New Deck of DM Things Merch: deck-of-dm-things-merch.print... Thank you for watching! SEO Stuff: Types of D20s Dice DnD dice spindown d20 mtg dice Dungeons and Dragons Dice Explained
Long ago, it had been explained to me that the reason spin-down D20s weren’t generally permitted in events (at least for the events I was playing in/judging) had less to do with inherent flaws of the number distribution in an “honest” roll, but rather the potential of their pattern’s exploitability for those intending to exploit that distribution. It would be interesting to test how much one could exploit the pattern to manipulate results (or, realistically, if such exploitation is practically possible).
I used to do magic and I had a trick that relied on rolling a dice in a specific way so it would land how you wanted but looked like it rolled. This is much harder to do with a d20 however after some trying I can kind of manipulate it so with practice I could probably make it so I only roll high on a spin down. This is however a small test I did at home for only a few days.
Yeah if you're going for high numbers, it's significantly easier on a spin down. Roll it against a surface, make it bump, even just start it in a specific orientation and what was a 1/20 chance affected by skill becomes a 4/20 to get something good enough affected by skill much more heavily. Hell you don't even have to be doing it intentionally, I used to roll against a box all the time and we just threw it in a way where it hit the sides most rolls. On a d20 that barely matters, but a spin down would've stopped at a number within the cluster of whatever hit the side. Edit: also, the majority of spin downs aren't manufactured to be balanced, they don't need to be balanced they just display a number.
@@bye1551and how would you be able to choose which side of the dice hits the wall? Maybe I'm missing something in your comment, but if you just throw the dice it shouldn't matter if it hits the wall or the floor. Simply because you can't guarantee or even influence wich side hits.
Dices where the numbers are cut you can cut more material in the numbers you want so they roll with more frequency. How much it affects I don't know but it is enough that I have heard and seen this trick done.
@@Jehty21 oww yes you can by checking the die in your hand and making the right flick or the wrist you CAN influence this. Tried an tested. Takes a little bit of practice but the skill can be developed quickly
So, the thing with spindowns is, I think, if they're being rolled fairly, they're probably not really any less random than a standard D20; considering that the standard D20 manufacturing process includes, presumably, making sure the die is balanced well enough, you'd probably have to do it on purpose to make the die poorly balanced. However, because all of the high numbers are on one side and all the low numbers are on the other, it makes it much easier to manipulate the die into always giving you a number in that 16-20 range.
Testing a die for fairness would take more time than actually making the die. whether the dice are mass manufactured or small batch, that's just not worthwhile for the manufacturer. think about how hard-edge dice are often marketed as more fair due to the tumbling process of typical dice allegedly reducing the fairness of each individual die. If the makers of typical dice had the testing records for this, it would be very clear cut whether hard-edge dice are an improvement, and that kind of clarity is just not what we see. Followup: the video mentions a "float test". I was implicitly assuming a higher standard of testing (rolls and statistics) in the claim about testing time. With small batch manufacturing, float testing each die is at least achievable, though still not worthwhile in my opinion. float testing each die with mass manufacturing is still intractable though.
@@LaBlueSkuld They do a little bit. A very little bit. And pretty much only for transparent and translucent dice. I know this because I buy them by the bucket on Chinese websites. Sometimes they have bugs stuck inside of them. That's pretty cool. They also roll hilariously biased. But it's pretty much impossible to tell what exact number they're biased at without spending way too much time doing the math. It's funny watching people get angry at one set of dice to swap them for another set of dice, they also get angry at.
As the only person at my table who recognises a spindown vs a standard d20, I always balk at one of my players bringing a spindown to DnD. And then I immediately mentally talk myself down because there's no real impactful difference and my player just picked that die because they think it's pretty. Excellent video!
I have absolutely no idea how I got here. I don't even play DnD, or any another dice rolling game. I am though definitely pleased with the algorithm, but I am a wee bit alarmed it knows me so well. Now you've got me down the rabbit hole on dice sir! I've just been googling what a "float test" is!
You and I both, brother. Have you been watching Bauldr's Gate 3 content too? (a game I don't even own because turn based RPG's are icky and yucky but that one looks nominally interesting)
I’ve totally played DnD, but I’ve never worried that much about my dice as long as we’re all using the same ones…still. I was absolutely and totally fascinated by this.
The way I've always understood it is that placing numbers so that opposites add to Dice Sides + 1 is an ancient measure intended to offset the fact that old dice weren't very precisely made, and to make it more difficult to 'weight' the dice. It might even go back to the use of knucklebone dice (aka Astragaloi, Talli, Shaggai) which had only four sides and were numbered 1, 3, 4, 6, with the numbers 1 and 6 being only 10% likely compared to the 3 and 4 being 40% likely. This required 1 and 6 to be opposite one another and 3, 4 likewise, because that's how the astragalus bone is shaped - opposite sides are roughly the same size and shape, meaning the die's average remained somewhere close to the middle of its range. These measures are no longer necessary with modern dice, which are much more uniformly shaped and weighted.
Having seen the rest of the video now, I think I'll also point out that simply being off-balance isn't enough to make a spin down die noticeably unfair, it specifically has to be unbalanced away from or towards the 'high point' (the centre point at which all the highest-rated facets are clustered around). As I noted above, the 'opposite sides' safety measure is only really effective at preventing deliberate cheating and correcting excessively poor manufacturing.
yeah, you're assuming that the imbalanced dice is something people don't want today, and is something that is all but eradicated. There are still cheaters around, plenty of them. They could be skill-based with sleight of hand, or have imbalanced dice on purpose. So why allow a die that allows for those by grouping all the good numbers on one side. It's real difficult to use sleight of hand or to imbalance a regular d20, since every good value (15+) is surrounded by bad values, and even the slightest miscalculation spoils the good result. But if all the good results are on one side, then with a miscalculation you just get a slightly worse result. Instead of a 20, you get a 17, stuff like that.
One thing to note about statistics is to get to a true distribution of something, you need a sample size that is so large that the thing that happens the least happens at least 30 times in your sample size. if you do that it will bring your t-distribution to the point that is is 95% accurate in comparison to the true z-distribution. so for the perfect case the smallest sample you need to get close to that for a 20 d would be 600 samples as that would be 30 cases of each side. So for your case here the sample 1000 should be counted as close to the true distribution of these cases. This is one of the main things I remember from my stats class when looking at sample sizes and how to tell if something was doing enough sampling to get to a true distribution.
I'm an applied cryptographer. Absolutely love these kinds of videos exploring practical real world rng scenarios. Your conclusions are correct, both in what you expected, and why you observed what you observed. To test a dice's balance by rolling, the number of rolls becomes basically impossible quickly. The more biased a dice, the fewer rolls you need to draw a conclusion, but even quite biased dice can be basically indistinguishable from a perfect dice for many thousands of rolls. Practically speaking, you cannot work out the actual bias of a dice, but you can give yourself statistical evidence that it's less (or more) biased than some given threshold. Even if you automate dice rolls, you're going to have some additional bias from the automated rolling technique which will not properly reflect the dice itself. Dice can be biased in different ways, too. It could be that a given dice is more likely to land on a specific region, as in your theoretical example, in which case, your expectation of being further from the unbiased distribution is correct. But a dice could be biased and land on two opposite clusters most of the time, and, if those clusters are opposites (eg: 20, 19, 18 and 1, 2, 3), you'll wind up with results which look more fair, even if the dice is actually more biased than the single cluster biased dice. If anyone is worried about dice bias, a float test is sufficient. If it's not obviously biased in that float test, for gaming purposes, any bias is simply not going to be relevant, and I'd even personally be comfortable using any float test passing dice for generating key material. Beats the hell out of software RNG. One other practical suggestion for those looking to get unbiased randomness from dice (or coins) is to throw the dice against a vertical surface, rather than rolling them, so it bounces off and then lands on the table, which will eliminate bias from rolling technique.
@@TalsBadKidney I can't say I've tried it, but your dice should have roughly the same buoyancy in beer as in water, maybe with a little lift from bubbles too. You're going to be displacing the same volume of liquid when dropping it in beer, and you might trap some bubbles under the dice, displacing a little extra. The problem is, the float test requires mixing in salt or sugar (salt requiring less for the same buoyancy, but much, much more sugar can be dissolved into the same volume of water, making it better overall), which would be a terrible waste of good beer. 😉
Why would you crap on software RNG? Sure, it's predictable if you know the input parameters, but it behaves exactly like a real randomness. You can have long streaks of the same number just like a real randomness would, but over a million rolls, each number gets rolled roughly the same amount of times. Of course it's not good for security, but for every other application you can safely call it random.
@@hvip4 Because he's in cryptography and talking about generating a key (likely in the context of cryptographic usage). So its literally the specific reason that you said it wasn't good for, that he is saying it's bad for.
Yeah, I would have really liked to just see the distributions. Since there are only 20 outcomes, binning isn't an issue and a plain old histogram would be fine. To be really nerdy and pedantic.. empirical cumulative distributions are usually the thing to use if you want to to compare stochastic things which have lots (or continuous) possible states/outcomes. You can also more easily fit functions to them.
Yeah, I wasn't really satisfied with just an average. Having a lot of 1s and a lot of 20s would still benefit the player more than a spread of 1-20. A 6 is still very likely to fail, and a 15 can still fail. And in games with crits, 20s are usually natural criticals. Median will just be 10 or 11 once you have over a hundred rolls, unless something is severely wrong with the die. A bar chart would've showed the actual distribution. How much each individual number was rolled. I know he had the numbers on the sides, but they weren't even talked about.
Yes but that isn’t actually what this discussion is about. It’s about the complete randomness of a random role. How someone can manipulate their dice role is a different matter.
@@JackWest-sp1zc in the video, he mentioned spindown dice had been banned in some tournament settings, and the concern in those cases was almost certainly to avoid intentional manipulation rather than concern over deviation from being absolutely random. So yeah, that's not what the video was about, but it would have been good to discuss at least briefly. But he preferred to make a long video answering a question nobody asked. (Which I did find interesting anyway.)
@@JackWest-sp1zcit is what the video claims to be about because he introduces it with the fact that those dice are widely banned and that is the sole reason that they are banned.
This video is about exactly the kinds of things that I think about in my head and have no idea how to actually test because I’m not a Maths person. I love how detailed this is and how much you break it down for the non-maths like myself. I’m a new sub just to see what other delightfully detailed information you have!
It is facinating to see the testing methods. I personally don't mind if someone has a spindown or a normal D20. If i notice a character has a propensity to cheat. I deal with the player, not find one million different ways to get them to not cheat.
Exactly. If you put a roll down in a cup, it doesn't matter, but use a careful and consistent rolling move and line up the dice in you hand when you "shake" and you can easily get some higher results. It just makes it easier to manipulate.
For finding unbalanced dice, you could drill a tiny hole in each, and then cover up the entrance to the hole with paint. That would change the mass distribution, and also you could forge similarly unbalanced dice, both normal and that other one
When I worked at a game store several years ago, This exact question game up. My Pathfinder group wanted to ban me using the MTG spin-down dice. So I spent a few slow days rolling the spin down 5000 times. I should have done a standard deviation like you, but instead I just used a more crude metric of average rolls, and highest and lowest rolled numbers. I compared this to 9 other sets of 5000 randomly generated dice rolls. Since my dice did not have the highest average or an unexpectedly high number of high rolls compared to the random sample, my group relented, and let me use the die. However, I think they really just wanted to shut me up. I have also confirmed that if you want to cheat, you can finesse the roll for a more favorable outcome on a spin down. In another test, I was able to roll a 20 in 20% (4/20) of rolls, and a 16 or better about 40% of the time after 300 rolls. But this involved holding it just so, and barely letting it tumble out of the hand on a specific surface after several minutes of practice. If you are rolling fairly, your spin down dice should give you just as random of a result, within reason. I say if you have someone cheating with spin down dice in your game, and you ban the dice, they will cheat in other ways, and probably already are.
Spindowns are the easiest possible die to cheat with. The only thing potentially easier is a coin flip. Die are gambling equipment. Any gambling equipment or randomizer that is less secure than THE STANDARD equipment should be banned across the board as essentially the only functional difference is being able to cheat with it easier. This is no different than allowing cards with slightly different design or textures on the back. Spindown die even being made in the first place is massively suspect. A normal d20 is not hard to track life on if you know all sides add to 21.
@@KyleTremblayTitularKtreyit's completely different. You're totally capable of using a spin down legitimately. There's no way to use a set of cards like that without seeing the differences. But even then someone who doesn't know the differences would be able to use the cards just the same as a normal deck. If you don't trust the people you play with not to cheat, just don't play with them. It's pretty simple my guy. Also it's a game. You don't have to take personal games between friends so bloody seriously.
@@KyleTremblayTitularKtreyWhat are the odds of rolling a 20 on a regular d20? I in 20 What are the odds of rolling a 20 on a spin down? 1 in 20. Y’all are making too big a deal out this. The arrangement of the numbers doesn’t change the odds, and the average person, and hell, even most sleight of hand artists, isn’t going to be able to reliably game a spin down. This is a nonissue.
@@Glmorrs1 You're missing the point. Sit down with a spin-down die and a normal die. Don't ~try~ to be fair, ~try~ to cheat with the spindown die, and you will find it's much easier. It's not about the probability, it's about abusibility. Is it a BIG deal? No. Can anybody learn to cheat with them after just a few minutes of practice? Yep.
So here's my take on this: - In any low stakes scenarios, the difference between a spin-down and a Regular D20 are so small as to be nonexistent. - Most spin-downs are made well enough that they *are* just as fair as the average Regular. However: - These dice configurations serve different purposes, and they may be designed with those purposes in mind. A spin-down may have a center weight, and a different surface finish so it's less likely to tip over on accident (f.e. when someone bumps the table) Also they may not be tested for weighting, because gain, they're not primarily designed to be rolled. - Conversely a Regular D20 is specifically designed to be rolled, hence they are more likely to be tested for fairness - *IF* either die configuration happens to favor a side, the Regular D20 will stay "fairer" with increasing bias, hitting a wider range of results, rather than a specific sequence.
Great Video Thanks for sharing. As a dm who later encountered spin downs from folk who played magic I immediately fell in love. Love me some giant MTG dice. With TTRPGs, I'm a lot more selective with who I play with and it's been a nice "can you be chill and hang" measure. Also great counters for things like frosthaven monster hp and such, can see why mtg players use them.
I carry both of these dice, and oddly enough i use a spindown dice as my DM descretion dice because it's easier to control a result to prevent total disaster
^^ the only use case for the spindowns is so the DM can cheat on saves and attack rolls to subtly prevent full party wipes or make his big bads last a bit longer.
@@Muhahahahaz it's easier to manipulate because, if you watch the video, the numbers have a more controlled group. you cant make it land on a number, but you have a better time to get a result you want with it
@@NEEDbacon Fair enough. I found it slightly distracting for this video but each to their own. I had some sound activated colored led lights that I rather enjoyed when listening to music.
@@NEEDbacon I thought it was a candle effect too and just happened to use a really bad/distracting pattern. Didn't realize it was tied to the sound level, that would be cool if it were tied to maybe hue or something instead. Or maybe just a slower on/off so it didn't look like power outages.
Question: are the numbers on these dices always carved in? Because if so, wouldn't spin down dices basically have a production fault since higher numbers have two digits and therefore more material carved out thus unbalancing the dice?
Was thinking the same. Spin down having one area/side with only two digit numbers would move the center of gravity to the singel digit side. Making it inherently unbalanced and more prone to rolling high numbers.
In general, I think the paint is supposed to be weighted to correct for that. That said, I've heard concerns that spindown dice would have less attention given to making them balanced in manufacturing because they're primary intended purpose is for rolling. That said, I think Wizards of The Coast has claimed that their spindowns are balanced for use when rolling, so it's probably fine.
Back in the day, I knew a guy who thought it was cool to melt different colored wax into the number grooves. He said it made the dice easier to read. Back then some dice were pretty plain, but now they come in nearly infinite varieties of colors, sparkly/not sparkly, etc. I questioned whether he'd noticed any difference in the performance of his dice because he'd added weight to them, but he didn't think so. I think we've all had one or two dies that we really liked, because we used them to pull off some incredible feat in a game. I had a d20 that was my favorite, but at the game table I was well known for being either incredibly lucky, or incredibly unlucky. That die was probably biased since I didn't know about float tests back then. In nearly every game we played, I did something great with a 20, or nearly died with a 1. And sometimes both in the same game.
It's as much physics as probability. The randomization effect of a single die in based on its physical geometry, not the arbitrary label we ascribe to each face. The momentum, shake, throwing position, bounce, etc combine with the uniformity. Every face has roughly a 1 in 20 chance of landing up.
Is it a silly question to ask a 'standard' die has a numbering arrangement that is not spindown, is the relationship between the numbers fixed beyond the requirement that opposite faces add to 21?
It might be a silly question, but I'd also like to know the answer. From my quick search of the internet I learned different manufactures use different patterns. The website "Alea Kybos’ Dice Collection" has a "Configurations" section which shows a bunch of different d20 layouts.
This entire video missed the point because you were assuming fair rolls. The whole issue is that it is very easy to cheat using a spindown. Test it for yourself, I have. It only takes a few minutes of practice to consistently roll high numbers every time.
@@WalterSMM2I would find out why people cheat before ditching them. For some people it's because they struggle with invisible disabilities. Read a story from someone who DMs public games. Had a player who cheated because they struggled so much with math that adding numbers for attack rolls was hard for them. They were ashamed of this, so instead being vulnerable and risking ridicule by asking for help, they cheated to get pre-calculated results. If the player was able to ask for and receive help, or was in an understanding and caring group who noticed the problem and offered help, the player wouldn't cheat. Even those who cheat for ego reasons can often be talked to and have their underlying issues addressed and the cheating potentially stopped. That said, not everyone has the time, energy or ability to handle cheaters this way, and not all cheaters can be handled this way. I think most cheaters can be helped though.
@@WalterSMM2 That's fine and all, but nobody thinks that a spindown is any less random on a fair roll. The entire issue is that they're easy to cheat with and ignoring that makes the video pointless
There is a similar test with coins where there is a small unbalance where if you flip a coin it was biased towards landing on the same face. Potentially the dice has a similar bias where it might land towards one face more often if rolled from a specific face. Someone could gain a tiny advantage by rolling from the same face.
While rolling a die, unless it's weighted, usually evens out the numbers you get. But with that spindown die, you could technically learn the exact way to hold the die to scew the odds in your favor. It will take a while, but if you roll the die the exact same way every time, the way you place the die in your palm gets more important. Seeing how the high numbers are grouped together the odds of rolling a high one gets increased.
I learned how to do this with a regular 6 sided die as a kid, the solution is a backboard that's why casino dice games make you roll them at the backboard first so you cant control them
For your efforts, a like, sub, and ding. I remember having this argument 15 years ago when mtg started giving out spindowns in precon packs. Kind of amazing it's been going this long.
No idea how I got here and while I'm a board gamer I don't usually play games with d20s, but, your video looks fun and I'll indulge in your invitation to engage. I speculate that they'll be equally random from a blind roll but the spin-down will be easier to chuck in a way that you'd have a better chance of getting your favourable numbers, because of their groupings.
I’ve never heard of this before and I have only been playing D&D for 2 months now. But I’ve been going down a rabbit hole of D&D videos trying to learn the game and this video popped up so here I am.
I love the research you did here. Though one thing that comes to my mind is that with an unbalanced spin down the data might differ based on which side is favored in the unbalancing. I would expect there to be a bigger deviation if the imbalance favored 1,2,3,4,5 or 16,17,18,19,20 as opposed to 8,9,10,11,12.
I've never heard of this before and don't know how I got here. The algorithmically demanded engagement is hereby complete and I will now watch the rest of the video, thank you.
I use numerically-balanced d20s and d30s from The Dice Lab. "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."
I feel like it doesn't matter at all where the numbers are. But there's a chance for manipulation if you don't have a watchful DM, doing "micro" rolls and/or "flips". but as long as you're yeeting the dice a similar way every time the results should be random.
I wish I still had my old d20s. They were made in the early days of AD&D, around 1979 or 1980. Back then, d10s didn't exist, since all the dice were Platonic solids, so percentile rolls were done with two d20s. As such, they were packaged and sold as a pair, and they were numbered 0-9 twice on each die - you had to fill in half the numbers with paint or something to differentiate between 1-10 and 11-20. They were opaque, so not as pretty I guess, but they also weren't rounded, and they were slightly larger IIRC. Quality stuff. Before I had something I could use to fill in half the numbers, I'd roll one of them to get a number from 1-10, and roll the other to determine whether or not to add 10 to the first roll (if it matched the first roll in terms of odd/even, add 10). Anyway, I guess that could be a way to reduce the possibility of unfairness, albeit a rather convoluted one compared to throwing dice against a vertical surface. Speaking of old dice, any old-timers remember the sets sold by TSR through the Dungeon Hobby Shop? It would take weeks to receive your order, then you open the package and saw the worst dice ever (there were no photos of the dice in catalogs or on the order form). Shockingly cheap plastic, ugly colors, concave/uneven faces and edges, I remember feeling so ripped off. I think they were also included in their other RPG boxed sets - Gamma World, Boot Hill, and Top Secret.
I never heard of this before, i don't know how i got here, but after the intro i gotta say, i am truly intrested on listening to you talkjng abou it, go ahead dear stranger!
1000 rolls are enough (by a long shot) to estimate if a dice is balanced. Usually we look for a confidence of 95% in the results so that they're both probable and specific so I'm going to work with that. For the estimation of a mean in a random distribution with std deviation S, one needs a sample size of n=4*Z^2*S^2/W^2 to achieve a confidence interval with a desired Z-score Z and width W. For your case a confidence interval of 95% gives a Z-score of roughly 1.96, the ideal deviation being 5.9 and width 1 gives a sample size of 536. Now, with the data you already collected I constructed said confidence intervals. For estimating the mean (with an unknown stantard deviation) the formula is X±ZS/√n where X is the sample mean and S is the sample standard deviation. For your 3 dice the intervals for the mean (with 95% confidence) are 9.95-10.72, 9.82-10.53, and 9.93-10.68, so all 3 dice cover the expected mean and are good to go. For estimating the standard deviation one uses √((n-1)S^2/Q) where Q is the quantile we want from a chi-square distribution with n-1 degrees of freedom (0.975 and 0.025 to achieve 95%). For your data the intervals for the standard deviation are 5.91-6.45, 5.41-5.91, and 5.74-6.27 so if anything the first dice is the "sketchiest" one, with desired value falling juuuuust outside the interval (I wouldn't worry too much tho). As a final note, if we want a confidence of 99% the sample size needed grows closer to what you did (927) and all the intervals expand a little (making all dice pass both the mean and std deviation test).
This was a really cool video, and I'm interested in your automated die-roller project if you ever do build it. Thanks for doing the math for fair/unfair dice, and then spending 4 hours rolling and recording d20s for our edutainment! I did have issues with your audio, you started out fine, then would fade out dramatically then come back to an acceptable level.
This is so cool! If you've got a video on float tests, it would be helpful to have a link in the video description. :) (If you don't have a video on float tests, I'd totally watch one if you made it!)
As was mentioned here in comments already, spindice seems less prone to cheating throws. It's hard to tell how much, but I think it's quite possible to roll dice to get gyroscopic effect to try to keep some part up, or master throw to be more deterministic.
Important thing to consider: Rolling by Hand or a (too) simple machine will actually influence the die roll esp on unbalanced dies. Also rolling a die alot of times will change its balance due to grime and oils and stuff from hands and wear and tear.
Hypothesis before seeing the rest of the video: Theoretically, a spindown should have the same odds/randomness as a standard since they have the same amount of sides and the same shape, so each side should have the same odds. But I feel like with enough practice, it could be really easy to manipulate rolls with a spindown to consistently roll high numbers, whereas the mixed layout of a standard die makes it much more difficult to do the same. The next paragraph will be me after I've seen the video. Hello future me, by the way! You look extra cute today. Aww, thanks past, pre-video me! You looked cute too! Anyways, the data was super interesting to see the results of, and I'm honestly a little sad that the spreadsheets weren't linked in the description. I would've loved to see if the "unbalanced" (in quotes because of the well-done manufacturing) spindown die had clusters of similar roll results or if the results would have been as evenly spread out as the balanced standard die. Perhaps my hypothesis would be correct? There's just not enough data to tell, but I did enjoy the video and will be sharing your efforts around to more people. Also, this is my plea for a link to a public form of the spreadsheets for the three sets of rolls 🙏
There is a way to accurately measure this. The perfect theoretical dice is using binomial distribution and we can test it our dice does as well. We should use the Chi2 compliance test to determine whether the dice is actually using the binomial distribution.
this is incredibly interesting! my mtg pod only rolls spindowns for heads/tails sorts of rolls because they have equal quantities of odd and even sides. i think that we all were just under the assumption that they are entirely unfair, but its exciting to see the mathematical evidence for that claim!
Very very interesting. Also of note. Tho the results were slightly different from each other, they are basically overlapped when accounting for sd. That means the results were statistically equal in all cases, so those would all be considered balanced if your 1000 roll test was representative enough. (edited for typos)
Very interesting topic. Thank you for your work. Just one thing, you actually don't need a very large sample size to get valid results in most cases. People often make a big deal about sample size, especially when the results do not match expectations, but it's really not necessary to have census level sample sizes for something with only one variable. 1,000 is a perfectly reasonable sample size for something like this considering there's only one variable, and, by the very nature of how data are obtained for this, it's already as random as it can be.
Something I feel you should add to your test is how easy is either dice to rig. If I throw the dice a certain way each time can I shift the odds in my favor. I Can get a coin to land on heads more than 50% of the time if I drop it from a certain distance or spin at a certain speed.
I think the initial landing is just as random, but a spindown becomes an advantage if it tips over. I.E A 19 can tip to a 20 or an 18 on a spindown vs a 3 or a 9 on a regular. Basically if its on the high number side of the die, you can (with some shifty rolling techniques) guarantee on a spindown that you will get a high roll.
I didn't know a spindown dice was even a thing but in hindsight there is an active item in Binding of Isaac called Spindown Dice in addtion to the D6, D20 etc. cool info!!
I literally did this as a statistics project in college (although I didn't know it was called a spindown die at the time, and just referred to it as non-standard numbering). Got roughly the same conclusion though, even though I only had time for 100 rolls per die. Got an A on that project.
I didn't know any of this before and I don't really know how I got here. You got me soo good with that one I just had to actually leave the comment as you asked 🤣
I think a bigger flaw in this experiment than the small sample and spindown only being slightly unbalances, is that it's starting from a false assumption. This video is actually the first time I've even heard the idea clustering of numbers in spindown could give unbalanced results in a normal roll. The main argument I've always seen is that clustering of numbers on a spindown makes it easier to use a rolling technique that could look fair but increases your likelihood of rolling high.
I have a few d20s that have a different layout than either the normal d20 or spindown. The opposite sides don't add up to 21 (other than 1 and 20, which are on opposite sides); the layout appears to be random (the numbers adjacent to 20 are 7, 14, & 11). I have 3 of them, all with the same layout (they all came from the Heroscape board game).
In some ultra competitive tourney settings they even go so far as to only allow clear dive from a specific trusted brand. If there were bubbles inside affecting the weight you can’t see them in a non transparent die. Then people say you can weight them even more by using a microwave to increase the air bubble or moving it in a different direction. Anyway this is why quality control is a big deal the biggest example I can think of are big money casinos in Las Vegas. Clear dice made but the casino with same in house controlled cards and chips.
My initial thoughts: I heard once that whether or not a die is rolled 'fairly' has more to do with how long you actually roll it around in your hand, whether or not you use a dice tower, etc. than the actual rolling across a surface. My instinct is to say that applies here, and that so long as the die is rolled/randomized enough, like thoroughly shuffling a pack of cards, it shouldn't make a difference whether it's standard or spindown.
Long ago, it had been explained to me that the reason spin-down D20s weren’t generally permitted in events (at least for the events I was playing in/judging) had less to do with inherent flaws of the number distribution in an “honest” roll, but rather the potential of their pattern’s exploitability for those intending to exploit that distribution.
It would be interesting to test how much one could exploit the pattern to manipulate results (or, realistically, if such exploitation is practically possible).
I used to do magic and I had a trick that relied on rolling a dice in a specific way so it would land how you wanted but looked like it rolled. This is much harder to do with a d20 however after some trying I can kind of manipulate it so with practice I could probably make it so I only roll high on a spin down. This is however a small test I did at home for only a few days.
Yeah if you're going for high numbers, it's significantly easier on a spin down. Roll it against a surface, make it bump, even just start it in a specific orientation and what was a 1/20 chance affected by skill becomes a 4/20 to get something good enough affected by skill much more heavily. Hell you don't even have to be doing it intentionally, I used to roll against a box all the time and we just threw it in a way where it hit the sides most rolls. On a d20 that barely matters, but a spin down would've stopped at a number within the cluster of whatever hit the side.
Edit: also, the majority of spin downs aren't manufactured to be balanced, they don't need to be balanced they just display a number.
@@bye1551and how would you be able to choose which side of the dice hits the wall?
Maybe I'm missing something in your comment, but if you just throw the dice it shouldn't matter if it hits the wall or the floor. Simply because you can't guarantee or even influence wich side hits.
Dices where the numbers are cut you can cut more material in the numbers you want so they roll with more frequency. How much it affects I don't know but it is enough that I have heard and seen this trick done.
@@Jehty21 oww yes you can by checking the die in your hand and making the right flick or the wrist you CAN influence this. Tried an tested. Takes a little bit of practice but the skill can be developed quickly
So, the thing with spindowns is, I think, if they're being rolled fairly, they're probably not really any less random than a standard D20; considering that the standard D20 manufacturing process includes, presumably, making sure the die is balanced well enough, you'd probably have to do it on purpose to make the die poorly balanced. However, because all of the high numbers are on one side and all the low numbers are on the other, it makes it much easier to manipulate the die into always giving you a number in that 16-20 range.
Supposedly that's the thing: they're not balanced because it's cheaper to not have to worry about that manufacturing step so they don't.
Allegedly.
@GameScience has excellent videos covering dice accuracy.
I trust the people who I play with. And the people I don't trust were kicked out of the group.
Testing a die for fairness would take more time than actually making the die. whether the dice are mass manufactured or small batch, that's just not worthwhile for the manufacturer.
think about how hard-edge dice are often marketed as more fair due to the tumbling process of typical dice allegedly reducing the fairness of each individual die. If the makers of typical dice had the testing records for this, it would be very clear cut whether hard-edge dice are an improvement, and that kind of clarity is just not what we see.
Followup: the video mentions a "float test". I was implicitly assuming a higher standard of testing (rolls and statistics) in the claim about testing time. With small batch manufacturing, float testing each die is at least achievable, though still not worthwhile in my opinion. float testing each die with mass manufacturing is still intractable though.
@@LaBlueSkuld They do a little bit. A very little bit. And pretty much only for transparent and translucent dice.
I know this because I buy them by the bucket on Chinese websites. Sometimes they have bugs stuck inside of them. That's pretty cool.
They also roll hilariously biased. But it's pretty much impossible to tell what exact number they're biased at without spending way too much time doing the math.
It's funny watching people get angry at one set of dice to swap them for another set of dice, they also get angry at.
That "Dear god... It's reality!" Needs to be made into a meme. It's way too relatable.
Happens to me at least once a day
Except he immediately disregarded reality right after it by not rolling them all as he claimed he would.
That honestly has huge meme potential :
As the only person at my table who recognises a spindown vs a standard d20, I always balk at one of my players bringing a spindown to DnD. And then I immediately mentally talk myself down because there's no real impactful difference and my player just picked that die because they think it's pretty. Excellent video!
I have absolutely no idea how I got here. I don't even play DnD, or any another dice rolling game. I am though definitely pleased with the algorithm, but I am a wee bit alarmed it knows me so well. Now you've got me down the rabbit hole on dice sir! I've just been googling what a "float test" is!
Welcome! 😂
You and I both, brother.
Have you been watching Bauldr's Gate 3 content too? (a game I don't even own because turn based RPG's are icky and yucky but that one looks nominally interesting)
Dice float testing can be fun. I've done some of it before.
Dude you should try Dnd
I’ve totally played DnD, but I’ve never worried that much about my dice as long as we’re all using the same ones…still. I was absolutely and totally fascinated by this.
The way I've always understood it is that placing numbers so that opposites add to Dice Sides + 1 is an ancient measure intended to offset the fact that old dice weren't very precisely made, and to make it more difficult to 'weight' the dice. It might even go back to the use of knucklebone dice (aka Astragaloi, Talli, Shaggai) which had only four sides and were numbered 1, 3, 4, 6, with the numbers 1 and 6 being only 10% likely compared to the 3 and 4 being 40% likely. This required 1 and 6 to be opposite one another and 3, 4 likewise, because that's how the astragalus bone is shaped - opposite sides are roughly the same size and shape, meaning the die's average remained somewhere close to the middle of its range. These measures are no longer necessary with modern dice, which are much more uniformly shaped and weighted.
Having seen the rest of the video now, I think I'll also point out that simply being off-balance isn't enough to make a spin down die noticeably unfair, it specifically has to be unbalanced away from or towards the 'high point' (the centre point at which all the highest-rated facets are clustered around). As I noted above, the 'opposite sides' safety measure is only really effective at preventing deliberate cheating and correcting excessively poor manufacturing.
yeah, you're assuming that the imbalanced dice is something people don't want today, and is something that is all but eradicated.
There are still cheaters around, plenty of them. They could be skill-based with sleight of hand, or have imbalanced dice on purpose.
So why allow a die that allows for those by grouping all the good numbers on one side. It's real difficult to use sleight of hand or to imbalance a regular d20, since every good value (15+) is surrounded by bad values, and even the slightest miscalculation spoils the good result. But if all the good results are on one side, then with a miscalculation you just get a slightly worse result. Instead of a 20, you get a 17, stuff like that.
A dice tower would make the entire issue moot, but this whole issue has only come up for me because of the MTG life counter dice.
@@nevadanate4957 a dice tower would eliminate skill-based cheating throws, but not the purposefully imbalanced dice.
@DifferentRussian oh, true. Man weighting a D&D die is ridiculous lol
When you make the Arduino dice-rolling bot, remember to build a thousand versions of them so you can identify the one that is perfectly balanced.
And roll thousands of different dices.
One thing to note about statistics is to get to a true distribution of something, you need a sample size that is so large that the thing that happens the least happens at least 30 times in your sample size. if you do that it will bring your t-distribution to the point that is is 95% accurate in comparison to the true z-distribution. so for the perfect case the smallest sample you need to get close to that for a 20 d would be 600 samples as that would be 30 cases of each side. So for your case here the sample 1000 should be counted as close to the true distribution of these cases. This is one of the main things I remember from my stats class when looking at sample sizes and how to tell if something was doing enough sampling to get to a true distribution.
I'm an applied cryptographer. Absolutely love these kinds of videos exploring practical real world rng scenarios. Your conclusions are correct, both in what you expected, and why you observed what you observed.
To test a dice's balance by rolling, the number of rolls becomes basically impossible quickly. The more biased a dice, the fewer rolls you need to draw a conclusion, but even quite biased dice can be basically indistinguishable from a perfect dice for many thousands of rolls. Practically speaking, you cannot work out the actual bias of a dice, but you can give yourself statistical evidence that it's less (or more) biased than some given threshold. Even if you automate dice rolls, you're going to have some additional bias from the automated rolling technique which will not properly reflect the dice itself.
Dice can be biased in different ways, too. It could be that a given dice is more likely to land on a specific region, as in your theoretical example, in which case, your expectation of being further from the unbiased distribution is correct. But a dice could be biased and land on two opposite clusters most of the time, and, if those clusters are opposites (eg: 20, 19, 18 and 1, 2, 3), you'll wind up with results which look more fair, even if the dice is actually more biased than the single cluster biased dice.
If anyone is worried about dice bias, a float test is sufficient. If it's not obviously biased in that float test, for gaming purposes, any bias is simply not going to be relevant, and I'd even personally be comfortable using any float test passing dice for generating key material. Beats the hell out of software RNG.
One other practical suggestion for those looking to get unbiased randomness from dice (or coins) is to throw the dice against a vertical surface, rather than rolling them, so it bounces off and then lands on the table, which will eliminate bias from rolling technique.
Ahhh, I never considered the vertical surface bit; makes all those movie scenes with people hucking dice at a wall make more sense!
does the float test work in a beer, in which a significant portion of the solution is a gas?
@@TalsBadKidney I can't say I've tried it, but your dice should have roughly the same buoyancy in beer as in water, maybe with a little lift from bubbles too. You're going to be displacing the same volume of liquid when dropping it in beer, and you might trap some bubbles under the dice, displacing a little extra.
The problem is, the float test requires mixing in salt or sugar (salt requiring less for the same buoyancy, but much, much more sugar can be dissolved into the same volume of water, making it better overall), which would be a terrible waste of good beer. 😉
Why would you crap on software RNG? Sure, it's predictable if you know the input parameters, but it behaves exactly like a real randomness. You can have long streaks of the same number just like a real randomness would, but over a million rolls, each number gets rolled roughly the same amount of times. Of course it's not good for security, but for every other application you can safely call it random.
@@hvip4 Because he's in cryptography and talking about generating a key (likely in the context of cryptographic usage). So its literally the specific reason that you said it wasn't good for, that he is saying it's bad for.
for future reference, a bar chart would be a nice addition to visualize the data
Yeah, I would have really liked to just see the distributions. Since there are only 20 outcomes, binning isn't an issue and a plain old histogram would be fine.
To be really nerdy and pedantic.. empirical cumulative distributions are usually the thing to use if you want to to compare stochastic things which have lots (or continuous) possible states/outcomes. You can also more easily fit functions to them.
I think sometimes having it is the difference between the deal and no deal.
This. And headlines. And possibly even a summarization of what was observed in a more clear manner.
Yeah, I wasn't really satisfied with just an average. Having a lot of 1s and a lot of 20s would still benefit the player more than a spread of 1-20. A 6 is still very likely to fail, and a 15 can still fail. And in games with crits, 20s are usually natural criticals. Median will just be 10 or 11 once you have over a hundred rolls, unless something is severely wrong with the die.
A bar chart would've showed the actual distribution. How much each individual number was rolled. I know he had the numbers on the sides, but they weren't even talked about.
The data looked like it was there for you to make your own chart. But I could be wrong. I do like a visual.
I'm sad that you didn't cover rolling technique. As far as I knew, that was the real concern.
Yes, a skilled manipulator of dice would definitely benifit from the spindown layout I think.
Yes but that isn’t actually what this discussion is about. It’s about the complete randomness of a random role. How someone can manipulate their dice role is a different matter.
@@JackWest-sp1zc in the video, he mentioned spindown dice had been banned in some tournament settings, and the concern in those cases was almost certainly to avoid intentional manipulation rather than concern over deviation from being absolutely random. So yeah, that's not what the video was about, but it would have been good to discuss at least briefly. But he preferred to make a long video answering a question nobody asked. (Which I did find interesting anyway.)
@pstrap1311 plenty of people asked the question. You specifically didnt
@@JackWest-sp1zcit is what the video claims to be about because he introduces it with the fact that those dice are widely banned and that is the sole reason that they are banned.
This video is about exactly the kinds of things that I think about in my head and have no idea how to actually test because I’m not a Maths person. I love how detailed this is and how much you break it down for the non-maths like myself. I’m a new sub just to see what other delightfully detailed information you have!
It is facinating to see the testing methods. I personally don't mind if someone has a spindown or a normal D20. If i notice a character has a propensity to cheat. I deal with the player, not find one million different ways to get them to not cheat.
This! 🙌Communicate with your crew!
Don't hate the Character, hate the player.
That is the best way to deal with a cheater.
Exactly. If you put a roll down in a cup, it doesn't matter, but use a careful and consistent rolling move and line up the dice in you hand when you "shake" and you can easily get some higher results. It just makes it easier to manipulate.
yo BRS
For finding unbalanced dice, you could drill a tiny hole in each, and then cover up the entrance to the hole with paint. That would change the mass distribution, and also you could forge similarly unbalanced dice, both normal and that other one
When I worked at a game store several years ago, This exact question game up. My Pathfinder group wanted to ban me using the MTG spin-down dice. So I spent a few slow days rolling the spin down 5000 times. I should have done a standard deviation like you, but instead I just used a more crude metric of average rolls, and highest and lowest rolled numbers. I compared this to 9 other sets of 5000 randomly generated dice rolls. Since my dice did not have the highest average or an unexpectedly high number of high rolls compared to the random sample, my group relented, and let me use the die. However, I think they really just wanted to shut me up.
I have also confirmed that if you want to cheat, you can finesse the roll for a more favorable outcome on a spin down. In another test, I was able to roll a 20 in 20% (4/20) of rolls, and a 16 or better about 40% of the time after 300 rolls. But this involved holding it just so, and barely letting it tumble out of the hand on a specific surface after several minutes of practice. If you are rolling fairly, your spin down dice should give you just as random of a result, within reason. I say if you have someone cheating with spin down dice in your game, and you ban the dice, they will cheat in other ways, and probably already are.
Spindowns are the easiest possible die to cheat with. The only thing potentially easier is a coin flip. Die are gambling equipment. Any gambling equipment or randomizer that is less secure than THE STANDARD equipment should be banned across the board as essentially the only functional difference is being able to cheat with it easier.
This is no different than allowing cards with slightly different design or textures on the back.
Spindown die even being made in the first place is massively suspect. A normal d20 is not hard to track life on if you know all sides add to 21.
@@KyleTremblayTitularKtreyit's completely different. You're totally capable of using a spin down legitimately. There's no way to use a set of cards like that without seeing the differences. But even then someone who doesn't know the differences would be able to use the cards just the same as a normal deck.
If you don't trust the people you play with not to cheat, just don't play with them. It's pretty simple my guy. Also it's a game. You don't have to take personal games between friends so bloody seriously.
@@KyleTremblayTitularKtreyWhat are the odds of rolling a 20 on a regular d20? I in 20
What are the odds of rolling a 20 on a spin down? 1 in 20.
Y’all are making too big a deal out this. The arrangement of the numbers doesn’t change the odds, and the average person, and hell, even most sleight of hand artists, isn’t going to be able to reliably game a spin down.
This is a nonissue.
@@Glmorrs1 You're missing the point. Sit down with a spin-down die and a normal die. Don't ~try~ to be fair, ~try~ to cheat with the spindown die, and you will find it's much easier. It's not about the probability, it's about abusibility. Is it a BIG deal? No. Can anybody learn to cheat with them after just a few minutes of practice? Yep.
...you didn't happen to record these results and format them into a quantitative study did you? This is genuinely useful research.
I can't stop looking at the flickering lamp.
Maybe you should look at the Kolmogorov-Smirnov or Chi-Squared tests
where H0 : data fits a Uniform CDF and
Ha : data does not fit a Uniform CDF.
So here's my take on this:
- In any low stakes scenarios, the difference between a spin-down and a Regular D20 are so small as to be nonexistent.
- Most spin-downs are made well enough that they *are* just as fair as the average Regular.
However:
- These dice configurations serve different purposes, and they may be designed with those purposes in mind. A spin-down may have a center weight, and a different surface finish so it's less likely to tip over on accident (f.e. when someone bumps the table) Also they may not be tested for weighting, because gain, they're not primarily designed to be rolled.
- Conversely a Regular D20 is specifically designed to be rolled, hence they are more likely to be tested for fairness
- *IF* either die configuration happens to favor a side, the Regular D20 will stay "fairer" with increasing bias, hitting a wider range of results, rather than a specific sequence.
Great Video Thanks for sharing. As a dm who later encountered spin downs from folk who played magic I immediately fell in love. Love me some giant MTG dice. With TTRPGs, I'm a lot more selective with who I play with and it's been a nice "can you be chill and hang" measure. Also great counters for things like frosthaven monster hp and such, can see why mtg players use them.
Thank you sincerely for learning and using the correct use of the singular and plural versions of the word "die".
I carry both of these dice, and oddly enough i use a spindown dice as my DM descretion dice because it's easier to control a result to prevent total disaster
^^ the only use case for the spindowns is so the DM can cheat on saves and attack rolls to subtly prevent full party wipes or make his big bads last a bit longer.
@@KyleTremblayTitularKtrey yep makez the experience fun for everyone :)
The first law of dnd, dramatic necessity @@KyleTremblayTitularKtrey
Broke: “Nah, you can’t use a spindown to cheat… it’s a nonissue”
Woke: “I intentionally cook my spindown rolls to improve player experience”
@@Muhahahahaz it's easier to manipulate because, if you watch the video, the numbers have a more controlled group. you cant make it land on a number, but you have a better time to get a result you want with it
Side note, why is the brightness of the lamp in the background seem to be tied to the level of noise in the room?
Because it's cool. TBH didn't even noticed it was tied to noise and thought it was just one of those "Candle effect" lights you can buy these days
@@NEEDbacon Fair enough. I found it slightly distracting for this video but each to their own.
I had some sound activated colored led lights that I rather enjoyed when listening to music.
@@NEEDbacon I thought it was a candle effect too and just happened to use a really bad/distracting pattern. Didn't realize it was tied to the sound level, that would be cool if it were tied to maybe hue or something instead. Or maybe just a slower on/off so it didn't look like power outages.
Y'all I didn't even notice the light level was changing ;-;
My husband and I were debating on this just a couple days ago--great analysis on this!
Really interesting and informative video! I'm new to DnD and have only played virtually so wasn't aware of this debate
Question: are the numbers on these dices always carved in? Because if so, wouldn't spin down dices basically have a production fault since higher numbers have two digits and therefore more material carved out thus unbalancing the dice?
Was thinking the same. Spin down having one area/side with only two digit numbers would move the center of gravity to the singel digit side. Making it inherently unbalanced and more prone to rolling high numbers.
In general, I think the paint is supposed to be weighted to correct for that. That said, I've heard concerns that spindown dice would have less attention given to making them balanced in manufacturing because they're primary intended purpose is for rolling. That said, I think Wizards of The Coast has claimed that their spindowns are balanced for use when rolling, so it's probably fine.
Back in the day, I knew a guy who thought it was cool to melt different colored wax into the number grooves. He said it made the dice easier to read. Back then some dice were pretty plain, but now they come in nearly infinite varieties of colors, sparkly/not sparkly, etc. I questioned whether he'd noticed any difference in the performance of his dice because he'd added weight to them, but he didn't think so.
I think we've all had one or two dies that we really liked, because we used them to pull off some incredible feat in a game. I had a d20 that was my favorite, but at the game table I was well known for being either incredibly lucky, or incredibly unlucky. That die was probably biased since I didn't know about float tests back then. In nearly every game we played, I did something great with a 20, or nearly died with a 1. And sometimes both in the same game.
guys... these are such small differences in weight that it doesn't matter.
Just check the balance if you're that concerned. It's really easy to float test
It's as much physics as probability. The randomization effect of a single die in based on its physical geometry, not the arbitrary label we ascribe to each face. The momentum, shake, throwing position, bounce, etc combine with the uniformity.
Every face has roughly a 1 in 20 chance of landing up.
Thanks for doing the rolls. Appreciate it.
thanks I didn't even know spin-downs existed until youtube randomly recommended me this video. FASCINATING science thank you for your service
Is it a silly question to ask a 'standard' die has a numbering arrangement that is not spindown, is the relationship between the numbers fixed beyond the requirement that opposite faces add to 21?
It might be a silly question, but I'd also like to know the answer.
From my quick search of the internet I learned different manufactures use different patterns.
The website "Alea Kybos’ Dice Collection" has a "Configurations" section which shows a bunch of different d20 layouts.
This entire video missed the point because you were assuming fair rolls. The whole issue is that it is very easy to cheat using a spindown. Test it for yourself, I have. It only takes a few minutes of practice to consistently roll high numbers every time.
Don't play people that you think would cheat. This is a problem of choosing better friends, not dice lol
@@WalterSMM2I would find out why people cheat before ditching them. For some people it's because they struggle with invisible disabilities. Read a story from someone who DMs public games. Had a player who cheated because they struggled so much with math that adding numbers for attack rolls was hard for them. They were ashamed of this, so instead being vulnerable and risking ridicule by asking for help, they cheated to get pre-calculated results. If the player was able to ask for and receive help, or was in an understanding and caring group who noticed the problem and offered help, the player wouldn't cheat. Even those who cheat for ego reasons can often be talked to and have their underlying issues addressed and the cheating potentially stopped.
That said, not everyone has the time, energy or ability to handle cheaters this way, and not all cheaters can be handled this way. I think most cheaters can be helped though.
@@WalterSMM2 That's fine and all, but nobody thinks that a spindown is any less random on a fair roll. The entire issue is that they're easy to cheat with and ignoring that makes the video pointless
If someone is gonna cheat on dice rolls they can cheat using other means as well. Maybe don’t play with someone who’s gonna cheat at dnd
Also he did mention “unless you are rolling in a specific way”
I don't know how I got here but I find it very interesting! Also quick nod to your passion for this video and doing that many dice rolls!❤
As a dnd geek and data geek. I’ve wondered this too. Thanks for trying to answer the question
those hours of me yelling about spindown dice in isaac got me here ig
I always understood spindown die are fine if you roll them the correct way. as if you roll them in a spinning fashion you can control your result
I’d love to see some breakdown on “coin dice” vs “standard d20”. Love the video!
There is a similar test with coins where there is a small unbalance where if you flip a coin it was biased towards landing on the same face. Potentially the dice has a similar bias where it might land towards one face more often if rolled from a specific face. Someone could gain a tiny advantage by rolling from the same face.
While rolling a die, unless it's weighted, usually evens out the numbers you get. But with that spindown die, you could technically learn the exact way to hold the die to scew the odds in your favor. It will take a while, but if you roll the die the exact same way every time, the way you place the die in your palm gets more important. Seeing how the high numbers are grouped together the odds of rolling a high one gets increased.
I learned how to do this with a regular 6 sided die as a kid, the solution is a backboard
that's why casino dice games make you roll them at the backboard first so you cant control them
Liked, subed only because of the 4k rolls alone. Awesome job, and backed up with good dice theory
Good video! Would like more of this!
hopefully i get to see more of your videos in the future, genuinely being reminded to sub made me do it
I've never heard of this but thank you for your hard and tedious work.
For your efforts, a like, sub, and ding.
I remember having this argument 15 years ago when mtg started giving out spindowns in precon packs. Kind of amazing it's been going this long.
Making the algorithm happy for all your hard work. Enjoy!
No idea how I got here and while I'm a board gamer I don't usually play games with d20s, but, your video looks fun and I'll indulge in your invitation to engage.
I speculate that they'll be equally random from a blind roll but the spin-down will be easier to chuck in a way that you'd have a better chance of getting your favourable numbers, because of their groupings.
I’ve never heard of this before and I have only been playing D&D for 2 months now. But I’ve been going down a rabbit hole of D&D videos trying to learn the game and this video popped up so here I am.
I would love to see a follow-up on this!! this seems very interesting
Leaving a like and a comment for your dice rolling labor, nice work!
I love the research you did here. Though one thing that comes to my mind is that with an unbalanced spin down the data might differ based on which side is favored in the unbalancing. I would expect there to be a bigger deviation if the imbalance favored 1,2,3,4,5 or 16,17,18,19,20 as opposed to 8,9,10,11,12.
I've never heard of this before and don't know how I got here. The algorithmically demanded engagement is hereby complete and I will now watch the rest of the video, thank you.
I use numerically-balanced d20s and d30s from The Dice Lab. "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."
Liked and commented and subbed just cause i respect the effort into your channel my friend. Keep going!
I feel like it doesn't matter at all where the numbers are. But there's a chance for manipulation if you don't have a watchful DM, doing "micro" rolls and/or "flips". but as long as you're yeeting the dice a similar way every time the results should be random.
this is a great video, props to you for putting in the effort for science
Your voice is fun. I like the dynamics, your diction, and the confidence in it.
Thank you for putting an unprecedented amount of time and effort into data collecting!
I've never used a 20 sided dice, didn't know any of this but found your video interesting. experiments are fun. Commenting to help your metrics.
Love your work man!
I wish I still had my old d20s. They were made in the early days of AD&D, around 1979 or 1980. Back then, d10s didn't exist, since all the dice were Platonic solids, so percentile rolls were done with two d20s. As such, they were packaged and sold as a pair, and they were numbered 0-9 twice on each die - you had to fill in half the numbers with paint or something to differentiate between 1-10 and 11-20. They were opaque, so not as pretty I guess, but they also weren't rounded, and they were slightly larger IIRC. Quality stuff. Before I had something I could use to fill in half the numbers, I'd roll one of them to get a number from 1-10, and roll the other to determine whether or not to add 10 to the first roll (if it matched the first roll in terms of odd/even, add 10). Anyway, I guess that could be a way to reduce the possibility of unfairness, albeit a rather convoluted one compared to throwing dice against a vertical surface.
Speaking of old dice, any old-timers remember the sets sold by TSR through the Dungeon Hobby Shop? It would take weeks to receive your order, then you open the package and saw the worst dice ever (there were no photos of the dice in catalogs or on the order form). Shockingly cheap plastic, ugly colors, concave/uneven faces and edges, I remember feeling so ripped off. I think they were also included in their other RPG boxed sets - Gamma World, Boot Hill, and Top Secret.
I never heard of this before, i don't know how i got here, but after the intro i gotta say, i am truly intrested on listening to you talkjng abou it, go ahead dear stranger!
1000 rolls are enough (by a long shot) to estimate if a dice is balanced. Usually we look for a confidence of 95% in the results so that they're both probable and specific so I'm going to work with that.
For the estimation of a mean in a random distribution with std deviation S, one needs a sample size of n=4*Z^2*S^2/W^2 to achieve a confidence interval with a desired Z-score Z and width W. For your case a confidence interval of 95% gives a Z-score of roughly 1.96, the ideal deviation being 5.9 and width 1 gives a sample size of 536.
Now, with the data you already collected I constructed said confidence intervals. For estimating the mean (with an unknown stantard deviation) the formula is X±ZS/√n where X is the sample mean and S is the sample standard deviation. For your 3 dice the intervals for the mean (with 95% confidence) are 9.95-10.72, 9.82-10.53, and 9.93-10.68, so all 3 dice cover the expected mean and are good to go.
For estimating the standard deviation one uses √((n-1)S^2/Q) where Q is the quantile we want from a chi-square distribution with n-1 degrees of freedom (0.975 and 0.025 to achieve 95%). For your data the intervals for the standard deviation are 5.91-6.45, 5.41-5.91, and 5.74-6.27 so if anything the first dice is the "sketchiest" one, with desired value falling juuuuust outside the interval (I wouldn't worry too much tho).
As a final note, if we want a confidence of 99% the sample size needed grows closer to what you did (927) and all the intervals expand a little (making all dice pass both the mean and std deviation test).
This was a really cool video, and I'm interested in your automated die-roller project if you ever do build it. Thanks for doing the math for fair/unfair dice, and then spending 4 hours rolling and recording d20s for our edutainment!
I did have issues with your audio, you started out fine, then would fade out dramatically then come back to an acceptable level.
I do love me a good video about Theoretical Probability vs Experimental Probability. Good video!
Liked and subbed for the amount of dice rolled alone
This is so cool! If you've got a video on float tests, it would be helpful to have a link in the video description. :) (If you don't have a video on float tests, I'd totally watch one if you made it!)
6:07 lol I skipped ahead to see if you actually did testing, I liked and will actually rewatch the whole thing.
Love your dedication 💪
The dedication to this omg
1:18 I have never used a D20 but I am happy to stay a while and listen.
the ending was like a lab conclusion
As was mentioned here in comments already, spindice seems less prone to cheating throws. It's hard to tell how much, but I think it's quite possible to roll dice to get gyroscopic effect to try to keep some part up, or master throw to be more deterministic.
Important thing to consider:
Rolling by Hand or a (too) simple machine will actually influence the die roll esp on unbalanced dies.
Also rolling a die alot of times will change its balance due to grime and oils and stuff from hands and wear and tear.
Thank you for your hard work
Crunch those numbers!! Great video!
Hypothesis before seeing the rest of the video: Theoretically, a spindown should have the same odds/randomness as a standard since they have the same amount of sides and the same shape, so each side should have the same odds. But I feel like with enough practice, it could be really easy to manipulate rolls with a spindown to consistently roll high numbers, whereas the mixed layout of a standard die makes it much more difficult to do the same. The next paragraph will be me after I've seen the video. Hello future me, by the way! You look extra cute today.
Aww, thanks past, pre-video me! You looked cute too! Anyways, the data was super interesting to see the results of, and I'm honestly a little sad that the spreadsheets weren't linked in the description. I would've loved to see if the "unbalanced" (in quotes because of the well-done manufacturing) spindown die had clusters of similar roll results or if the results would have been as evenly spread out as the balanced standard die. Perhaps my hypothesis would be correct? There's just not enough data to tell, but I did enjoy the video and will be sharing your efforts around to more people.
Also, this is my plea for a link to a public form of the spreadsheets for the three sets of rolls 🙏
the algorithm is putting in the work for your hours of dice rolling
great video, analogue linus tech tips
serious time commitment, respect 💯
There is a way to accurately measure this. The perfect theoretical dice is using binomial distribution and we can test it our dice does as well. We should use the Chi2 compliance test to determine whether the dice is actually using the binomial distribution.
Been playing AD&D since 1985. Never heard of this!
I went on Amazon last night to buy some dice. Then the algorithm takes me here today. Now I know more about dice then I ever wanted to.
You can make roll-down dice that have the standard "opposite sides add to 21" layout. I have several of them.
I have this old green d20. Loved it as a player, that thing rolled 20's. Had to retire it as a DM, it could TPK a party.
this is incredibly interesting! my mtg pod only rolls spindowns for heads/tails sorts of rolls because they have equal quantities of odd and even sides. i think that we all were just under the assumption that they are entirely unfair, but its exciting to see the mathematical evidence for that claim!
Very very interesting.
Also of note. Tho the results were slightly different from each other, they are basically overlapped when accounting for sd. That means the results were statistically equal in all cases, so those would all be considered balanced if your 1000 roll test was representative enough. (edited for typos)
Very interesting topic. Thank you for your work. Just one thing, you actually don't need a very large sample size to get valid results in most cases. People often make a big deal about sample size, especially when the results do not match expectations, but it's really not necessary to have census level sample sizes for something with only one variable. 1,000 is a perfectly reasonable sample size for something like this considering there's only one variable, and, by the very nature of how data are obtained for this, it's already as random as it can be.
Not sure how I got here but happy to have found it
Something I feel you should add to your test is how easy is either dice to rig. If I throw the dice a certain way each time can I shift the odds in my favor. I Can get a coin to land on heads more than 50% of the time if I drop it from a certain distance or spin at a certain speed.
When you asked for a pause I did but to to type this and share in my MtG Discord. I want those juicy numbers
When dice are so well made that they send you into an existential crisis of mathematical proportions
I think the initial landing is just as random, but a spindown becomes an advantage if it tips over. I.E A 19 can tip to a 20 or an 18 on a spindown vs a 3 or a 9 on a regular. Basically if its on the high number side of the die, you can (with some shifty rolling techniques) guarantee on a spindown that you will get a high roll.
I appreciate the time you took to make this video
I didn't know a spindown dice was even a thing but in hindsight there is an active item in Binding of Isaac called Spindown Dice in addtion to the D6, D20 etc. cool info!!
I literally did this as a statistics project in college (although I didn't know it was called a spindown die at the time, and just referred to it as non-standard numbering). Got roughly the same conclusion though, even though I only had time for 100 rolls per die. Got an A on that project.
Awesome work!
I didn't know any of this before and I don't really know how I got here. You got me soo good with that one I just had to actually leave the comment as you asked 🤣
I have no idea how i got here and i love it
I think a bigger flaw in this experiment than the small sample and spindown only being slightly unbalances, is that it's starting from a false assumption. This video is actually the first time I've even heard the idea clustering of numbers in spindown could give unbalanced results in a normal roll. The main argument I've always seen is that clustering of numbers on a spindown makes it easier to use a rolling technique that could look fair but increases your likelihood of rolling high.
I have a few d20s that have a different layout than either the normal d20 or spindown. The opposite sides don't add up to 21 (other than 1 and 20, which are on opposite sides); the layout appears to be random (the numbers adjacent to 20 are 7, 14, & 11). I have 3 of them, all with the same layout (they all came from the Heroscape board game).
In some ultra competitive tourney settings they even go so far as to only allow clear dive from a specific trusted brand. If there were bubbles inside affecting the weight you can’t see them in a non transparent die. Then people say you can weight them even more by using a microwave to increase the air bubble or moving it in a different direction. Anyway this is why quality control is a big deal the biggest example I can think of are big money casinos in Las Vegas. Clear dice made but the casino with same in house controlled cards and chips.
My initial thoughts: I heard once that whether or not a die is rolled 'fairly' has more to do with how long you actually roll it around in your hand, whether or not you use a dice tower, etc. than the actual rolling across a surface. My instinct is to say that applies here, and that so long as the die is rolled/randomized enough, like thoroughly shuffling a pack of cards, it shouldn't make a difference whether it's standard or spindown.