions you generate a new character, then it doesn't make a huge impact if a character is way outside the expectations.
Abilities do not affect too many details, or has very small impact. If a character's strength only increases damage with melee weapons, or the highest bonus you can get is +2, then once again it shouldn't be a very big deal someone gets those bonuses.
Keep in mind that we're operating under the assumption of players getting upset if someone else gets exceptionally good results, or if they get similarly bad results. If you're unconcerned with such behaviour (or, alternatively, want to encourage them!) you can use random generation as you see fit.
In light of the two points about random abilities, we see that The Unnamed Three fits the first criteria but not the second: each +1 stat point increases success chances significantly. Not only that, but that there's only 3 stats mean about one-third of your checks will be made using that high stat. This is not the worst scenario ever, however we noted above that since we're rolling 6 dice total to generate stats, it is not unlikely to generate all stats to be relatively high.
Food for thought for a "second edition"!