# Is there a pattern for d8 dice?

I've just bought a d8, and noticed that the number arrangement is different from my other one. My new die has only even numbers on one half, and only odd on the other half. My old die has 1,8,5,4 on one half and 2,3,6,7 on the other.

Is there any correct pattern for it? Does it make any difference?

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There are three (obvious) ways to divide a d8 into two halves. It's perfectly possible for both of your descriptions ("only even / only odd" vs. "1,8,5,4 / 2,3,6,7") to correctly describe the same die. – Ilmari Karonen Apr 11 '14 at 21:10

There's no correct pattern, and in a fair die it makes no difference.

In practice, most standard dice sets are not entirely fair, because of how they're tumble-polished after removal from the molds.† How an unfair die is numbered can make it more unfair if the manufacturer decided to cluster all high (or all low) numbers near each other. Few manufacturers do this though, exactly for that reason—both your dice mix high a low numbers in each half, just in different ways.

However, the imperfect shape caused by tumbling affects the "rounder" dice more (such as the d20), and it's unlikely for a d8 to suffer noticeable unfairness.

† Due to demand for fairer dice, manufacturers such as GameScience and Chessex make dice that haven't been tumble-polished.

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There is no "correct" pattern, but a very common one, seen on 6-sided dice, and sometimes extended to higher-sided ones is to pair up numbers on opposite sides.

For 6-sided dice it is normal to have sides paired 1,6 / 2,5 / 3,4, each pair adds to 7. There are two different ways of having this arrangement. If you take a large number of 6 sided dice from different sources it is very likely you will find you can group them into two sets that both follow this arrangement, but which vary in how you can rotate them to match.

For 8-sided dice, it seems common to have sides paired 1,8 / 2,7 / 3,6 / 4,5 but I have seen exceptions (which are generally fine, you should not be concerned if it is not true for a die you own). There are 16 possible to arrange those pairings, see below for a full list.

For why this arrangement is common, many sources claim that it helps to keep averages correct for imperfectly-shaped dice. If your 'cube' is shorter on one edge, it would favour two opposite sides - if those sides don't give you an overall advantage, this is seen as fairer. Although it may also have been driven by numerology, and the design kept by tradition.

Identifying D8 variations (those with opposite sides adding to 9).

Rotate the die so that you are looking down onto a point with the 1 at "12 o'clock" and with the 2 at either "3 o'clock" or "6 o'clock" (one of these positions will be possible, if not then you have already got 1 and 2 on opposite sides, which of course makes the total 3). Read the numbers, starting from the 1, in clockwise order.

The following variations are possible:

• 1-2-3-4
• 1-2-3-5
• 1-2-4-3
• 1-2-4-6
• 1-2-5-3
• 1-2-5-6
• 1-2-6-4
• 1-2-6-5
• 1-3-2-4
• 1-3-2-5
• 1-4-2-3
• 1-4-2-6
• 1-5-2-3
• 1-5-2-6
• 1-6-2-4
• 1-6-2-5

These variations are the complete set for opposing sides summing to 9. It is not possible to take one of them and then rotate the die so that it exactly matches another one.

If you see one of the above variations, it does not prove that the opposite sides sum to 9. If you are not sure, then you need to check that also. And worth repeating: It is not a problem if you find a d8 that does not have one of the above patterns or does not have opposite sides sum to 9.

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I believe there are actually 16 distinct d8 patterns that satisfy the "opposite sides sum to 9" constraint. Specifically, the sides numbered "1" and "2" can share either an edge or just a corner. (They can't be opposite due to the constraint.) Either way, rotate the die so that "1" is facing you and "2" is to the left of it; that's enough to fix the orientation of the die, and leaves four choices for the placement of the "3" side and, once that's determined, two choices for the placement of the "4" side, for a total of 2 × 4 × 2 = 16 unique configurations. – Ilmari Karonen Apr 12 '14 at 21:19
@Ilmari Karonen: That's good logic. I'm going to have to double-check now, my original thinking was just finding an N!/M! style formula that made sense to me and fit 2 for a 6-sided die :-) – Neil Slater Apr 13 '14 at 6:33

It sounds like you have a dice designed for tracking numbers (life totals, mana, money, etc.) moreso than for rolling.

i.e. A 20-sided dice that goes from 1 to 20 sequentially.

I've haven't seen an 8 sided die before that wasn't the "1,8,5,4 // 2,3,6,7" combination before as life total die are normally higher using d10s and d20s. When you have a die that doesn't have the smallest paired up with the highest values, there is the chance to increase the odds of a better than average roll depending on how you throw it. That said, if you're not trying to cheat with it and throwing it intentially so it rolls to one side over the other it shouldn't matter.

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