What Do You Do with 120-Sided Dice?
newyorker.com
newyorker.com
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.
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.
Thank you! Reading the submission title, I was like, "um, replace every other die"?
They remind me of the (absolutely fascinating) "Go first" dice[1], any subset of which are guaranteed to produce a perfectly fair ranking.
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-...
I have not seen the d120, I don't know if the points would bounce it off its axis or not.
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.
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.
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.
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'.
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?
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. :)
Rolled a 19? Oh.. well actually I meant that the RED one was the tens. Now it's a 91! :)
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.
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!"
EDIT: check out other DiceLabs creations, crazy stuff in there. Link:
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.
Click on 'Add to Cart' for 'd120 Disdyakis Triacontahedron'
The advantage of polyhedral dice is that congruency of faces implies fairness.
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.
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.
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.
"“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".
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.
- http://thedicelab.com/d120tables.html
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.
Reducing game mechanics to one or more d6s is within the power of the game makers, but they use weird effects to differentiate themselves.
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.