Skill checks: 3d6 vs. d20 and d100

One of the first crossroads I came to when starting my journey of creating the Altrix adventure game was what kind of dice should be used for skill checks. I knew skill checks would be a central part of the game, so I wanted the decision to be well thought-through. I now think that 3d6 – or some other combination of dice added together – in many ways is a far better option than having a single die, such as a d20 or d100. In this blog post I will tell you why.

My starting points and means for evaluation

My stated goals for the game were, briefly

1. to give impressions of adventures, fantasy and exploration;
2. to give the feeling of developing one’s character; and
3. to give good experiences together with friends and parents/children.

A lot of inspiration comes from Talisman (1983 edition) and Drakar och Demoner (kind of the Swedish version of Dungeons & Dragons). Talisman uses 1d6 for skill checks, which is one of the things I feel I wanted to improve. 1d6 gives to narrow width of useful skill values, with the result that skill checks in Talisman quickly becomes uninteresting (with a guaranteed success).

Drakar och Demoner (DoD) uses 3d6 a lot for rolling character stats, but 1d20 for skill checks. I wanted to evoke nostalgia for old DoD players, so using either 3d6 or 1d20 became the two options I explored in depth.

The feeling says d20…

My first thoughts were that d20 are cool and give a nice feeling. Kids who sees d20 for the first time are fascinated by them, and so are many grownups (like myself). Using d20 in the game thus seemed like a good idea. If kids opening the game box go wow and pick up some beautiful d20 and starts playing them, the game has a good start. Also, if a kid encounters d20 for the first time playing Altrix, and play it a lot, they will think about the game whenever they encounter d20 in the future.

So d20 is has a good start in the analysis. (The same arguments could be made for d100, but my firm opinion is that d20 are way cooler than two d10 and even the golf-ball d100. Which I own two of.)

…but the math says 3d6

Then I started looking at the “outcome space” of d20 and 3d6. The d20, like d100, has a flat distribution – all outcomes are equally probable. 3d6, on the other hand, has the useful property of the sum being distributed in a bell curve (ish):

Shorter scale but more flexibility

The non-flat distribution of 3d6 has a counter-intuitive effect. Even though the scale is shorter than for 1d20 (3–18 compared to 1–20), you can play around with it a lot more. To make it easier to see how, I will introduce some labels for probabilities:

• Certain: 100 percent chance of success. This is uninteresting in games.
• Very easy: ~90 percent chance of success.
• Easy: ~75 percent chance of success.
• Normal: ~50 percent chance of success.
• Hard: ~25 percent chance of success.
• Very hard: ~10 percent chance of success.
• Impossible: 0 percent chance of success. This is uninteresting in games.

The “very hard” range for 3d6 is 14–18 (5 steps). For 1d20 the range is 19–20 (2 steps). This means that negative modifiers on skill checks is much more likely to push the probabilities into “impossible” if you use 1d20 than if you use 3d6. Similar conclusions can be made for the easy end of the scale. At the ends of the scale, modifiers make little difference for 3d6.

If you look at the middle of the scale, the opposite is true: When rolling 3d6 a sum of at least 11 is “normal” – right at 50 percent probability. Adding or subtracting two steps would push the the probabilities into easy or hard (74 and 26 percent of success). For a d20, the normal difficulty is also at 11. But if you want to change it to easy or hard you would have to move no less than 5 steps in each direction. In the middle of the scale, modifiers make a lot of difference for 3d6.

Let’s say that again:

• If you use 3d6 for skill checks, you can often add modifiers without pushing the probabilities into certain or impossible, even if you started off with something that was very easy or very hard. On the other hand, you only need small modifiers to make a big difference when the difficulty is in the normal range.
• If you use 1d20, you can only use very small modifiers on skill checks that are very easy or very hard or they will become certain or impossible. On the other hand, you need big modifiers to make a difference when the difficulty is in the normal range.

Now the 3d6 option starts looking pretty attractive, right?

Seek the new normal

The math above has some interesting and useful effects when applied in board games. It becomes meaningful to seek challenges that match the player’s skill levels. Here’s an example to tell you how:

Let’s say that an adventurer in the game of Altrix has a skill value of +2 for “one-handed weapons” and also a one-handed weapon that gives another +1. The “normal” difficulty level for this adventurer would be 14, while 12 would be “easy” and 16 “hard”.

Also assume that the player can, to some degree, control how fearsome encounters the adventurer has. It then makes sense that the player steers towards challenges that are around “normal” – mostly 12–15 and the occasional 16 or even 17. At some point the adventurer levels up to +3 and gets hold of a +2 weapon, and so challenges between 14 and 17 becomes the new “normal”, leading the player onwards in the game. With just two steps on the scale!

In the game of Altrix I use this effect to guide/force the players to stay in certain regions on the board, but it could of course be used in a number of different ways in other games. (In the case of Altrix there is also a significant bonus if you exactly match the difficulty value with your skill check, making it attractive to match your skill level rather than seeking trivial challenges.)

Side note: The final argument for using 3d6 came when I started playing around with the idea of allowing re-rolls. Re-rolling 1d20 isn’t very meaningful, since you will end up anywhere on the outcome scale, independent of where you just were. Re-rolling one die in a 3d6 roll means that you select the lowest die. You can know in advance that it is more or less meaningful to re-roll – a roll of 3-4-4 isn’t meaningful to re-roll, but 1-4-6 is. This brings more meaningful choices to the players, and turns 3d6 from merely a randomness generator to a part of the game where players make meaningful decisions. That felt good.

Then I started playing with the idea that players should get “lucky crystals” to use for re-rolls whenever they roll a straight. (The probability for straight turned out to be 1/9, which felt right.) That finished the case for me, and I went for 3d6. Also, the “lucky crystals” turned out to be a starting point for the in-game story. But that’s a different blog post.

What about other dice combinations?

In this blog post I talk about 3d6 versus 1d20. What happens if you use other dice combinations? Here’s the long story short:

• What matters most is how many dice you use. 1d20 or 1d100 will basically behave in the same way.
• The more narrow your bell curve is, the stronger the effects described above will become. The bell curve becomes more narrow the more dice you roll, and the fewer sides each die has. 6d4 will give stronger differences between steps in the middle and at the end of the scale than 3d6. 3d20 will give you smaller differences.

There are, of course, other ways of making skill checks than rolling dice and adding modifiers – for example rolling a variable number of dice and counting every 5 or 6 as a success. I have not dived into the maths of other kind of skill checks, but feel free to leave a comment if you’d like me to look at some particular model. I kind of like analyzing the maths of board games. 🙂

Note: This blog post is a re-write of https://creatingboardgames.wordpress.com/2021/11/05/skill-rolls-3d6-vs-1d20/. I’m moving my blog to BGDL+.