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Six-sided dice traditionally have opposite faces adding to a constant, and this tradition is carried over (unquestioningly, it seems) to other dice. Is there a good reason for it? Why wouldn't you instead seek to make opposite ‘hemispheres’ as equal as possible, ideally arranging that the center of gravity of the pips is the geometric center of the die?

Added four years later: I recently did some searches: There are no ideal arrangements for D4 (obviously), D6, D10, D12; three arrangements for D8; 876 arrangements for the rhombic dodecahedron; and somewhere between seven and gazillions (the search is a long one!) for D20.

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    To make the result more independent of how it's thrown. Can you make a D6 so fair that one can't learn to throw it with a preference for {6,5,4} over {1,2,3}?
    – Anton Sherwood
    Feb 16, 2017 at 9:29
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    MtG D20s actually have hemispheres, because they are used as health counters. Numbers are in order next to the face. So, 15 will be right next to 14 and 16, to make it easy to go up or down health. But without a reason to change the layout, why would game makers even bother?
    – CyberClaw
    Feb 16, 2017 at 11:23
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    @CyberClaw MTG spindown dice are also not legal for use in tournaments for the reason Anton is talking about; because a skilled player could learn to throw the dice so that it always lands in the higher range of numbers. A regular d20, on the other hand, is designed so that even if you could throw it so it would land in a general area, that general area would have both high and low numbers.
    – GendoIkari
    Feb 16, 2017 at 15:33
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    Surprised no-one championed this as off topic. Seems an appropriate question for history, engineering or math SOs to name a few. I guess games have dice so we get it here?
    – joedragons
    Feb 17, 2017 at 15:49
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    @joedragons, heh, well, I thought of taking it to Math but: isn't gaming the primary function of dice, and therefore the proper context for questions of their design? I wonder whether any other exchange has a ‘dice’ tag!
    – Anton Sherwood
    Feb 17, 2017 at 20:18

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To prevent skill from being a factor in rolling

Dice have an even distribution of the numbers around the faces to prevent (or at least reduce) the ability to modify your chances of a result by skillfully rolling the die. Dice are intended to be entirely luck based, and depending on how the numbers are distributed around the faces of the die, could lead to skilled rolling (generally considered cheating).

It is for this reason that Spindowns are generally not allowed to be rolled anywhere that a random result is required (IE Tournaments, Organized Play, etc). For the same reason, d10s shouldn't be rolled to get an Even/Odd result as you can very easily force the desired result.

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    That last part about the D10s is something I didn't realise. Since some games use only D10s (e.g. World of Darkness games), they are also often used as a D2 by rolling Odd/Even. I might have to see if there's another way to simulate a D2 on a D10 in our gaming sessions
    – Warpspace
    May 7, 2017 at 2:59
  • High/Low for d2 works just fine with a d10. Just make sure you decide whether a 0 is high or low before you roll!
    – aslum
    May 7, 2017 at 3:22
  • Seems to me, the conventional arrangement for D6 is the furthest possible from “even distribution”. The most even would (I guess without checking) have 1 opposite 2, 3 opposite 4, 5 opposite 6.
    – Anton Sherwood
    Jun 16, 2018 at 6:11
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    Casino dice have the pips filled with a coloured material of the identical density as the matrix.; making OP's concern over weight irrelevant. (Often white pips in a red or green matrix.) Then the only concern is to minimize "skill" in the rolling action itself. Casinos manage this in games such as craps by requiring the dice to hit the floor of the table prior to hitting the wall, introducing an element of uncertainty near impossible for the player to exert control through.
    – Forget I was ever here
    Nov 25, 2022 at 21:46

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