EricJackson |

A while back, while demonstrating the difference between MtG spin-down dies and RPG d20s, I used the red d20 from the Beginner Box set. To my surprise, only a few sides actually added up to 21 on opposite sides--where as on all my other d20s, all opposite sides add up to 21. I thought mine was a defect until I checked the second copy of the BB I own and it was the same.

Anyone else notice this?

Tempest_Knight |

Most of the 'starter-set' poly sets I have gotten, from multiple different companies, are not properly pip'd...

The cheapest suppliers that most companies seem to be using have not understanding of Dice.

All opposing face pairs on a die should equal the minimum result plus the maximum result. (Generally speaking; Die size + 1)

Properly pip'd dice value thus;

D4: 5

D6: 7

D8: 9

D10: 11

D12: 13

D20: 21

Most poly sets have a Percentile D10 pair that value to 9 instead of 11.

The difference comes from the base math... the minimum value of a percentile d10 is 0, maximum value of 9.

I have one or two True D10s (value 11) and a bunch of Percentile D10s (value 9).

Sean K Reynolds Contributor |

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Any have any actual stats on whether or not the arrangement of the tiny, shallow numbers (not pips) on modern polyhedral plastic dice have any significant impact on the randomness of the die? Or is that just a precedent decided by on person at a dice company 40 years ago?

(Story: Mom makes a pot roast. Her kid asks her why she cuts a tiny bit off one end of it before she puts it in the pot. Mom says she learned that from her mother. Mom goes to grandma and asks her about it, grandma says she learned that from HER mother. They call up great-grandma and ask her about it, and she says, "oh, the pot I had was too small to fit the entire roast, so I'd cut a little bit off the end to make it fit.")

Tempest_Knight |

For most modern poly dice the big issue is clumping... take a spindown life counter... one physical half of the die is 11+.

I have not done a Scientific study, but my observations over many years of gaming tend to mediate any great variance in a non-clumped, improperly 'pip'd' die.

Clumped die (all high on one side) tend to roll higher, this trend is also seen in 'properly' pip'd Clumped Die.

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If I could get my hands on a 'frictionless' die spinner, I could test the dice for wobble.

Sean K Reynolds Contributor |

1 person marked this as a favorite. |

Okay, as long as you understand that your anecdotal experience is merely an impression based on your overall memory of hundreds of dice rolls of various dice, not statistical data that can be analyzed. So far... no actual evidence that the positioning of the numbers has any effect on the die's probability.

(Note that if 20-opposite-1 on a d20 is the "balanced" way to distribute the numbers, the die should actually be **more** likely to roll a 20 than a 1, because the 20-face has more material carved out of it than the 1-face does, which means the 1-face is heavier, which means the 1-face should tend to end up on the bottom of the die, which means the 20-face should end up on top more.)

(Note that this also means that variations in the **font** used on a die, such as serif or sanserif, should have an impact on its probability as well.)

(As would whether or not you mark the bottom of a 6 or a 9 with a dot or an underline.)

(As would heavily-decorated dice like these ones.)

(As would whether the numbers were inked, painted, or colored in with a crayon, all of which would have different weight contributions to the die.)

(And note that I don't think any of these things really play a significant part in the bias of a die.)

(And I'm a guy who wrote a program in the 1980s to use the chi-square method to test whether or not a die is biased...)

(In other words, I think you have bigger things to worry about than questions like, "does the relative positioning of the faces on my dice mean I'm rolling lower overall?" Your character's hair color has about as much impact on your dice rolls. :p)

LoneKnave |

I actually read a few scientific studies on this back in the day; I recall the statistics being that cheap dice actually rolling more 1s (GW dice being brought up as a prime offender).

Not sure if anyone did any on d20s tho. Feels like because of the massively smaller surface area ratio per side compared to a d6, small inaccuracies in the weight distribution because of uneven drilling/etching contribute less to the result of the roll.

Tempest_Knight |

If we want to get in to the scientific understanding of the dice...

Physics dictates that it has an effect.

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Look at a standard Chessex D20; the three connected faces of the 20 are 2, 14, and 8.

Look at a spiral down Life Counter D20; the three faces are 13, 16, and 19.

Physics dictates that the different distributions of mass will cause the dice to behave differently.

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Having gotten the 'pure' science answer out of the way...

Since we are not looking for 'perfect' randomization, we can ignore some variances in the behavior of the dice.

The amount of variance that gets ignored is up to the GM.

I hold MY dice to a stricter allowance (Opposing Faces rule) then I hold the dice used at MY table (non-Spiral/Half-and-Half).

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Also... I'll see your 'appeal to authority' with one of my own; I learned about dice from one who set standards in validating gaming(Casino) dice.

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Since Physics tells us that Font, Cut, Decoration, etc; all effect the behavior of the die, the question becomes: "How much?" or more importantly... "How significantly?"

"How much?" has a quantitative answer... I don't thing anyone has a grant set aside to fund the study to get the answer.

"How significantly?" has a subjective answer.

I come from a competitive games background and have a stricter mentality on rules/dice/etc (I call it my 'Gamer OCD'). I look to remove variance. To me an answer should never be "Expect Table Variation". This is reflected in My dice; I check them for the Opposing Faces rule and use only those that pass.

I play with people who are of the opinion that 'dice, is dice, is dice.' As long as it isn't a loaded die, it is good enough.

And just about everywhere else in between...

chbgraphicarts |

The main reason for spindowns not being legal for play in events at places like GenCon is because crafty players can manipulate the dice to roll certain ways, attaining a higher roll more often.

Spindowns are also not legal for determining who goes first at game tournaments for games like Magic the Gathering (who ironically are probably the BIGGEST producers of Spindowns in the world) for the exact same reason.

The numbers cut out of dice, as well, do in fact alter the rolls to a small degree (fractions of a percent to certain rolls).

The surest way to counteract this problem would be to have geometrically perfect dice with no beveling at all, nor any painted-on numbers on the dice, either - in other words, to have, say, a purple d20 with gold numbers built into the faces themselves, with the whole thing be made of the exact same material for both body and numbers, and all sides geometrically perfect and even.

This was much harder to do years ago, or even impossible, really, but now with 3D printing technology it's actually quite simple (in theory) to produce mathematically "perfect" dice that will give you absolutely even rolls every single time.

chbgraphicarts |

I actually read a few scientific studies on this back in the day; I recall the statistics being that cheap dice actually rolling more 1s (GW dice being brought up as a prime offender).

Not sure if anyone did any on d20s tho. Feels like because of the massively smaller surface area ratio per side compared to a d6, small inaccuracies in the weight distribution because of uneven drilling/etching contribute less to the result of the roll.

Part of this comes from how cheap dice are tumbled - they are polished like rocks and their edges are rounded. This often leads to imperfect edging and significantly greater rolling as well.

Cheap dice roll forever. Good dice, like Chessex dice, will roll only a few times before settling because of their sharper edges. Laser-shaped dice will probably not roll at all unless you apply enough force to purposefully MAKE them roll.

Ross Byers RPG Superstar 2008 Top 32 |

The main reason for spindowns not being legal for play in events at places like GenCon is because crafty players can manipulate the dice to roll certain ways, attaining a higher roll more often.

This. When used in a properly randomized fashion (dice cups, dice towers, or being rolled by a player who is not trying to cheat), a spindown is going to be as a fair as a similarly-made 'regular' die.

But a spindown is much easier to cheat with, because all the 'good' numbers are clustered together. You still can't get a 20 on demand, any more than with a regular die, but it gets a lot easier to guarantee a 10+.

I haven't taken a close look at my beginner's box dice, but they aren't spindowns. There is no reason fair dN's must have opposite sides that equal N+1, as long as they are 'random-ish'.

Nikosandros |

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I haven't taken a close look at my beginner's box dice, but they aren't spindowns. There is no reason fair dN's must have opposite sides that equal N+1, as long as they are 'random-ish'.

This careless attitude towards proper randomization is unacceptable to me. I demand that a new printing of the Beginner Box be issued immediately containing a randomization tool based on the observation and collapse of a quantum wave function.

2097 |

To see if a particular die is good or not, the easiest test is a Chi² or chi square test. There are calculators for this online or you can use a statistics package. I've checked all dice I regularly use. All sides are equally likely to show up.

To me, having the opposite sides add up is important, not for any "real" reason but for mystical reason. I even stopped using some very beautiful dice becaue they were wrong in this regard.

willwrk4internet |

If you're really worried about die fairness, then you shouldn't fuss about the manufacturing method of your die so much as you should worry about your die in particular. (Many people have already mentioned that defects in the plastic, settling, and other small variance can make even the most carefully crafted dice biased).

So how do you tell if your die is fair or biased? Test it. There's an article in Dragon Magazine #78 on how to compute chi-square values for any die. Basically the test amounts to rolling the die several times and then plugging the results into a formula. Some people have made online applets that do the math for you. See, for instance, this site

http://axiscity.hexamon.net/users/isomage/misc/chi2.cgi

You can do as many trials as you want to get an arbitrarily high degree of accuracy. I just tested my beginner box dice, and they are fair.

As long as your dice are fair according to this formula, you shouldn't care how the edges are distributed. Here fairness means that your dice are random within a very small margin of error. Even "electronic dice" (i.e. dice rolling apps) aren't truly random, because it's been known for a while that computers aren't able to produce totally random data. So at some point you'll have to live with almost random.

The only caveat would be the way that you roll your dice. Some people have perfected the art of rolling a spindown die so that it rolls high, but this sort of behavior should be noticeable to an observant DM. To ensure that your dice rolling technique is sufficiently random, it's best to cup your hands together with the dice inside and shake your cupped hands up and down or side to side. I think three shakes is enough to ensure your rolls are highly randomized, but again you can increase this number if you'd like.

That's my take on dice randomness. Math always saves the day.

Vic Wertz Chief Technical Officer |

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Ultra•PRO makes these high-precision aluminum dice... the pips are laser-etched, and they have varied the depth of the etching on each face to ensure that the amount of material removed from the single pip on the "1" face is equal to the total amount of material removed from the six pips on the "6" face, and so on.

Sadly, they only offer d6s right now. Also, they're about $10/die. But they're pretty awesome.

Erik Mona Publisher, Chief Creative Officer |

Garrett Guillotte |

A very incomplete sample of experiments regarding the effects of dice composition, rolling techniques, and shapes on the results:

**Informal:**

**Formal:**

*et al.*, Okanagan University College, presented at the 6th Experimental Chaos Conference, 2001, Potsdam, Germany): On casino dice, "all six faces have a probability of one in six, p = 0.1667 to within plus or minus 0.0010." On the toy die, they observed vastly larger variations.

*Dynamics of Gambling: Origins of Randomness in Mechanical Systems*(Strzalko

*et al.*, 2009): Includes detailed methods of analyzing different dice compositions and dice-rolling methods, and measuring their effects on the results. One of the findings from part of this book's research team in a later study (Kapitaniak

*et al.*, "The three-dimensional dynamics of the die throw",

*Chaos*, 2012) found that initial placement of a die in the hand has significant effects on the outcome of a toss onto a soft surface (2), but that effect is mitigated—though not eliminated—with each bounce on a hard surface. Or, "randomness in mechanical systems is connected with discontinuity as the die bounces."

I'll plumb my Reed College connections to try to get a copy of *Dynamics of Gambling* that appears to be in their collection. The excerpts I've seen suggest it's one of the more thorough accessible scientific examinations of dice rolls. There's a ~$25 paperback version on Amazon that's out of stock, and the ebook from the publisher is a typically academic $80 (discounted to a mere $64 on Google).

Vic Wertz Chief Technical Officer |

For whatever reason, a number of companies that manufacture polyhedral dice (especially those in China) have identical molds. I don't have any clue whether that mold originated at Koplow, or in China. (If you look closely, especially comparing the digits "3" and "1," you'll find that there are actually several fonts in use across the set.)