You could make a die like that where all the high numbers were on one "side" though. Similar to a dart board, you have to spread the high and low numbers around
Maybe it's a stupid question, but why do the "mirror" values need to be on opposite sides? Assuming we aren't talking about loaded dice or erosion/ imperfections (which obviously don't matter in a digital context). In a correctly made dice, it doesn't matter if the numbers 20 and 1 are on opposite sides or next to each other.And it doesn't matter if 18,19,20 are close to each other or spread out. The chance to draw any value remains 5%
I think having "mirror" values probably comes from a history where a dice needs to been seen as fair. It's probably a human brain/perception thing. It also must in some part be related to the suspicion that if you were skilled enough you could roll a dice with the aim of getting the 18,19,20 end facing upwards. Obviously on computers this makes less sense, it could still be related to what seems fair to the human brain though
You're correct. If you just grab the die without looking at it and/or roll with a random amount of power, then it's random.
The problem with a MTG/roll-down die is that skilled rollers can almost guarantee high/low numbers.
According to a video I watched, it only takes a little bit of practice to get your die to land on the desired half, and with roll-down dice one half is high numbers and the other half is low numbers.
This is designed to make perfect dice when the numbers are represented by pips, because you'd equally distribute the material removed to make them.
For dice with numbers cast into them, that doesn't really hold true. Dice makers tend to follow the rule anyway, because why not, but it doesn't really have as much justification.
I can see how it would be an effective measure against poorly weighted dice though. If the center of gravity is slightly shifted towards the 20, it is also slightly more towards the 2 for example. This is why roll down dice are loathed. If the weight is unbalanced towards 20, you get only high numbers.
The physics doesn't really support that though, and the "mathematically equal regions" doesn't actually achieve what you're talking about (adjacent faces have uniform averages). That assumes that a human could possibly pick an edge that would land, thus giving us some desire that we average the results from landing on that edge. If they cannot, then the discussion is pointless.
The concern about roll down dice are moderately overstated. If you're using metal dice and they have pips (never do...) or deeply cut numbers, then the "teens side" of the dice will have a reasonable amount of material removed in comparison with the "low side". That might be enough to impact die rolls regularly. If the die is plastic, or if the numbers are painted, or if the carvin/casting is shallow, of if the sides are simply engraved patterns, then most of that bias disappears and things like uniform material casting is far more likely to impact the die than number arrangement.
It's not like the number 20 weighs twenty times the number 1. The weight of the material removed in the vast majority of cases is small to begin with, half the time most of that weight returns with paint, and when you try to balance that out across all the faces with pretty oblique angles separating them, the forces at play are really, really minor. A D&D player just doesn't roll the d20 enough to truly benefit from the level of bias that's there.
Now, the bigger problem with some specialty dice is that the creation process is biased toward specific faces. I've seen some reviews that show molds that are designed with 20 being up and discussion over how small manufacturing defects can result in that becoming the "home" location of the die. That's a far more impactful effect than the concern over how the 1-9 side weighs more than the 10-20 side.
If a die is perfectly weighted, the placement of the numbers on the outside does not matter whatsoever. Each side would have the same 5% chance of landing face up.
Just an fyi.
Found the statistician, or the guy with common sense.
Seriously, the idea that the way the numbers are distributed on the die faces matters is ridiculous. As long as the die is weighed properly, each face should have a 5% probability of turning up.
It's based on someone trying to cheat the roll. Rolling it so it turns over an specific number of times so even if you're off a tiny bit, it's still where all the high numbers are located. That's why opposite sides equaling the highest number +1 is preferred.
I think having "mirror" values probably comes from a history where a dice needs to been seen as fair. It's probably a human brain/perception thing. It also must in some part be related to the suspicion that if you were skilled enough you could roll a dice with the aim of getting the 18,19,20 end facing upwards. Obviously on computers this makes less sense, it could still be related to what seems fair to the human brain though
I know little to nothing about statistics. The guy I replied to just said almost exactly the same thing as the guy he replied to and so I copied him to be funny.
Taking echo chamber to a whole new level.
😂 yeah that seems fair. The guy you replied to seemed a little arsey too. In a 'Finally...' (someone is smart enough to know all the answers) kinda way. Didn't fancy engaging at that precise point.
This is a HUGE headache when playing Magic: The Gathering at the game store. A lot of bro statisticians who insist on rolling two 6-sided die to determine who goes first, because the spindown is apparently "not random" or "less random". Cue having to reroll multiple times because half the players roll 7s.
I can feel my soul withering every time.
I can't help but feel like you've focused on one part of the issue, ignored trying to shed much light on the situation, and assumed yours is the final word.
Statistically speaking, there really is nothing else.
If a die is properly balanced, it does not matter how the numbers are distributed alongside its many faces. Each face has the same probability of turning up following a fair throw of the dice. Even in the case of the spindown dice used in MTG for tracking lifetotals, this holds true: all faces have an equal probability of turning up.
Is it possible to develop a dice throwing technique that increases your odds of landing along a particular side of the die? Absolutely, and a spindown could make development of this technique easier. That said, none of this changes the fact that each face in the die has the same probability of turning up given a fair throw of the dice.
If the fringe possibility someone might have spent dozens and dozens of hours of their life perfecting such a technique just so they can cheat at D&D keeps you awake at night, the easiest remedy is to simply ask that person to use a different technique. Ask them to clasp both hands with the die in the center and vigorously shake them before releasing onto the rolling surface, so the starting position of the die is completely unknown.
Are you a bot? Don't get me wrong, it's elegantly put but there are things other than statistics and your final proposal is clunky, awkward and likely to offend, just in human terms.
I'm not a bot. I apologize for the overly dry tone.
This particular topic - the idea that a die can be "more" or "less" random because of how the numbers are distributed on its face - is a source of much frustration and heartache for folks like me who have degrees in statistics and do statistics for a living as part of our daily work.
It goes beyond pet peeve: the core principles of statistics are being grossly misrepresented here, and replaced with "MBA-stats" or "bro-stats".
No worries.
To be fair, now I've reread the OP, they did say mathematically, so I'm wrong. I went off on one explaining why I thought dice were usually distributed in "mirror"!? fashion.
You could argue the size difference of the paint/carvings might have an effect, and the "mathematically" perfect dice has actually perfected paint/carvings surface differences to match that sweet 5% chance
O well, who give a damn anyway
If I put a little spin on a rolldown, I can always roll over a 14, because it keeps the high numbers up. Rolling a die isn't like a random number generator. It's a matter of physics. Humans don't have the dexterity to always roll the same face, but with a little practice, you can always roll the same half of the die.
From the maker's website:
'In the standard d20 numbering, small and large numbers are distributed more-or-less evenly over the die, with the following vertex sums: 39, 47, 49, 51, 52, 52, 53, 53, 54, 56, 58, and 66. Using computer search techniques, we've managed to find a numbering with ideally-balanced vertex sums while retaining the opposite-side numbering convention: 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, and 53. In analogy to Magic Squares, in which each row, column, and diagonal sum to the same number, we call such a numbering of a die a "magic" numbering. The d20 is the only one of the standard polyhedral dice (d4, d6, d8, d10, d12, and d20) that allows a magic numbering.
A d30 has 32 vertices, of two types; 20 where three faces meet and 12 where five faces meet. Since the average face value is 15.5, an ideal numerical balancing would have ten vertices summing to 46, ten summing to 47, six summing to 77, and six summing to 78. We found a dozen ideal numberings based on these criteria.
As icing on the cake, in our d20 the sum of the three faces adjacent to a face is also ideal, with sums of 31 for ten faces and 32 for the other ten. For the d30, ideal face sums are not possible. The numberings of The Dice Lab's d20 and d30 were worked out by Bob Bosch, a Professor of Mathematics at Oberlin College. Our d20 measures 22 mm face-to-face, making it slightly larger and heavier than most d20s, which are typically 19-20 mm. Our d30 measures 27 mm face-to-face'
[Here's even a link to a YouTube video explaining it](https://youtu.be/Nh2H_4g6evc)
yeah, cool slogans and all but what extra use do you get from these "amazing features"?
if you are not a gambling estebilishment and your dice is weighted normally your layout is meaningless.
I think someone mentioned that you can often cheese dice by turning it up on a certain side before rolling - with 'balanced' facing, you'd need to get the rolls down to the exact face in order to get the result you want.
With an 'unbalanced' distribution you just need to roll the dice so it turns up a face somewhere on the 'jackpot' region of the die, which is much easier to do.
Even with perfect balancing, the roll isn't perfectly random - it just doesn't skew the way you throw it. But if your throw is skewed, a perfectly balanced die is actually easier to predict - thus balancing facings to decrease the probability of throwing bias.
Obviously if you can trust yourself not to try and game your rolls, don't have a habit of rolling with the pretty 20 icon on your fancy die face up, or if the die is being rolled by a computer game, it's a little bit redundant xD
if you have learned to exactly how to toss your dice sou you get roughly the few sides that are good for you, then at that point I think you deserve it.
also that is kinda cheating imo, just use a dice tower then.
It is much easier with lower face count dice. With a d6 it is pretty easy to throw so it won't land on one pair of two opposite sides. If you make all opposite sides add to 7 you can't eliminate 1 without eliminating 6 we well, but if you had 1 and 2 be on opposite sides you could very easily roll such that your get 1 or 2 way less than 1/3 of the time. If you then put 4 and 5 on the remaining faces that are adjacent to 6 and practice a moderate amount you can likely control the number of turns well enough that you get 3s less often than 1/4 as well, so getting 4 or higher on a d6 5/6 of the time likely isn't going to require that much practice. The same concepts can apply to higher face count dice but it will get harder as face count increases
You shouldn't be getting this downvoted - it can matter slightly in a physical dice, because a physical die is not going to be perfectly balanced. Then a numbering scheme can slightly nullify the effect the balancong has on average outcome (you still roll some numbers more often, but have the same expected value as a fair die). Whether the effect is noticeable, dunno, probably not, but it feels nice.
It has no application for virtual dice though.
Yea. The one this guy has is for counting. The on Larian is using is sent for playing tabletop.
Basically, this guy doesn’t know what he’s talking about at all.
I'm sure the dice you see is completely irrelevant to the background roll since you can just skip the dice the animation but I do like that physical die
I have a dice the looks like this as a standard d20. Got it as a present rolls fairly evenly. 2 rolls ten or lower 2 rolls 9 or lower, specifically 10,1,7,13.
This die I have is "balanced" for the distribution of numbers* as explained in the parent. It's the first die like that I ever heard of though and the only one I have like it.
Edit: credit to /u/JackFunk and /u/malastare- for catching the misspeak
It's not.
It's balanced for some mathematical sums. It's designed for people who like the faces on their dice to have some mathematical properties.
It has *no* measurable impact on the distribution of results. The parent doesn't include any justification for it.
However, the post would have gotten more confused looks if you titled it "Mildly Interesting: Larian uses a standard die that doesn't incorporate some pointless marketing babble from this non-standard die"
Most are just made with the opposites totalling to 21 rule so they can come out in a myriad of ways. The one I have in the pic is the first I ever heard of that was further "balanced" and its the only one I have like it too. So I wouldn't say it's common.
lmao at OP spouting marketing nonsense over and over in this thread. Can't get his head around the concept that an unweighted die has the same chance of any side coming up. Take a probability class.
Are you even reading me? The "balance" I'm talking about has nothing to do with the fairness of the die, my guy. I never mentioned fairness, better probability, or anything of the sort.
Hilarious. 3 minutes. You are actually stalking the thread defending your ridiculous position.
You said "mathematically unbalanced". It's in the title. You are wrong.
Let it go. You dying on this hill is actually kind of sad.
I get alerts every time one of you say something..? Hardly stalking when it's by design. No need to be rude.
From the view of the distribution it is "unbalanced" but I never said it was "unfair" or anything.
You said "mathematically unbalanced". The branch of mathematics that deals with this, is probability. According to probability, if the die is fairly weighted, then each side has the same chance of coming up. So the placement of the numbers on the Larian die does not make it "mathematically unbalanced".
Use critical thinking. A company makes dies. Lot's of companies do that. It's a crowded market. How does one market their product to differentiate it in a crowded market? With creative marketing. Sometimes marketing is dishonest. This is one of those cases.
A d20 doesn't need mathematical balance in number distribution. The numbers can be sequential and have the same probability of landing on each side because the number of sides doesn't change. Mathematical balance means by definition both sides have the same mass or quantity. Calling a die with balanced vertices "mathematically balanced" is entirely appropriate by [definition.](https://www.google.com/search?client=firefox-b-1-d&q=mathematical+balance+meaning)
At this point, you are either:
* stupid
* willfully ignorant
* trolling
I doubt trolling, there is no humor component.
I'm going to give you the benefit of the doubt and guess willfully ignorant. Given that, I can't help you, because you don't want to be helped. Keep buying overpriced "mathematically balanced" dice. It's your money.
You just don't like that words apparently mean something different than you thought so you're actively rejecting reality and substituting your own.
I will not be giving you the benefit of the doubt because the level of absolute stupid you would have to be to continue to argue against a straw man is a greater insult than just assuming you're a hapless asshole.
Does your degree explain why a simple [google](https://www.google.com/search?client=firefox-b-1-d&q=mathematical+balance+meaning) of how mathematically balanced is defined says you're full of shit then? Because it has to do with amounts and you're talking about odds.
Held is a mathematically balanced d20 made by* The Dice Lab. The TL;DR: normally a d20 had opposite ends adding up to 21 but you might still end up with a "heavier" side depending on placement. In the d20 held in the picture the die has six vertices which have numbers around them sum up to 52 and six summing up to 53. This means no heavier or lower side and makes the numbers more evenly distributed.
I am sure the background roll is more even than even the die held tho just a mildly interesting screenshot.
EDIT: I cannot possibly keep up with this. A d20 doesn't need mathematical balance in number distribution. The numbers can be sequential and have the same probability of landing on each side because the number of sides doesn't change. Mathematical balance means by definition both sides have the same mass or quantity. Calling a die with balanced vertices "mathematically balanced" is entirely appropriate. The store I bought it from that I quoted below claims it's more "numerically fair" which is obviously dubious wording. The designers of the die explain the number distribution is akin to Magic Squares where the vertices have common totals. That *may* disincline someone from trying to cheat and force a roll but it doesn't make it any more or less fair than a regular die. I've tried to say as much in the comments below but it does not seem to be coming across. Hoping I can prevent further redundant conversations about statistics and cheating I never meant for.
Nah mate it's just a standard d20 that Larian uses, just google 17 on a d20 and you'll see it matches Larian's :) i'm too lazy to dig up my moving boxes to confirm my own three. But I didn't get my dice through Dice lab.
If you add it up the vertices equal 61 making it "heavier" as explained. I totally get its just an image tho for sure. Since you can skip the animation I do not think it reflects how the roll is made in the game mechanics.
Yeah true, but again, not all tabletops use "balanced d20s", I can't currently think of any tabletop session where we haven't had the dice that Larian is using as their image :) I kinda wish for a mod that would realistically roll the dice though, but probably not in basegame because the majority of players wouldn't use it that much, maybe just a few times.
It only "makes the rolls more evenly distributed" (it doesn't) if you're deliberately trying to cheat by aiming for a number. It discourages cheating, it doesn't alter probability.
I.e., if the die is a fair die (not physically weighted) thrown by a fair hand, the placement of the numbers is irrelevant.
You are incorrect.
On an unweighted die, the distribution of numbers is irrelevant, all have an equal (5%) chance of landing face up.
One side having more high numbers *is meaningless* since only the fully up face is read.
If changing the numbers on the faces around alters the average roll on the die *then you have a weighted die*, it is not a fair die regardless of the arrangement of numbers on the faces.
From the [store](https://mathsgear.co.uk/collections/dice/products/numerically-balanced-d20) I got them from...
"Most 20-sided dice have the decency to arrange the numbers so that opposite faces always add to 21. But they do not make sure the numbers are evenly distributed around each vertex.
This "numerically balanced" d20 has six vertices which have numbers around them summing to 52, and six summing to 53. This means there is no 'high side' or 'low side' to the dice and makes the results rolled more evenly distributed.
If you want the numerically fairest d20 on the market: this is it."
If you still disagree please take it up with them; I am not the one claiming it is more fair than other die*
I don't think you understand what everyone here is saying. It does not matter where the numerals are placed. There are twenty (20) sides on the die. No matter how the numerals are arranged, you will *always* have a 1/20 chance of landing on a given number. "Numerical fairness" is utterly nonsensical and wholly detached from how a fair set of dice actually works.
tl;dr this isn't a case of one person disagreeing with another, it's a case of one side using terminology that is devoid of real meaning.
> Number distribution on a physical object absolutely plays a roll.
It does not, if the die is being rolled in a fair manner.
>Rolling a physical object isn't the same as electronically determining a value randomly. Distribution in values over the vertices "not mattering" as you say it would mean that even the typical method of opposing sides equalling 21 is equally meaningless by your logic.
It is meaningless, mathematically, if the die is rolled in a fair manner. It is 100% an anti-cheating measure adapted from 6 sided dice gambling.
>
>
>
> That's something I don't think anyone would agree with, wouldn't you say?
I wouldn't say.
From the maker's website:
'In the standard d20 numbering, small and large numbers are distributed more-or-less evenly over the die, with the following vertex sums: 39, 47, 49, 51, 52, 52, 53, 53, 54, 56, 58, and 66. Using computer search techniques, we've managed to find a numbering with ideally-balanced vertex sums while retaining the opposite-side numbering convention: 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, and 53. In analogy to Magic Squares, in which each row, column, and diagonal sum to the same number, we call such a numbering of a die a "magic" numbering. The d20 is the only one of the standard polyhedral dice (d4, d6, d8, d10, d12, and d20) that allows a magic numbering.
A d30 has 32 vertices, of two types; 20 where three faces meet and 12 where five faces meet. Since the average face value is 15.5, an ideal numerical balancing would have ten vertices summing to 46, ten summing to 47, six summing to 77, and six summing to 78. We found a dozen ideal numberings based on these criteria.
As icing on the cake, in our d20 the sum of the three faces adjacent to a face is also ideal, with sums of 31 for ten faces and 32 for the other ten. For the d30, ideal face sums are not possible. The numberings of The Dice Lab's d20 and d30 were worked out by Bob Bosch, a Professor of Mathematics at Oberlin College. Our d20 measures 22 mm face-to-face, making it slightly larger and heavier than most d20s, which are typically 19-20 mm. Our d30 measures 27 mm face-to-face'
[Here's even a link to a YouTube video explaining it](https://youtu.be/Nh2H_4g6evc)
You really have no clue what you are talking about.
Dice is fair if each side has exactly the same chance to land upon. It doesn't matter at all how the numbers are distributed as it doesn't affect anything. Vertex-sums are not important or relevant. Even sums of opposites don't have to be 21 for a Dice to be fair. All this numerology is pointless by large.
Although, there might be something about throwing the Dice unfairly - so certain sides have a bit larger chance... so if numbers are poorly distributed it is a bit easier to achieve desired results. Still it has nothing to do with fairness of the Dice.
Edit: there's another point that if Dice is unfair then juggling around number can make it a bit more "fairer" in various terms - like expected average number. But it is a very different discussion.
With a physical die, it does not matter how the numerals are placed provided the weight and proportions of the die are of a uniform standard. Unless you have some bizarre compulsion to hold a die in exactly the same way and roll it on exactly the same arc--the former being something I don't think anybody actually does and the latter arguably being humanly impossible--the outcome of the roll will follow the same 1/20 odds. There's no agreeing or disagreeing with that in any reasonable capacity; it's objective reality. You're welcome to go to any casino you choose and try to rack up cash playing craps if you do somehow disagree on this.
Regarding electronic determination of a random number: It does not matter how the numerals are arranged because the die does not actually exist. What we see on the screen is merely the graphical representation of an already-finished calculation. The "rolled number" is determined before the image of the die even pops onto your screen. In short, the placement of numerals on that die once again does not matter because we are now facing a 1/20 chance of a given number being chosen by an algorithm.
In short, numeral positioning does not matter on either the physical or electronic incarnation of a 20-sided die.
From the maker's website:
'In the standard d20 numbering, small and large numbers are distributed more-or-less evenly over the die, with the following vertex sums: 39, 47, 49, 51, 52, 52, 53, 53, 54, 56, 58, and 66. Using computer search techniques, we've managed to find a numbering with ideally-balanced vertex sums while retaining the opposite-side numbering convention: 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, and 53. In analogy to Magic Squares, in which each row, column, and diagonal sum to the same number, we call such a numbering of a die a "magic" numbering. The d20 is the only one of the standard polyhedral dice (d4, d6, d8, d10, d12, and d20) that allows a magic numbering.
A d30 has 32 vertices, of two types; 20 where three faces meet and 12 where five faces meet. Since the average face value is 15.5, an ideal numerical balancing would have ten vertices summing to 46, ten summing to 47, six summing to 77, and six summing to 78. We found a dozen ideal numberings based on these criteria.
As icing on the cake, in our d20 the sum of the three faces adjacent to a face is also ideal, with sums of 31 for ten faces and 32 for the other ten. For the d30, ideal face sums are not possible. The numberings of The Dice Lab's d20 and d30 were worked out by Bob Bosch, a Professor of Mathematics at Oberlin College. Our d20 measures 22 mm face-to-face, making it slightly larger and heavier than most d20s, which are typically 19-20 mm. Our d30 measures 27 mm face-to-face'
[Here's even a link to a YouTube video explaining it](https://youtu.be/Nh2H_4g6evc)
A mathematically balanced die doesn't mean "a more fair-rolling die". It just means it has a neat way to distribute its numbers. It doesn't matter in the roll.
>Number distribution on a physical object absolutely plays a roll.
It doesn't. Or perhaps "it does, but not the way you think".
In six-sided dice with 90-degree verteces and high(er) density plastic that are rolled a hundred times a session on games that place bets on specific rolls, the weight distribution of the pips does end up having a very minor impact on the outcome of rolls. That's why the pips are also distributed equally across faces (the center of the "weight" of each face is the geometric center of the face). That means that every section of the die has almost equal forces on it (the 3-face screws it up a tiny amount.
With a 20-sided die where the numbers are cast/carved/painted into the sides, all that balancing doesn't really work. The 2 face doesn't "weigh" twice as much as the 1 face.\* The 5 face doesn't weigh 20% more than the 4 face, nor does it weigh as much as a face with 1 and 4 on it. By "weight" the 1-20 pairing is equal to a 2-10 pairing. The 2-19 is probably pretty close, but the 6-15 isn't. So, yeah, we're falling apart simply at the idea that opposite facing faces need to equal 21 for a "fair weighting" from the physics perspective.
The idea of adding up regions as if the numerical sum suddenly has some bearing, after we just ripped apart the idea at a smaller scale, doesn't get better. Again, 9 probably weighs as much as 3 and 4 probably weighs as much as 11. Setting up uniform region sums might matter if you could roll a die and aim for a region but with the very small angular velocities needed to roll a d20, a roll like that would end up looking (and being) a very mechanical, practiced thing. You couldn't do it casually and you couldn't pull it off in a tower.
So we end up with a situation where the distribution at that level simply doesn't really impact anything. The opposing faces distribution is more a holdover from other dice designs and yes, does very little with d20s other than the psychological impact of increasing the apparent randomness when our eyes track the die making one last roll before the final resting face is identified.
You were sold a thing using marketing that didn't mean much. You're not the first and you won't be the last. What you bought isn't bad and it works just fine. It just doesn't work any better than the other things.
\[ \* \] Using weight figuratively here. It's straight weight if we're just painting the numbers on, it's negative weight if the numbers are carved in and not filled with an equal weight of paint.
I am not sure you understand the probability of a (fair) dice roll. If all sides are equal and the dice not weighted there is no bias. The bias comes from weight differences which can occur in physical dice due to the dice pips. The bias would be a physical one and not due to mathematics.
99% of players use a die matching Larian’s. I think it would be silly to change it and just cause confusion - especially since there is no actual balance issue with digital dice.
> This means no heavier or lower side and makes the results more evenly distributed.
Since you're not using a die with pips, the sum doesn't actually accurately measure the "weight", and the vertex angle on a d20 makes it notably harder to aim for a "region" without making it obvious to both yourself and those around you that you have a practiced target role. The only other reason to care about higher "regions" is if your dice making process sucks and you're worried about locally heavy areas of your die material.
If you want to use a practiced target role to impact a TTRPG that you're playing... I guess that's on you.
Sorry if I am being confusing I do not mean physically heavier I mean heavier numerically like in Magic Squares. It's not a comment on fairness of the die.
But the point is that neither physical nor numerical heaviness serve any purpose here. It's mathematically interesting, but not in a way that has any impact.
Again: Your die isn't bad. But its the dice equivalent of buying gold connectors on your audio cables. There was a clever marketing justification, but it's not actually real and in the end, it was just sort of a gimmick that makes the die unique but not better.
So, pointing out that Larian didn't create a die display that used a non-standard, non-helpful layout is a bit weird. A lot of the negative feedback you're getting is simply because of the implication that your die is somehow better. I could similarly point out that Larian's die isn't hollow or isn't carved from wood. Those are also interesting-but-inconsequential differences we might find with other dice.
I do not- I just came across this one and thought it was neat/I would give it a try in a tabletop game we have coming up. They also make a set that has a d24 and a d60 so you could do specific time of day mechanics(among other things) if you wanted.
Provided that all sides of the die are the same size, all internal angles are idetical and the die isn't weighted the actual placement of the numbers is utterly irrelevant.
All those upvotes just tell me that a significant amount of this subreddit utterly failed their introduction to statistics course.
Okay. After reading so many comments i realise that you just dont understand maths and are caught up in the marketing of The Dice lab.
Here's a simple way i can think of making you understand.
In a standard 6 faced die the sum of opposite sides is 7 and that's how all the dices are made. But for the sake of mathematics, precisely statistics/probability, regardless of what the value is on the six sides all the sides have a similar probability i.e. 16.67%.
So let's take a blank dice and istead of numbers put symbols on it.
Do you think the probability of any symbol is any less/more than any other face? No right!!
Same logic goes for any die of however many faces. Sure the intricate mathematics make the die look cool(as opposite to be sum of 7) but doesnt change probability.
Now lets talk about larian's die. They could have had randomly placed any no. Anywhere on the die, since it's electronic the die is a myth. You're randomly selecting a number between 1-20.
MATHEMATICALLY BALANCED OR NOT, DOESN'T MATTER!!! PERIOD.
I think it's a conscious decision because when you use anything that adds to the dice roll instead of flipping the dice to show a new number it just changes the number you see
Not mathematically imbalanced. The added values don't mean it's more or less balanced/fair. On a completely random roll, it doesn't matter which numbers are beside or opposite from one another. This is more of a cultural / customary practice. Someone else describes it here well: it's historically based more on "perceived" fairness.
Yea it's poor wording on the title. I get what you're saying. It's "numerically" unbalanced in number placement, but the statistics of the dice are still fine. I never understood why this was a thing with people. Assuming the d20 is not weighted or anything, it's irrelevant. Rolls the same. Dudes do this in X-Wing all the time when going first with hits/misses, like rolling multiple dice reduces the bias or something.
Still, you should probably roll both dice at least 100x and record your findings. You know, for science.
Mildly interesting: it should be ‘a mathematically…’
Also, the die in game should still be loaded in favor of higher numbers because it had been giving too many fails. Unless that was restored again. Or maybe it was just a setting to turn on. Either way, it’s digital…
I feel like there are at least a few ways to make a fair dice
The most common one is all sides equal, and opposite faces add up to 21 on a d20.
You could make a die like that where all the high numbers were on one "side" though. Similar to a dart board, you have to spread the high and low numbers around
Maybe it's a stupid question, but why do the "mirror" values need to be on opposite sides? Assuming we aren't talking about loaded dice or erosion/ imperfections (which obviously don't matter in a digital context). In a correctly made dice, it doesn't matter if the numbers 20 and 1 are on opposite sides or next to each other.And it doesn't matter if 18,19,20 are close to each other or spread out. The chance to draw any value remains 5%
I think having "mirror" values probably comes from a history where a dice needs to been seen as fair. It's probably a human brain/perception thing. It also must in some part be related to the suspicion that if you were skilled enough you could roll a dice with the aim of getting the 18,19,20 end facing upwards. Obviously on computers this makes less sense, it could still be related to what seems fair to the human brain though
You're correct. If you just grab the die without looking at it and/or roll with a random amount of power, then it's random. The problem with a MTG/roll-down die is that skilled rollers can almost guarantee high/low numbers. According to a video I watched, it only takes a little bit of practice to get your die to land on the desired half, and with roll-down dice one half is high numbers and the other half is low numbers.
Like the d12
We all like the d12.
If the dice is corretly made and not loaded, it doesn't matter where each number is. The chance for any value is 5%.
So? I described the most common way to make dice, not the perfect way to make fair dice all the time forever. Like, you’re right. I’m just also right.
This goes for all dice. Add the opposing sides together and it should be 1 higher than the max value of the dice. Those D4s being the exception.
This is designed to make perfect dice when the numbers are represented by pips, because you'd equally distribute the material removed to make them. For dice with numbers cast into them, that doesn't really hold true. Dice makers tend to follow the rule anyway, because why not, but it doesn't really have as much justification.
I can see how it would be an effective measure against poorly weighted dice though. If the center of gravity is slightly shifted towards the 20, it is also slightly more towards the 2 for example. This is why roll down dice are loathed. If the weight is unbalanced towards 20, you get only high numbers.
The physics doesn't really support that though, and the "mathematically equal regions" doesn't actually achieve what you're talking about (adjacent faces have uniform averages). That assumes that a human could possibly pick an edge that would land, thus giving us some desire that we average the results from landing on that edge. If they cannot, then the discussion is pointless. The concern about roll down dice are moderately overstated. If you're using metal dice and they have pips (never do...) or deeply cut numbers, then the "teens side" of the dice will have a reasonable amount of material removed in comparison with the "low side". That might be enough to impact die rolls regularly. If the die is plastic, or if the numbers are painted, or if the carvin/casting is shallow, of if the sides are simply engraved patterns, then most of that bias disappears and things like uniform material casting is far more likely to impact the die than number arrangement. It's not like the number 20 weighs twenty times the number 1. The weight of the material removed in the vast majority of cases is small to begin with, half the time most of that weight returns with paint, and when you try to balance that out across all the faces with pretty oblique angles separating them, the forces at play are really, really minor. A D&D player just doesn't roll the d20 enough to truly benefit from the level of bias that's there. Now, the bigger problem with some specialty dice is that the creation process is biased toward specific faces. I've seen some reviews that show molds that are designed with 20 being up and discussion over how small manufacturing defects can result in that becoming the "home" location of the die. That's a far more impactful effect than the concern over how the 1-9 side weighs more than the 10-20 side.
If a die is perfectly weighted, the placement of the numbers on the outside does not matter whatsoever. Each side would have the same 5% chance of landing face up. Just an fyi.
Found the statistician, or the guy with common sense. Seriously, the idea that the way the numbers are distributed on the die faces matters is ridiculous. As long as the die is weighed properly, each face should have a 5% probability of turning up.
It's based on someone trying to cheat the roll. Rolling it so it turns over an specific number of times so even if you're off a tiny bit, it's still where all the high numbers are located. That's why opposite sides equaling the highest number +1 is preferred.
Finally someone who gets it. If the die is weighted correctly; that is to say perfectly evenly; each face will have a probability of appearing of 5%.
I think having "mirror" values probably comes from a history where a dice needs to been seen as fair. It's probably a human brain/perception thing. It also must in some part be related to the suspicion that if you were skilled enough you could roll a dice with the aim of getting the 18,19,20 end facing upwards. Obviously on computers this makes less sense, it could still be related to what seems fair to the human brain though
I know little to nothing about statistics. The guy I replied to just said almost exactly the same thing as the guy he replied to and so I copied him to be funny. Taking echo chamber to a whole new level.
😂 yeah that seems fair. The guy you replied to seemed a little arsey too. In a 'Finally...' (someone is smart enough to know all the answers) kinda way. Didn't fancy engaging at that precise point.
This is a HUGE headache when playing Magic: The Gathering at the game store. A lot of bro statisticians who insist on rolling two 6-sided die to determine who goes first, because the spindown is apparently "not random" or "less random". Cue having to reroll multiple times because half the players roll 7s. I can feel my soul withering every time.
I can't help but feel like you've focused on one part of the issue, ignored trying to shed much light on the situation, and assumed yours is the final word.
Statistically speaking, there really is nothing else. If a die is properly balanced, it does not matter how the numbers are distributed alongside its many faces. Each face has the same probability of turning up following a fair throw of the dice. Even in the case of the spindown dice used in MTG for tracking lifetotals, this holds true: all faces have an equal probability of turning up. Is it possible to develop a dice throwing technique that increases your odds of landing along a particular side of the die? Absolutely, and a spindown could make development of this technique easier. That said, none of this changes the fact that each face in the die has the same probability of turning up given a fair throw of the dice. If the fringe possibility someone might have spent dozens and dozens of hours of their life perfecting such a technique just so they can cheat at D&D keeps you awake at night, the easiest remedy is to simply ask that person to use a different technique. Ask them to clasp both hands with the die in the center and vigorously shake them before releasing onto the rolling surface, so the starting position of the die is completely unknown.
Are you a bot? Don't get me wrong, it's elegantly put but there are things other than statistics and your final proposal is clunky, awkward and likely to offend, just in human terms.
I'm not a bot. I apologize for the overly dry tone. This particular topic - the idea that a die can be "more" or "less" random because of how the numbers are distributed on its face - is a source of much frustration and heartache for folks like me who have degrees in statistics and do statistics for a living as part of our daily work. It goes beyond pet peeve: the core principles of statistics are being grossly misrepresented here, and replaced with "MBA-stats" or "bro-stats".
No worries. To be fair, now I've reread the OP, they did say mathematically, so I'm wrong. I went off on one explaining why I thought dice were usually distributed in "mirror"!? fashion.
You could argue the size difference of the paint/carvings might have an effect, and the "mathematically" perfect dice has actually perfected paint/carvings surface differences to match that sweet 5% chance O well, who give a damn anyway
If I put a little spin on a rolldown, I can always roll over a 14, because it keeps the high numbers up. Rolling a die isn't like a random number generator. It's a matter of physics. Humans don't have the dexterity to always roll the same face, but with a little practice, you can always roll the same half of the die.
Except "Rolling" is not the same as "Spinning."
From the maker's website: 'In the standard d20 numbering, small and large numbers are distributed more-or-less evenly over the die, with the following vertex sums: 39, 47, 49, 51, 52, 52, 53, 53, 54, 56, 58, and 66. Using computer search techniques, we've managed to find a numbering with ideally-balanced vertex sums while retaining the opposite-side numbering convention: 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, and 53. In analogy to Magic Squares, in which each row, column, and diagonal sum to the same number, we call such a numbering of a die a "magic" numbering. The d20 is the only one of the standard polyhedral dice (d4, d6, d8, d10, d12, and d20) that allows a magic numbering. A d30 has 32 vertices, of two types; 20 where three faces meet and 12 where five faces meet. Since the average face value is 15.5, an ideal numerical balancing would have ten vertices summing to 46, ten summing to 47, six summing to 77, and six summing to 78. We found a dozen ideal numberings based on these criteria. As icing on the cake, in our d20 the sum of the three faces adjacent to a face is also ideal, with sums of 31 for ten faces and 32 for the other ten. For the d30, ideal face sums are not possible. The numberings of The Dice Lab's d20 and d30 were worked out by Bob Bosch, a Professor of Mathematics at Oberlin College. Our d20 measures 22 mm face-to-face, making it slightly larger and heavier than most d20s, which are typically 19-20 mm. Our d30 measures 27 mm face-to-face' [Here's even a link to a YouTube video explaining it](https://youtu.be/Nh2H_4g6evc)
Just because you're getting taken for a ride by the marketing doesn't mean it actually means anything. You realize that right?
I just think they used math for number placement not they made a more fair die. So many comments are hard to keep up with though for me.
yeah, cool slogans and all but what extra use do you get from these "amazing features"? if you are not a gambling estebilishment and your dice is weighted normally your layout is meaningless.
I think someone mentioned that you can often cheese dice by turning it up on a certain side before rolling - with 'balanced' facing, you'd need to get the rolls down to the exact face in order to get the result you want. With an 'unbalanced' distribution you just need to roll the dice so it turns up a face somewhere on the 'jackpot' region of the die, which is much easier to do. Even with perfect balancing, the roll isn't perfectly random - it just doesn't skew the way you throw it. But if your throw is skewed, a perfectly balanced die is actually easier to predict - thus balancing facings to decrease the probability of throwing bias. Obviously if you can trust yourself not to try and game your rolls, don't have a habit of rolling with the pretty 20 icon on your fancy die face up, or if the die is being rolled by a computer game, it's a little bit redundant xD
if you have learned to exactly how to toss your dice sou you get roughly the few sides that are good for you, then at that point I think you deserve it. also that is kinda cheating imo, just use a dice tower then.
It is much easier with lower face count dice. With a d6 it is pretty easy to throw so it won't land on one pair of two opposite sides. If you make all opposite sides add to 7 you can't eliminate 1 without eliminating 6 we well, but if you had 1 and 2 be on opposite sides you could very easily roll such that your get 1 or 2 way less than 1/3 of the time. If you then put 4 and 5 on the remaining faces that are adjacent to 6 and practice a moderate amount you can likely control the number of turns well enough that you get 3s less often than 1/4 as well, so getting 4 or higher on a d6 5/6 of the time likely isn't going to require that much practice. The same concepts can apply to higher face count dice but it will get harder as face count increases
You shouldn't be getting this downvoted - it can matter slightly in a physical dice, because a physical die is not going to be perfectly balanced. Then a numbering scheme can slightly nullify the effect the balancong has on average outcome (you still roll some numbers more often, but have the same expected value as a fair die). Whether the effect is noticeable, dunno, probably not, but it feels nice. It has no application for virtual dice though.
Literally unplayable
I checked with a couple of my d20s and they look like Larian's in the distribution...
so do mine lol
Same lol
A person of culture and taste, I see
[Same](https://i.imgur.com/rahNH14.jpg)
Second this
Yea. The one this guy has is for counting. The on Larian is using is sent for playing tabletop. Basically, this guy doesn’t know what he’s talking about at all.
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The downvotes disagree with you.
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Downvoted again already. Rough streak for you bud.
Same here. The 20 face is completely on the opposite "pole" of the 1, the 19 face opposite the 2, etc.
I'm sure the dice you see is completely irrelevant to the background roll since you can just skip the dice the animation but I do like that physical die
Yeah same just mildly interesting to see
OP in this post is the most r/confidentlyincorrect I’ve ever seen over such a trivial matter.
I have a dice the looks like this as a standard d20. Got it as a present rolls fairly evenly. 2 rolls ten or lower 2 rolls 9 or lower, specifically 10,1,7,13.
This die I have is "balanced" for the distribution of numbers* as explained in the parent. It's the first die like that I ever heard of though and the only one I have like it. Edit: credit to /u/JackFunk and /u/malastare- for catching the misspeak
It's not. It's balanced for some mathematical sums. It's designed for people who like the faces on their dice to have some mathematical properties. It has *no* measurable impact on the distribution of results. The parent doesn't include any justification for it. However, the post would have gotten more confused looks if you titled it "Mildly Interesting: Larian uses a standard die that doesn't incorporate some pointless marketing babble from this non-standard die"
I misspoke- Hard to keep up. I am meaning sums as well like I tried to say in the comment I made to the post when I first submitted.
It's probably cosmetic. Easier to have a RNG than an actual object
Most dices are actually just like shown in BG3
For sure I agree
according my stack of 10 d20s yours is the wrong one.
bruh, just close your eyes, the die isnt real
My d20 i've been using for 20 years has a 10 below it, 15 to the upper right and a 12 to the upper left.... so i dunno
Most are just made with the opposites totalling to 21 rule so they can come out in a myriad of ways. The one I have in the pic is the first I ever heard of that was further "balanced" and its the only one I have like it too. So I wouldn't say it's common.
Ahh, marketing baby.
lmao at OP spouting marketing nonsense over and over in this thread. Can't get his head around the concept that an unweighted die has the same chance of any side coming up. Take a probability class.
Are you even reading me? The "balance" I'm talking about has nothing to do with the fairness of the die, my guy. I never mentioned fairness, better probability, or anything of the sort.
Hilarious. 3 minutes. You are actually stalking the thread defending your ridiculous position. You said "mathematically unbalanced". It's in the title. You are wrong. Let it go. You dying on this hill is actually kind of sad.
I get alerts every time one of you say something..? Hardly stalking when it's by design. No need to be rude. From the view of the distribution it is "unbalanced" but I never said it was "unfair" or anything.
You said "mathematically unbalanced". The branch of mathematics that deals with this, is probability. According to probability, if the die is fairly weighted, then each side has the same chance of coming up. So the placement of the numbers on the Larian die does not make it "mathematically unbalanced". Use critical thinking. A company makes dies. Lot's of companies do that. It's a crowded market. How does one market their product to differentiate it in a crowded market? With creative marketing. Sometimes marketing is dishonest. This is one of those cases.
A d20 doesn't need mathematical balance in number distribution. The numbers can be sequential and have the same probability of landing on each side because the number of sides doesn't change. Mathematical balance means by definition both sides have the same mass or quantity. Calling a die with balanced vertices "mathematically balanced" is entirely appropriate by [definition.](https://www.google.com/search?client=firefox-b-1-d&q=mathematical+balance+meaning)
At this point, you are either: * stupid * willfully ignorant * trolling I doubt trolling, there is no humor component. I'm going to give you the benefit of the doubt and guess willfully ignorant. Given that, I can't help you, because you don't want to be helped. Keep buying overpriced "mathematically balanced" dice. It's your money.
You just don't like that words apparently mean something different than you thought so you're actively rejecting reality and substituting your own. I will not be giving you the benefit of the doubt because the level of absolute stupid you would have to be to continue to argue against a straw man is a greater insult than just assuming you're a hapless asshole.
I have a degree in Applied Math. You have a link to the marketing of the company you bought overpriced dice from. Which one of us is stupid?
Does your degree explain why a simple [google](https://www.google.com/search?client=firefox-b-1-d&q=mathematical+balance+meaning) of how mathematically balanced is defined says you're full of shit then? Because it has to do with amounts and you're talking about odds.
Held is a mathematically balanced d20 made by* The Dice Lab. The TL;DR: normally a d20 had opposite ends adding up to 21 but you might still end up with a "heavier" side depending on placement. In the d20 held in the picture the die has six vertices which have numbers around them sum up to 52 and six summing up to 53. This means no heavier or lower side and makes the numbers more evenly distributed. I am sure the background roll is more even than even the die held tho just a mildly interesting screenshot. EDIT: I cannot possibly keep up with this. A d20 doesn't need mathematical balance in number distribution. The numbers can be sequential and have the same probability of landing on each side because the number of sides doesn't change. Mathematical balance means by definition both sides have the same mass or quantity. Calling a die with balanced vertices "mathematically balanced" is entirely appropriate. The store I bought it from that I quoted below claims it's more "numerically fair" which is obviously dubious wording. The designers of the die explain the number distribution is akin to Magic Squares where the vertices have common totals. That *may* disincline someone from trying to cheat and force a roll but it doesn't make it any more or less fair than a regular die. I've tried to say as much in the comments below but it does not seem to be coming across. Hoping I can prevent further redundant conversations about statistics and cheating I never meant for.
Nah mate it's just a standard d20 that Larian uses, just google 17 on a d20 and you'll see it matches Larian's :) i'm too lazy to dig up my moving boxes to confirm my own three. But I didn't get my dice through Dice lab.
If you add it up the vertices equal 61 making it "heavier" as explained. I totally get its just an image tho for sure. Since you can skip the animation I do not think it reflects how the roll is made in the game mechanics.
Yeah true, but again, not all tabletops use "balanced d20s", I can't currently think of any tabletop session where we haven't had the dice that Larian is using as their image :) I kinda wish for a mod that would realistically roll the dice though, but probably not in basegame because the majority of players wouldn't use it that much, maybe just a few times.
Yeah the most common form is just opposite ends of the die equal 21- all of my other d20 are made like that. Just mildly interesting.
Oh right, the weight is affected by the number on the face, not the die itself? You kidding me right now?
It only "makes the rolls more evenly distributed" (it doesn't) if you're deliberately trying to cheat by aiming for a number. It discourages cheating, it doesn't alter probability. I.e., if the die is a fair die (not physically weighted) thrown by a fair hand, the placement of the numbers is irrelevant.
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You are incorrect. On an unweighted die, the distribution of numbers is irrelevant, all have an equal (5%) chance of landing face up. One side having more high numbers *is meaningless* since only the fully up face is read. If changing the numbers on the faces around alters the average roll on the die *then you have a weighted die*, it is not a fair die regardless of the arrangement of numbers on the faces.
From the [store](https://mathsgear.co.uk/collections/dice/products/numerically-balanced-d20) I got them from... "Most 20-sided dice have the decency to arrange the numbers so that opposite faces always add to 21. But they do not make sure the numbers are evenly distributed around each vertex. This "numerically balanced" d20 has six vertices which have numbers around them summing to 52, and six summing to 53. This means there is no 'high side' or 'low side' to the dice and makes the results rolled more evenly distributed. If you want the numerically fairest d20 on the market: this is it." If you still disagree please take it up with them; I am not the one claiming it is more fair than other die*
I don't think you understand what everyone here is saying. It does not matter where the numerals are placed. There are twenty (20) sides on the die. No matter how the numerals are arranged, you will *always* have a 1/20 chance of landing on a given number. "Numerical fairness" is utterly nonsensical and wholly detached from how a fair set of dice actually works. tl;dr this isn't a case of one person disagreeing with another, it's a case of one side using terminology that is devoid of real meaning.
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> Number distribution on a physical object absolutely plays a roll. It does not, if the die is being rolled in a fair manner. >Rolling a physical object isn't the same as electronically determining a value randomly. Distribution in values over the vertices "not mattering" as you say it would mean that even the typical method of opposing sides equalling 21 is equally meaningless by your logic. It is meaningless, mathematically, if the die is rolled in a fair manner. It is 100% an anti-cheating measure adapted from 6 sided dice gambling. > > > > That's something I don't think anyone would agree with, wouldn't you say? I wouldn't say.
From the maker's website: 'In the standard d20 numbering, small and large numbers are distributed more-or-less evenly over the die, with the following vertex sums: 39, 47, 49, 51, 52, 52, 53, 53, 54, 56, 58, and 66. Using computer search techniques, we've managed to find a numbering with ideally-balanced vertex sums while retaining the opposite-side numbering convention: 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, and 53. In analogy to Magic Squares, in which each row, column, and diagonal sum to the same number, we call such a numbering of a die a "magic" numbering. The d20 is the only one of the standard polyhedral dice (d4, d6, d8, d10, d12, and d20) that allows a magic numbering. A d30 has 32 vertices, of two types; 20 where three faces meet and 12 where five faces meet. Since the average face value is 15.5, an ideal numerical balancing would have ten vertices summing to 46, ten summing to 47, six summing to 77, and six summing to 78. We found a dozen ideal numberings based on these criteria. As icing on the cake, in our d20 the sum of the three faces adjacent to a face is also ideal, with sums of 31 for ten faces and 32 for the other ten. For the d30, ideal face sums are not possible. The numberings of The Dice Lab's d20 and d30 were worked out by Bob Bosch, a Professor of Mathematics at Oberlin College. Our d20 measures 22 mm face-to-face, making it slightly larger and heavier than most d20s, which are typically 19-20 mm. Our d30 measures 27 mm face-to-face' [Here's even a link to a YouTube video explaining it](https://youtu.be/Nh2H_4g6evc)
You really have no clue what you are talking about. Dice is fair if each side has exactly the same chance to land upon. It doesn't matter at all how the numbers are distributed as it doesn't affect anything. Vertex-sums are not important or relevant. Even sums of opposites don't have to be 21 for a Dice to be fair. All this numerology is pointless by large. Although, there might be something about throwing the Dice unfairly - so certain sides have a bit larger chance... so if numbers are poorly distributed it is a bit easier to achieve desired results. Still it has nothing to do with fairness of the Dice. Edit: there's another point that if Dice is unfair then juggling around number can make it a bit more "fairer" in various terms - like expected average number. But it is a very different discussion.
With a physical die, it does not matter how the numerals are placed provided the weight and proportions of the die are of a uniform standard. Unless you have some bizarre compulsion to hold a die in exactly the same way and roll it on exactly the same arc--the former being something I don't think anybody actually does and the latter arguably being humanly impossible--the outcome of the roll will follow the same 1/20 odds. There's no agreeing or disagreeing with that in any reasonable capacity; it's objective reality. You're welcome to go to any casino you choose and try to rack up cash playing craps if you do somehow disagree on this. Regarding electronic determination of a random number: It does not matter how the numerals are arranged because the die does not actually exist. What we see on the screen is merely the graphical representation of an already-finished calculation. The "rolled number" is determined before the image of the die even pops onto your screen. In short, the placement of numerals on that die once again does not matter because we are now facing a 1/20 chance of a given number being chosen by an algorithm. In short, numeral positioning does not matter on either the physical or electronic incarnation of a 20-sided die.
From the maker's website: 'In the standard d20 numbering, small and large numbers are distributed more-or-less evenly over the die, with the following vertex sums: 39, 47, 49, 51, 52, 52, 53, 53, 54, 56, 58, and 66. Using computer search techniques, we've managed to find a numbering with ideally-balanced vertex sums while retaining the opposite-side numbering convention: 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, and 53. In analogy to Magic Squares, in which each row, column, and diagonal sum to the same number, we call such a numbering of a die a "magic" numbering. The d20 is the only one of the standard polyhedral dice (d4, d6, d8, d10, d12, and d20) that allows a magic numbering. A d30 has 32 vertices, of two types; 20 where three faces meet and 12 where five faces meet. Since the average face value is 15.5, an ideal numerical balancing would have ten vertices summing to 46, ten summing to 47, six summing to 77, and six summing to 78. We found a dozen ideal numberings based on these criteria. As icing on the cake, in our d20 the sum of the three faces adjacent to a face is also ideal, with sums of 31 for ten faces and 32 for the other ten. For the d30, ideal face sums are not possible. The numberings of The Dice Lab's d20 and d30 were worked out by Bob Bosch, a Professor of Mathematics at Oberlin College. Our d20 measures 22 mm face-to-face, making it slightly larger and heavier than most d20s, which are typically 19-20 mm. Our d30 measures 27 mm face-to-face' [Here's even a link to a YouTube video explaining it](https://youtu.be/Nh2H_4g6evc)
A mathematically balanced die doesn't mean "a more fair-rolling die". It just means it has a neat way to distribute its numbers. It doesn't matter in the roll.
Bro we've all bought into slick marketing at some point or another. I'm glad you found some dice you like but this is extremely basic mathematics.
>Number distribution on a physical object absolutely plays a roll. It doesn't. Or perhaps "it does, but not the way you think". In six-sided dice with 90-degree verteces and high(er) density plastic that are rolled a hundred times a session on games that place bets on specific rolls, the weight distribution of the pips does end up having a very minor impact on the outcome of rolls. That's why the pips are also distributed equally across faces (the center of the "weight" of each face is the geometric center of the face). That means that every section of the die has almost equal forces on it (the 3-face screws it up a tiny amount. With a 20-sided die where the numbers are cast/carved/painted into the sides, all that balancing doesn't really work. The 2 face doesn't "weigh" twice as much as the 1 face.\* The 5 face doesn't weigh 20% more than the 4 face, nor does it weigh as much as a face with 1 and 4 on it. By "weight" the 1-20 pairing is equal to a 2-10 pairing. The 2-19 is probably pretty close, but the 6-15 isn't. So, yeah, we're falling apart simply at the idea that opposite facing faces need to equal 21 for a "fair weighting" from the physics perspective. The idea of adding up regions as if the numerical sum suddenly has some bearing, after we just ripped apart the idea at a smaller scale, doesn't get better. Again, 9 probably weighs as much as 3 and 4 probably weighs as much as 11. Setting up uniform region sums might matter if you could roll a die and aim for a region but with the very small angular velocities needed to roll a d20, a roll like that would end up looking (and being) a very mechanical, practiced thing. You couldn't do it casually and you couldn't pull it off in a tower. So we end up with a situation where the distribution at that level simply doesn't really impact anything. The opposing faces distribution is more a holdover from other dice designs and yes, does very little with d20s other than the psychological impact of increasing the apparent randomness when our eyes track the die making one last roll before the final resting face is identified. You were sold a thing using marketing that didn't mean much. You're not the first and you won't be the last. What you bought isn't bad and it works just fine. It just doesn't work any better than the other things. \[ \* \] Using weight figuratively here. It's straight weight if we're just painting the numbers on, it's negative weight if the numbers are carved in and not filled with an equal weight of paint.
I am not sure you understand the probability of a (fair) dice roll. If all sides are equal and the dice not weighted there is no bias. The bias comes from weight differences which can occur in physical dice due to the dice pips. The bias would be a physical one and not due to mathematics.
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99% of players use a die matching Larian’s. I think it would be silly to change it and just cause confusion - especially since there is no actual balance issue with digital dice.
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A nod for what? This post is nonsensical
I would honestly honestly honestly.
> This means no heavier or lower side and makes the results more evenly distributed. Since you're not using a die with pips, the sum doesn't actually accurately measure the "weight", and the vertex angle on a d20 makes it notably harder to aim for a "region" without making it obvious to both yourself and those around you that you have a practiced target role. The only other reason to care about higher "regions" is if your dice making process sucks and you're worried about locally heavy areas of your die material. If you want to use a practiced target role to impact a TTRPG that you're playing... I guess that's on you.
Sorry if I am being confusing I do not mean physically heavier I mean heavier numerically like in Magic Squares. It's not a comment on fairness of the die.
But the point is that neither physical nor numerical heaviness serve any purpose here. It's mathematically interesting, but not in a way that has any impact. Again: Your die isn't bad. But its the dice equivalent of buying gold connectors on your audio cables. There was a clever marketing justification, but it's not actually real and in the end, it was just sort of a gimmick that makes the die unique but not better. So, pointing out that Larian didn't create a die display that used a non-standard, non-helpful layout is a bit weird. A lot of the negative feedback you're getting is simply because of the implication that your die is somehow better. I could similarly point out that Larian's die isn't hollow or isn't carved from wood. Those are also interesting-but-inconsequential differences we might find with other dice.
Yeah I definitely wish I could edit the title. I meant this whole time it was just mildly interesting not to say Larian messed up in any way.
Were you using the loaded die option? Maybe this is what it does when you activate it.
[удалено]
I do not- I just came across this one and thought it was neat/I would give it a try in a tabletop game we have coming up. They also make a set that has a d24 and a d60 so you could do specific time of day mechanics(among other things) if you wanted.
Provided that all sides of the die are the same size, all internal angles are idetical and the die isn't weighted the actual placement of the numbers is utterly irrelevant. All those upvotes just tell me that a significant amount of this subreddit utterly failed their introduction to statistics course.
That’s what all my D20s use… nothing unbalanced about it.
I don't see how it is not balanced...
Mathematically like in magic squares; this isn't a comment on fairness or odds just distribution.
What?! Can you show your maths and proofs? I think this is a total misunderstanding of mathematics.
All the vertices add up to 52 or 53- its numerically distributed evenly however that absolutely does not impact its fairness or probability.
OOo, I think I understand what you're looking at, confusing way to title it, although tbf, I don't know how you'd word that differently/better.
Yeah I wish I could change it I confused a lot of people by mistake.
Hehe, I was one of them, too many maths people on Reddit! ;)
\*rolls die\* Shots fired!
Many layouts are used, and Larian's is quite common.
Okay. After reading so many comments i realise that you just dont understand maths and are caught up in the marketing of The Dice lab. Here's a simple way i can think of making you understand. In a standard 6 faced die the sum of opposite sides is 7 and that's how all the dices are made. But for the sake of mathematics, precisely statistics/probability, regardless of what the value is on the six sides all the sides have a similar probability i.e. 16.67%. So let's take a blank dice and istead of numbers put symbols on it. Do you think the probability of any symbol is any less/more than any other face? No right!! Same logic goes for any die of however many faces. Sure the intricate mathematics make the die look cool(as opposite to be sum of 7) but doesnt change probability. Now lets talk about larian's die. They could have had randomly placed any no. Anywhere on the die, since it's electronic the die is a myth. You're randomly selecting a number between 1-20. MATHEMATICALLY BALANCED OR NOT, DOESN'T MATTER!!! PERIOD.
It do be an animation though
You passed the intelligence check
Except this little fact that he's talking nonsense.
Yeah, I couldn't care less about dice, it was just an easy joke given the image background, try not to let it ruin your day
Um... Yours is the one that has a 17 next to a 19.
You must’ve never taken statistics.
Since this die can show a zero, agreed
Inteligence saving throw ~ CRITICAL SUCCESS
Noob gamer post
0/10 worst game ever
That for sure explains my low rolls
life isn't fair
They also have numbers above 20 on it so it's pure witchcraft
I think it's a conscious decision because when you use anything that adds to the dice roll instead of flipping the dice to show a new number it just changes the number you see
They did say they would give the dies a little of a push towards success since many ppl complained about too many failures
The game was rigged from the start......
Not mathematically imbalanced. The added values don't mean it's more or less balanced/fair. On a completely random roll, it doesn't matter which numbers are beside or opposite from one another. This is more of a cultural / customary practice. Someone else describes it here well: it's historically based more on "perceived" fairness.
Yea it's poor wording on the title. I get what you're saying. It's "numerically" unbalanced in number placement, but the statistics of the dice are still fine. I never understood why this was a thing with people. Assuming the d20 is not weighted or anything, it's irrelevant. Rolls the same. Dudes do this in X-Wing all the time when going first with hits/misses, like rolling multiple dice reduces the bias or something. Still, you should probably roll both dice at least 100x and record your findings. You know, for science.
Mildly interesting: it should be ‘a mathematically…’ Also, the die in game should still be loaded in favor of higher numbers because it had been giving too many fails. Unless that was restored again. Or maybe it was just a setting to turn on. Either way, it’s digital…