
What Do You Do with 120-Sided Dice? - anthotny
http://www.newyorker.com/tech/elements/the-dice-you-never-knew-you-needed
======
SwellJoe
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.

~~~
egypturnash
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.

~~~
robocaptain
You captured a particular feeling I have as well - perfect!

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agrona
The mathematical properties of the distribution of the numbers on the sides
are very pleasing.

They remind me of the (absolutely fascinating) "Go first" dice[1], any subset
of which are guaranteed to produce a perfectly fair ranking.

1 -
[http://www.ericharshbarger.org/dice/go_first_dice.html](http://www.ericharshbarger.org/dice/go_first_dice.html)

~~~
cousin_it
Why not use a single d24?

~~~
Dylan16807
It takes some of the fun away not to give everyone their own die to throw.

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laxatives
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.

~~~
dsp1234
_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.

[0] - [http://www.newyorker.com/wp-
content/uploads/2016/04/Roberts-...](http://www.newyorker.com/wp-
content/uploads/2016/04/Roberts-Hundred-Twenty-Sided-
Die-690x516-1461623452.jpg)

~~~
logicallee
> 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...)

~~~
dsp1234
I'm not really sure what the argument here is.

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'.

~~~
logicallee
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.)

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YeGoblynQueenne
Oh, nice.

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?

~~~
Shivetya
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?

~~~
noarchy
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.

~~~
gknoy
> 10, 8

Me: "Sweet! I rolled 18." Friend: "Er, that's 9." Me: "... shoot."

I'd have noticed it sooner if it had been one of the other sides. :)

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donw
A bag of dice lives in my backpack, as it serves as the Ultimate Decision
Making Tool.

Sometimes there is just no obvious good decision, even after all the options
have been analyzed and considered.

So whenever I -- or my team -- gets stuck at one of those no-idea-which-road-
to-follow points, we roll the dice.

Because a bad decision is usually better than no decision.

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rrauenza
Also seen on Numberphile:
[https://www.youtube.com/watch?v=uAnCL3vhVIs](https://www.youtube.com/watch?v=uAnCL3vhVIs)

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11thEarlOfMar
Haha...

I'm going to pick one up and head straight over to The Embarcadero: "Guess the
number and roll the dice! Pays $10! only $1 to play!"

~~~
caf
You could pay $100 and still have an edge.

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nxzero
Buy a Dice Labs' 120-sided dice (d120) here:
[http://thedicelab.com/d120.html](http://thedicelab.com/d120.html)

~~~
jdcarter
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:

[http://www.mathartfun.com/DiceLabDice.html](http://www.mathartfun.com/DiceLabDice.html)

~~~
Nadya
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.

~~~
nabaraz
Here is the store page:
[http://www.mathartfun.com/DiceLabDice.html](http://www.mathartfun.com/DiceLabDice.html)

Click on 'Add to Cart' for 'd120 Disdyakis Triacontahedron'

~~~
Nadya
Thanks - but I was just replying that they hadn't missed a link. I've already
placed an order for a few dice. :)

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rodeoclown
Couldn't you just use a dimpled ball to get however many numbers you'd like?

~~~
dogecoinbase
Yes, but the currently-manufactured ones tend to be unfair:
[https://en.wikipedia.org/wiki/Zocchihedron](https://en.wikipedia.org/wiki/Zocchihedron)

The advantage of polyhedral dice is that congruency of faces implies fairness.

~~~
ars
You could also make a cylinder and roll it, or a top and spin it.

~~~
deepnet
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.

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Animats
You start looking for a really flat, hard surface. It should ship with a
polished granite tile and a level.

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nate_martin
Technically I think you could make any n-sided die for even n > 2:

1) Take an n-gon cylinder.

2) Smooth off the two ends to be spherical so that it never lands on either.

Now all sides have equal probability of facing up after a roll.

~~~
carstimon
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.

------
navbaker
I'm boycotting the New Yorker for failing to mention D&D even once in the
article.

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coldcode
I would like one the size of a softball. It's pretty cool looking to put on
your desk and roll when you get stuck.

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deepnet
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".

~~~
chronial
Yes, that is true. See here for a full explanation:
[https://www.youtube.com/watch?v=uAnCL3vhVIs](https://www.youtube.com/watch?v=uAnCL3vhVIs)

~~~
user2994cb
As noted elsewhere, bipyramids and trapezohedra can have unlimited (even)
numbers of sides - not very practical though.

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shostack
Extend the magic item table?

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p1mrx
In 4 dimensonal space, the 120-cell would make a d120 that's completely
regular, like a platonic solid:

[https://en.wikipedia.org/wiki/120-cell](https://en.wikipedia.org/wiki/120-cell)

~~~
user2994cb
If you are going to go 4 dimensional, you'll be wanting the dual of an
omnitruncated 120-cell, giving a d14400:

[https://en.wikipedia.org/wiki/Runcinated_120-cells](https://en.wikipedia.org/wiki/Runcinated_120-cells)

~~~
apricot
I had a modem like that once.

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amelius
It seems to me that the fewer sides, the more "perfect" the die can be, and
hence the more fair.

Unless of course near sides have almost equal effect in the particular game of
interest, in which case imperfections will have not a big impact.

~~~
wmil
The bigger issue is that once you go past the 5 platonic solids (4,6,8,12,20
sided) you have to play games with the shape and placement of faces.

~~~
user2994cb
You can also use the duals of (convex) uniform polyhedra (as here) - uniform
polyhedra have equivalent vertices, their duals have equivalent faces.

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JoeAltmaier
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).

~~~
tgb
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.

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todd8
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](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.

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johngalt
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.

~~~
protomyth
We had one player that would roll a d100 in a bowl. It was the ultimate
cheater's die. We banned it after two sessions.

~~~
saganus
Why? I don't see how a d100 in a bowl would make it easy to cheat.

~~~
protomyth
The sides are so small that its easy to bs the result or play with the bowl to
change the result. 100 sides make for hard tell on the top.

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Nadya
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.

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f_allwein
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?

~~~
NegativeK
Fun, not practical.

Reducing game mechanics to one or more d6s is within the power of the game
makers, but they use weird effects to differentiate themselves.

~~~
WorldMaker
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.

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venomsnake
Knowing my luck, I will be using it to roll natural 1s on the social saving
throws.

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henpa
Wow... I just learned that the singular of "dice" is "die".

[http://grammarist.com/usage/dice-die/](http://grammarist.com/usage/dice-die/)

~~~
defen
[https://en.wikipedia.org/wiki/Alea_iacta_est](https://en.wikipedia.org/wiki/Alea_iacta_est)

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userbinator
Looks like they go up to 144:

[https://commons.wikimedia.org/wiki/Dice_by_number_of_sides](https://commons.wikimedia.org/wiki/Dice_by_number_of_sides)

~~~
HelloNurse
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.

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jws
Wait around for it to stop rolling?

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grimmdude
It must be very difficult to figure out which number is up.

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zafka
I will let you know when I get mine. :)

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tahirafd17
Just rolling

