When I was a kid, I played RPGs (AD&D, mostly) a lot, and we all loved the oddball dice. 30 sided die and 100 sided got a lot of use. The 100 sided one was a dimpled ball with some sort of pellets inside (to make it stop rolling faster). I'm not sure how fair it was, but it was fun. There were, at the time, several little books of random/funny things that could happen in the game based on a 30 sided die roll; battle results, random encounters, etc. Published by the dice manufacturer, I presume.
I long ago got rid of all of the books and boxed sets. But, I still carry the little faux leather bag of dice from house to house. Not sure why. Something about the feel of the dice has the strongest memory association with that time and those friends.
I don't really have anything to say about this particular die, but if I still played RPGs, I would find something to use it for. I would have bought it in a heartbeat, as a kid.
What with one thing and another I've long since lost the collection of polyhedral dice I accumulated as a teenager. And I don't have time in my life for RPGs. But I have a modest collection of dice stashed away. Including weird-ass ones like big transparent D10s with smaller red D10s inside.
They're just kind of... totems, I guess. Symbols of the kind of nerd I am.
I have absolutely no earthly use for this damn thing. But I ordered one. And a set of these folks' interestingly-shaped d4/8/12/24/60, as well. And their "numerically balanced" d20. I may never use any of these dice. But there is a part of me that is intensely satisfied by owning them.
This same phenomenon, BTW, is precisely why base-12 is far, far, hilariously far better than base-10, which is somewhat sad and pathetic by comparison.
Snarky answer is to divide by 20. But I wonder if a die that large is even fair. Presumably a lot of the randomness in a coin or 6 sided die is that each bounce can flip the object multiple times, generating a roughly uniform distribution after a few bounces. If its too large, it may only reach a portion of the neighboring values at each bounce.
only reach a portion of the neighboring values at each bounce
From the picture of the dice[0], it looks like it would still be fair enough due to the fact that there is a large difference in the numbers available 'nearby' any one spot. But since it's big (but not super big), I'd guess that it would probably be rolled towards some sort of back stop, which would allow for additional opportunities for it to bounce.
One of the problems with a d100 that I saw is that it can be rolled along an axis somewhat reliably. If the numbers are well distributed, the average and those above/below average may still be sufficient. Specific numbers would be avoided by putting them at the poles, or others given greater chance by putting them along the equator of the roll.
I have not seen the d120, I don't know if the points would bounce it off its axis or not.
If you want a random value in the range, that's probably fine, but it would be bad for a roulette-style game, where you bet on a single, specific number. If you can indeed roll it on an axis reliably, you can increase your odds significantly.
Yes, it always was a neat gimmick, but in practice, using two ten-sided dice was a far superior approach. d30s were bad enough, but at least with them simulating (e.g. with a d6 and d10) wasn't as intuitive.
That enforces that the mean value should be close to 60, but doens't say much about whether it is fair in that it should have also have a uniform distribution.
> it looks like it would still be fair enough [if it only reaches a portion of the neighboring values at each bounce] due to the fact that there is a large difference in the numbers available 'nearby' any one spot
what is this, NSA logic day? :-D
(This is my way of saying that your argument actually results in really low randomness. It means the random process has some memory and has far less distribution of states than you would expect. your argument is like saying a good way to get a random number between 1 and 1,000,000 is to flip a coin, then heads it's 170,158; tails it's 587,439. There's a large difference between 170,158 and 587,439 but those two numbers wouldn't be random AT ALL, because all the other numbers couldn't come up. you're saying the die would 'still be fair enough' because the numbers that can come up are far from each other... well, no...)
No matter how you lay out the numbers, a nice hard roll will give you a completely uniform result. The goal here is to make it harder to cheat when you can partially control how the die rolls.
Nobody is pretending there is more entropy than the number of outcomes. What we want is a design that can't be influenced in favor of the roller, even when entropy is a bit low.
Let's design two layouts for a d100. We'll say that you can roll each design two ways. You can roll it properly and get a random number from 1-100, or you can roll it improperly and it will stay within a cluster of 10 numbers, giving you a random number out of that cluster.
The first layout puts similar numbers together. 1-10 are all together, as are 11-20, etc.
The second design is laid out so that every tens digit show up in each cluster, and every ones digit shows up in each cluster.
Both designs can give you equally random numbers. A proper roll gives you a uniform distribution over 100 numbers, and an improper roll gives you a uniform distribution over 10 numbers.
But look at what happens when you apply certain functions to the output. A common use for the d100 might be emulating a d10. If you divide the first die by ten, a proper roll acts like a d10, and an improper roll lets the cheater pick what result they want. With the second die, a proper roll acts like a d10, and an improper roll also acts like a d10.
Fairness is preserved when the imperfections in the randomness don't matter. Your coin method looks like it would be a fair way to pick lottery numbers if it was only used once. But it would be a fair way to pick even or odd indefinitely.
I don't think I'm reading that post wrong! The original poster said " But I wonder if a die that large is even fair." Then the response said it's "fair enough" because even if it only spins part of the way, you'll still get one of a group of dissimilar numbers.
but that's not fair by the definition of what a fair die is. (it has a definition, if you search google you get "In mathematics we say 'fair dice' when we mean that there is an equally likely chance of landing on any face.")
You're basically arguing that dice don't need to be fair. also you completely missed my jab at the NSA breaking RNG's while making them seem "random enough", i.e. getting to quite dissimilar next states while in fact having only a few possible next states.
It's "fair enough" because it gets the important parts right of having a large number of states. Just like your coin flip would get the important parts right if it was used in specific ways.
A coin in the real world isn't fair, because it could land on its side. But it's fair enough.
Statistical sampling doesn't give you guaranteed-accurate results. But the biases cancel out across the metrics you're measuring, so it's good enough.
I didn't ignore your jab at the NSA, but it's pretty weak. The backdoored CSPRNG doesn't give numbers that are worse than any non-backdoored CSPRNG. Depending on your perspective, it can give you uniformly any number, or it can give you only a single number, and the same is true of good algorithms too.
I enjoyed this perspective and it changed my thinking, you've convinced me. It's also unlikely that humans can keep track of the distribution of 120 numbers on a die (in any distribution) so even if the game the cheater is playing is "Pick 20 numbers, then roll. If you roll any of the 20 you win" it is unlikely that they can remember what the die looks like well enough to cheat - except perhaps after massive effort. Fair enough :)
Given the fact that each vertex of the die has 10 triangles that sum to 595, and including a non-malicious roll against a backdrop, I don't see how this die is any more or less fair than a normal d6 (which I believe we can concede is 'fair'). After all, if you want to cheat at dice, then you can cheat at dice regardless of any common understanding of 'fairness'.
In particular, I was responding to the following comment, "If its too large, it may only reach a portion of the neighboring values at each bounce".
My argument was only that if you drop the dice from say a distance of 3", and it doesn't bounce then at a minimum, you wouldn't get a large grouping of numbers that are all near each other (Even if you were able to somehow pick a specific 'vertex' to always land up, you're going to have a total average of 59.5). In other words, you couldn't drop the die such that you could guarantee a range of 110-120 (which you could for example do on a MTG spindown die, which is fair but not uniform). In other words, even if there is no bounce, a typical rolling of the dice would be 'good enough' for say a pen and paper RPG, and even just dropping it without the bounce is likely enough to give non-Vegas levels of 'fairness' even if 'it may only reach a portion of the neighboring values at each bounce'.
mathematically, if your "range" is one of the ten numbers 108, 43, 21, 18, 32, 40, 79, 50, 94, 59 then it is just as broken as if your "range" is 110-120. it's not considered fair. fair means random and evenly distributed. (when it comes to dice and coins.)
not sure how someone can downvote me, if you google "define dice fair" you get "In mathematics we say 'fair dice' when we mean that there is an equally likely chance of landing on any face", i.e. random and equally distributed.
When I was a kid, I played D&D once or twice, and noticed on one of the dice, that the edges were somewhat rounded off, and the faces had different areas. I don't know if it was by intent, but I was pretty sure that those dice would favor certain faces.
I used to make up RPG rules for fun and one of my systems used a die scale that went: d20, d40, d60, d80, d100, d120.
Those are just die sizes that are easy to make with the commonly available dice: a d20 is a single die, a d40 is a d4 and a d10 (reading units on the d4 and tens on the d10) and so on.
The thing is that d[20,40,60,80,100,120] is a nice, smooth scale, unlike what you get if you use the d[4,6,8,10,12,20] on their own.
And that works alright, but it's always nice to have the exact sizes.
"What do you do with 120-sided dice" indeed! Roll, them, duh. What else?
We went through rolling d100 using three d10. One die determined which of the other two was the tens die. It was odd, but some people thought it gave them an edge and why argue with a harmless tweak?
That seems odd, maybe because I am used to the "conventional" way of rolling d100: roll two d10s, where the first die is concatenated with the second. A roll of 0 on both dies indicates 100. Some d10s are even sold with a zero tacked on, so you actually see 10, 20, 30, etc, instead of 1, 2, 3, etc... just so there is no question as to which is the "tens" die.
We would always roll two d10 for 1-100. You would call one as the "tens" die before you rolled, but inevitably, this would be a great opportunity to fudge things a bit.
Rolled a 19? Oh.. well actually I meant that the RED one was the tens. Now it's a 91! :)
Thank you! I read the whole article but couldn't find the "here's where to buy it" link. (Maybe I just missed it.) I have no need for a d120 but I have the WANT for one.
EDIT: check out other DiceLabs creations, crazy stuff in there. Link:
There was no link to buy it! Just a mention of Dice Labs. That or I missed the "buy it here" link myself.
I found it a little strange since the purpose of the article seems to be to try and sell some pre-orders of the die but there wasn't a link to go order it.
No, because the group G of rotations of the 2-sphere that preserve the set of all "dimples" X (so for all g in G, g(X) = X) on the sphere has to have a member g(x,y) in G for all x, y in x such that the action of g(x,y)x = y; that is, any point can be transformed into any other point by a rotation that nonetheless preserves the whole lattice. This is called face-transitivity* and there are a finite number of recursively enumerable sets of face-transitive solids: the bipyramids, the trapezohedra, the prisms and antiprisms (as log dice), and the Catalan solids. Bipyramids and trapezohedra are quite impractical at high face counts because they take on a biconical shape whereas spheroids are ideal. Log dice are fair if they roll a lot, but they're not as cool.
Or a bag filled with numbered tiles, but a dice is a dice not the general category of random generators.
I have seen both your suggestions used in games so fair enough, and the cylinder reminds me of the inelegance of the 10 sided dice, but that had no end face to land on like a cylinder.
You can even make it polygonal. Even more interesting, you can make it non symmetrical, contradicting the article's claim that
dice must be symmetrical to be fair.
You make an (n-2)-gon cylinder. This has n faces (the sides, the top, and the bottom). If you make the top and bottom very small, the probability of landing on them is smaller than the probability of landing on the sides. If you make the top and bottom huge (compared to the sides) the probability of landing on a side is smaller. Somewhere in the middle, the probabilities are balanced.
The article states no higher sided fair dice can exist:
"“ultimate fair die allowed by Mother Nature (i.e., mathematics!),” since a die couldn’t, practically speaking, possess more sides or more symmetry, and dice must be symmetrical to be fair."
Mathematicians is this true ? Or only "practically speaking".
I've always imagined using a cylindrical die to get arbitrary odds. E.g. a 17-face cylinder that you roll. The numbers could be printed on the ends, you take what appears at the bottom (flat with the table).
These are moderately common. Pointed ends (without numbers) and skinny triangles that approximate a cylinder (with numbers) roll nicely and, allow unusual face counts. But I've actually seen it most often for the humble d4 which has a reputation, in some circles, for not rolling great in its usual tetrahedral form.
I have a small plastic container of different kinds of dice, which I use to generate passwords from my own Diceware-style word lists (see http://world.std.com/~reinhold/diceware.html). I like the 10 sided dice so that I can roll 4 and pick any number from 0000 to 9999. For an RPG that needs a "random" percentage, two of these (in different colors) would suffice. Any board game store has an assortment of crazy dice for sale.
Generally we would just use die combinations for anything over a d20. D10s are great for this. We had a d100, but it would never stop rolling. Much faster to roll two d10s.
Buy it, of course. Though it will be more of a novelty item on my desk to go alongside other oddities rather than see any "real use". I don't play any tabletops and the board games I do play don't warrant any die with more than 20 faces.
Wonder what the practical use for gamers would be. There's obviously good reasons for having 20-sided dice (e.g. more granular results in fights). Would 120-sided dice have added benefits, or is there a point at which more sides don't matter?
"The d120 can be used as a dn, where n is any proper factor of 120. For the standard seven-dice polyset, a d120 is the ideal "multi-die", as 120 is the least common multiple of 4, 6, 8, 10, 12, and 20."
So you could whip one of these out instead of the usual Crown Royale bag full of a zillion different dice if you wanted to have a minimalist flair at your regular gaming session.
Mostly though I think it's just a cool thing to add to that bag full of dice. You're playing these games in part to fantasize about collecting lots of pretty gems, and this is like adding a big diamond the size of your fist to that collection of little rubies and sapphires.
There's an aesthetic difference in rolling different sorts of dice, they have a different look and feel, so game developers could reduce all rolls to some standard die like d6, but rolling a variety of dice is "more interesting" to players.
There are systems that are all d6s, there are systems that are all d10s. There are systems that like to pick dice based on the whims of what seems most interesting to players.
Games are typically more about fun than practicality.
Asymmetrical. You'd need to divide the pentagons in a regular dodecahedron or the rhombi in a rhombic dodecahedron into 12 congruent parts, which isn't possible.
I long ago got rid of all of the books and boxed sets. But, I still carry the little faux leather bag of dice from house to house. Not sure why. Something about the feel of the dice has the strongest memory association with that time and those friends.
I don't really have anything to say about this particular die, but if I still played RPGs, I would find something to use it for. I would have bought it in a heartbeat, as a kid.