14

I am currently in the process of prototyping a game that revolves around triangles. I want my players to roll 3d4 dice to move, but am worried about the effects it might have vs. a traditional 2d6 setup.

The reasons I want to use d4s are:

  1. They are triangular prisms.

and

  1. I can use three of them and still only have a maximum of 12 rolled at any one time.

I am worried about the rolls always being just a few numbers. For 2d6, the odds of rolling a 12 (or the lowest #) are 1 in 36. For 3d4, the odds are 1 in 64, making my rolls less diverse. I seem to roll 7, 8 or 9 every time I roll 3d4.

I need to know if this would pose any problem to the movement factor in my game (for now, assume it has 40 squares).

  • 5
    @PhilipKendall No, it's not. A d8 is two square-based pyramids stacked back to back (square to square). Tetrahedra are triangle-based pyramids. – Arthur May 8 at 7:50
  • 3
    @ilkkachu and yet many of the most popular board games use dice for movement. From Monopoly and Ludo to stuff like Hero Quest or D&D inspired board games. In addition, 3d4 will mean a high tendency for an average and thus reduce the wild swings you might get (e.g., getting 2 or 12 using 2d6). – VLAZ May 8 at 9:42
  • 3
    Just as a personal opinion, I'm not a huge fan of d4s and how they roll and would shy away from them simply because of that. – Veskah May 8 at 13:00
  • 2
    Why not glue 2d4 together to make d6s? Now you have triangle-faced d6s. Obviously for production you'd want to get a mold or 3d print, but for testing purposes that should be sufficient. Bonus points: you can now include a "if you lose the dice, any normal dice will do in a pinch" – TemporalWolf May 8 at 20:14
  • 1
    As an aside, board game publishers will not look favourably on roll and move mechanics, which are largely seen as out of date and completely unmarketable. If you must use this mechanic, you should hide it as much as is possible (e.g. using cards/deckbuilding). – Stephen May 9 at 0:51
20

Doing some research shows you will still 5-9 range but it will be slightly more when you are using d4. Now if that difference causes a problem that would be up to you to decide. One other thing to note is you will no longer be able to roll a 2.

This comes from https://anydice.com/program/51b6

enter image description here

#    |  % for 2d6   |  % for 3d4   |
2    |   2.777778   |     0.0000   |
3    |   5.555556   |     1.5625   |
4    |   8.333333   |     4.6875   |
5    |   11.11111   |     9.3750   |
6    |   13.88889   |     15.625   |
7    |   16.66667   |     18.750   |
8    |   13.88889   |     18.750   |
9    |   11.11111   |     15.625   |
10   |   8.333333   |     9.3750   |
11   |   5.555556   |     4.6875   |
12   |   2.777778   |     1.5625   |
  • 2
    I wouldn't say it's "slightly more". 3d4 gives 6-9 nearly 70% of the time; 2d6 is just 55%. – David Richerby May 8 at 8:50
  • 3
    "Now if that difference causes a problem that would be up to you to decide" just to elaborate here - assuming a single line of movement (e.g., Monopoly), then players will tend to stay relatively close together as they have a high chance to either roll the same numbers on this movement, or get equivalent scores over multiple rolls (e.g., player A rolls 7, then 9, player B rolls 9, then 7). This "clumping together" need not be a problem and indeed might be useful. If there are multiple paths available, that becomes less of a concern. – VLAZ May 8 at 9:54
  • You are usually not aiming for a specific target when rolling speed, but rather "greater than or equal to a value". As such a CDF is more informative. – Yakk May 8 at 17:46
12

In general, rolling more, smaller dice will give a narrower range of possible answers and a distribution that's more concentrated around the average value, compared to rolling fewer, larger dice. This is easy to see by looking at the extremes: rolling a single d12 will give every value between 1 and 12 with equal probability (broad range, no peak at all), whereas rolling twelve d1s will give you 12 every time (narrow range, nothing but the peak).

This is, essentially, the central limit theorem in probability theory, which says that adding up more and more independent random numbers (e.g., dice rolls) gives a better and better approximation to a normal distribution. The width of the "bell curve" depends on the variance of the random numbers that are being added, and the variance of a single dice roll decreases as you decrease the number of faces it has.

Joe W's answer gives the specific stats for the two cases you're considering, so I'll not repeat those.

4

General opinion is that D4s are unsatisfying to roll.

D8s have triangular sides and roll well. You can get D8s with different values to bias your distribution.

3 D8s with distribution: 1, 2, 2, 2, 3, 3, 3, 4 will still give you outputs ranging from 3-12, but your bell curve will be more extreme.

link with distribution: https://anydice.com/program/14e90

  • Interesting idea, I'll think about it. – TheCentaur May 8 at 22:00
  • Why are they unsatisfying to roll? I have never heard that before. – Joe W May 8 at 22:30
  • 4
    D4s are unsatisfying to roll because the corners are too sharp for it to properly roll. Root specifically got around this issue by creating custom d12s that simply had 0-3 on an equal number of faces. – Stephen May 9 at 0:56
  • 2
    @JoeW Because they simply don't roll. If you cast them flat, they just land and skid across the table the same way up as they landed. – David Richerby May 9 at 12:38
2

Of interest is the number of rolls to finish. For a 40 square game, rolling 2d6, it takes an average of 40/7 or 5.7 rolls to finish.

The Var(2d6) is 70/12. Variance of "5.7" rolls of 2d6 is 33.25, SD is then about 5.76, and 95% confidence is then around +/- 11.3 or about +/-1.6 rolls. So naively, it will take 4.1-7.3 rolls to finish.

For 3d4, average is 7.5, so 5.333 rolls to finish. Var(3d4) is 45/12, over 5 and a third rolls that is 20 variance, so 4.47 SD and +/- 8.76 confidence, or +/- 1.17 rolls; so 4.16 to 6.5 rolls to finish.

(This uses napkin math based distributions; the actual statistics are a bit more annoying, but will be close.)

Feeling the difference between those game lengths is going to be hard.


I'd argue you should start upside down. How many rounds do you want the game to be? How should the on-board stuff (say, move forward) have impact compared to dice rolls?

I'd also argue that "rolling a bunch of dice and adding them up" isn't a great mechanic. There is so much more you can do with dice -- pairs, runs, etc.

  • This game will have many go-arounds (like monopoly), and the spaces landed upon will have an impact on gameplay. There are certain spaces that may eventually require players to pay other players, and some spaces that will reward the roller with an extra roll or currency. – TheCentaur May 8 at 21:15
1

If you want to have something very similar to 2d6 but using d4's, do 4d4 - 1d4. This can be implemented by having five d4's, four of which are the same color and one is a different color. This is not exact, and it does add a 2% chance of getting numbers higher than 12 or less than 2, but it's closer than 3d4.

https://anydice.com/program/14e8a Dice graph

If you want to go heavier on the flavor, use 3-sided dice rather than 4-sided (these can also just be 6-sided dice numbered 1, 1, 2, 2, 3, 3):

3-sided die

3d3 will give you a much lower average roll than 2d6, but you could adjust for this by making the map smaller or just putting things closer together on the map.

https://anydice.com/program/8667 dice stats 2

  • Using 4d4-1d4 breaks the theme of three in my game, so this would not work. – TheCentaur May 8 at 20:10
  • @TheCentaur what aspect of the theme does this break? – Zags May 8 at 21:25
  • The entire idea of the game is that everything comes in threes, which was my entire idea for rolling 3 triangular pyramid dice. I see your point, though. I may have to make a sacrifice. – TheCentaur May 8 at 21:49
  • @TheCentaur I added another suggeston – Zags May 8 at 21:56

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