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I'm thinking about designing some custom dice, and the easiest way to prototype would just be to put stickers/paint on wooden cubes.

Does their fairness (clearly imperfect, especially so with artisanal dice) actually come up in real life, or is die fairness more of a theoretical problem? How can I roll dice so that their "unfairness" is dampened?

How often have you noticed a die being unfair in real life?

  • One thing to remember about dice is the way you roll them can have a big impact on how fair or unfair they are so it is not just on the quality of the dice to determine fairness. – Joe W Dec 10 '17 at 15:24
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    Related: Using cowrie shells as dice. – Tim Lymington supports Monica Dec 10 '17 at 23:17
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    Loaded dice have a venerable history in gambling: en.wikipedia.org/wiki/Dice#Loaded_dice – DukeZhou Jan 10 '18 at 17:46
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    @xorsyst is right. Amazon has 50 blank dice for under $10 as my first result there, ebay has 25 for $3 right now. stickers on these are your best bet for fairness of the dice in prototyping, though your production model will need some care as to how you intend to handle the balance, unless you go with stickers in production (not really recomended) without knowing the specifics of the faces, there's not much more we can suggest. – Andrew Jan 11 '18 at 17:09
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    It sounds to me like the question really is: is the margin of error for the physical dice great enough to meaningfully skew the results in play testing. You are much better at statistics than I, but my feeling is, if the margin of error is not slim, you might need to use an algorithm for rolling until you can get balanced, physical dice... But, Andrew's suggestion seems quite sound, b/c magic marker on blank dice won't affect the rolls. – DukeZhou Jan 11 '18 at 17:09
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I think all it's really possible to say here is that yes, it's a real potential problem. Dice can be unfair, and if they are, you can't really avoid it with rolling technique, and it will skew your game.

I think it's fairly uncommon with commercial games, but I'm not sure how that's relevant to your homemade dice. For what it's worth, my copy of Small World has a wooden die that I eventually found to be slightly unfair (based on test rolls, it has a statistically significant bias), so if it can happen with commercially manufactured wooden dice, I wouldn't be optimistic about homemade ones.

For your actual problem, initial playtesting with custom dice, I would personally just use regular dice with a mapping from numbers to your custom dice faces. If that bothers you too much, or you're to the point where you really need to be prototyping the actual design, I'd put stickers on real dice (preferably blank - it's easier, and they're likely more fair), rather than wooden cubes, so you know they started out as fair as possible, and if the stickers are the same size and placed the same on all the faces, you shouldn't have anything to worry about.

  • Don't use real dice, they are actually unfair (as laid out in my answer below) but their unfairness is handled by the numbers in the dice, if your faces are custom you could deal with it but it is better to get blank balanced cubes and sticker on them, this handles the pip fairness issue. – Andrew Jan 11 '18 at 17:06
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    @Andrew Properly made real dice are fair, and are certainly more fair than homemade wooden cube dice. – Cascabel Jan 11 '18 at 17:09
  • While I agree that they are more fair than any wooden dice, the blank cube starts out fair and balanced, then 1 and 6 are placed opposite each other, with 1 having 1/6 the amount drilled out, the same with 2 and 5 (2/5) and 3 and 4 (3/4). This creates a weight imbalance in the cubes. – Andrew Jan 11 '18 at 17:13
  • I understand the issue you're describing, but not all dice have it. – Cascabel Jan 11 '18 at 17:13
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    I've edited slightly. I still don't think that "don't use real dice" is a helpful thing to say, though. They're all better than the OP's proposal, and if you want to be careful about fairness among the choices for real dice, I would say "use the blank kind". Those are still real dice. – Cascabel Jan 11 '18 at 18:06
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Dice fairness is a real issue, not only in imperfections in the material, which would be more common in wood or any natural material, but also the way the faces are designed, 6 is opposite 1 on a traditional dice, the weight of the 1 side is higher on the traditional die as more is drilled out to make the 6.

There have been many ways attempted to handle this issue in the past, sometimes holes for pips on a die are larger if there are less of them, removing the same material for each size, other times the sides have numerals not pips, allowing for a more equal removal of material, the other largely suggested option is printing or stickers, adding the same amount to each face to show the difference. Some games handle the unfairness of dice by changing the target as time goes on and using a combined score between multiple dice (though multiple dice introduces it's own unfairness as the edge combinations are rarer than the average, there are many more ways to hit a 7 on 2 traditional dice than a 2 or 12), Craps for instance does both of these.

  • Great answer re: holes for pips (Just had to say it!) However, I might rethink categorizing "edge rarity" as unfairness, as opposed to a distinct probability distribution, because Catan players seem to love that effect: cs.stanford.edu/people/nick/settlers/DiceOddsSettlers.html – DukeZhou Jan 10 '18 at 17:40
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    @DukeZhou true, that he rarity of edge values when more and more dice are added is probability distribution, the unfairness for that potentially comes into play from game design, more than the probability of the role itself. – Andrew Jan 10 '18 at 19:56
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    I guess my main point was that such distributions can be useful. I'm been thinking a bit about mixed dice, like a white d6 for + and a black d6 for -. Caps the max at +5/-5. Or a d6 with [1,1,1,2,2,3], where you want the integers small, but still want a varied distribution. The possibilities are endless. But you make a good point that these probability distribution must to be analyzed, and harnessed by the designer in a conscious manner to be useful. – DukeZhou Jan 10 '18 at 20:27
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    It's also worth pointing out that the unfairness of dice is fair... if everyone uses the same dice. Since every player experiences the same unfairness equally, if may be unfair in the roll results but it is fair between the players of the game. This is also true of different traditional dice, the size of pips, as long as they are the same across the die, would have the same effect on the fairness of each die, assuming no balance issues in the cube the die was made from. – Andrew Jan 11 '18 at 16:51
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It's definitely not just theoretical - if say in Settlers of Catan one of your dice was unfair, it would skew the probabilities of the number coming up and thus screwing up the strategy.

Fair dice also makes it easier to properly balance the game. I would suggest using website such a http://anydice.com/ to verify your game is properly balanced.

  • Nice reference to anydice.com for testing. It's bewildering that this answer was downvoted! (The OP was asking about validating his system through testing, so this is the most practical answer, from a game design standpoint.) – DukeZhou Jan 10 '18 at 17:41
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    (I didn't downvote) - yes, anydice is a great resource. But this answer is rather incoherent. "Fair dice also makes it easier to properly balance the game..." - yes, and cards that are all cut the same size makes it easier to shuffle. These truisms don't really cut to the heart of the matter. It's absolutely paramount to have dice be as "fair" as possible. This question is almost better suited for a physics forum. – The Chaz 2.0 Jan 10 '18 at 18:50
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    @TheChaz2.0 Fair points. And I know for a fact, the OP uses anydice extensively. Nevertheless, I still feel this short post will be useful for those not aware of the resource. Also worth pointing out that loaded dice in Catan would only be unfair if they were intentionally introduced by a player who knows the imbalance. If all players are unaware of the flaw, the game is still fair, just won't be as predictable. But for the OP's question, related to testing, unbalanced dice will skew the evaluation of the mechanics. – DukeZhou Jan 10 '18 at 20:31
  • Hi. Thank you for the feedback, I admit my answer could have been better structured and more informative. My point was simply if the dice aren't fair in a significant way, all bets are off. You can't rely on "special" rolling techniques and even if all players are unaware of the unfairness, if in game of Catan 6 is more likely than an 8 then whoever chooses the former has unfair an advantage. – Hai Jan 14 '18 at 11:11
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    True. The shuffle of the cards would definitely be different from the action of dice, and affect distribution. (Thanks for bringing that up--I was in the realm of "Platonic ideals" when I proposed it;) However, you might find this of interest re: dice physics.stackexchange.com/a/339984/152803 – DukeZhou Jan 16 '18 at 23:31

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