+iluvatar003 Getting killed? Nope. Rolling a 1 on D120 twice would be like your DM would say "You tried to swing your sword in a dungeon underground, but your character jumps off of a building head first into concrete and gets stabbed 4 times on the way down.
+TheRancidMarshmallow it's all depends on a system. There's a fair number of those that favor smaller rolls (like GURPS as an example)... so... mb that was a crit hit?
> Hammering a nail in a board "rolling 120 for success in hitting the nail" > Rolls 1 "rolling 120 for crit" > Rolls 1 "You attempt to hit the nail on the head but utilizing your otherworldly clumsiness, you critically fail and manage to let the grip of the hammer slip from your hand, at which point it just so happens to be traveling fast enough to smash open a notorious dictator's window and land on his missile launch button. You end up killing off an entire country, the death count totaling to 300 million."
If i was this guy, in fact i would be very impressive with how much luck i have to do so much rare unluckiness in just a single event. I think i'm an unlucky person, so i feel it precisely.
Anything greater than 1 can still hit if ya got the skill but that damned 1 with my +360 no scope still fails. The list of doom is fun or funny when ya drop you weapon and it shatters like a grenade killing everyone but you in the party. Leaving you weaponless and easily captured for a life of slavery and torture. The remains of your allies, creature snacks. Family back home wondering why you don't write as the end of their world slow creeps upon them.
+true reality Certainly, the laws of nature govern everyone indiscriminately. But that's not what anyone is refuting when they complain that "life isn't fair," so making that argument in response is kind of irrelevant. instead, I think people are generally getting at the problems I described in my initial comment, which is more of an indictment of our society than it is a misunderstanding of the laws of nature.
+KlaxonCow Thank you very much! I wouldn't necessarily disagree with your characterization of reality as "solid lines through 4D spacetime," but I don't think we can call fairness "illusory" just yet. Without the ability to perfectly predict where these solid lines will end up in the future, we can't exhaustively say that they will never end up in a configuration that might be described as "fair." Honestly, if nothing else, the eventual heat death of the universe will remove any possibility of unfairness, so boom! de facto fairness! at least there's that to look forward to.
Rolls 1 on d60. Rolls 1 on d120. ROLLS 1 AGAIN ON d120. The critical fail is so intense, it wraps around the entire multiverse and becomes an epic legendary win. You become an immortal agent of entropy and order; the world is your biscuit.
as long as all the faces are the same, and are all arranged in the same way, those dies are fair... i think so, atleast. maybe there was a balance problem in the die itself ?
@@Anaklusmos42 If there were unbalanced enough to make it roll a 1 twice on purpose It would be unbalanced enough for it to be noticable while it's rolling
+Dan S Or for games, especially roll-playing games, where a larger number of sides may be required. (Because rolling multiple dice and adding them up actually results in a bell curve of results, and rolling a separate die for, say, multiples within the largest possible number, may add unneeded complication)
+HaniiPuppy Oh, I get that. Been playing wargames and TRPGs for over 40 years. Old school way is to use two ten sided, and discard any results higher than the desired range. So if you need random 64, roll two ten sided until a result 64 or less is obtained. Also should add that if the rules are designed around a bell curve (from multiple dice), you NEED the bell curve.
+Canadian Bacon You attempt to cut the orc in half with your axe, and only succeed in making yourself cry. The orc takes pity on you and lets you have another go.
+Rabbit Cube not rigged. Henry's first two rolls of the prototype for me were 1s.... he later sent me some non-1s to show the D120 wasn't faulty and one of them was included at the very end of this video.
+Rabbit Cube It's not scripted he's simply channeling his inner pen and paper rpg player. No point in playing if you don't slip on a wet cobble stone and ram your own sword through your abdomen at the first roll, am I right?
+MrSerrrg88 Yeah he did have a very low probability of getting those ones but I was implying that getting a one is generally considered unlucky and although maths does not have a concept of 'luck', in this analogy he will be 'unlucky'
A cool form of dice is one that has a water bubble inside, so it "points" out the top, makes it way easier to identify what you roll on the huge dices. Also nice, a dice with more dice in it, so you can roll multiple dice with just 1 throw of a big dice (and allways keep them together).
I literally have three dice-within-dice. A d10-within-d10, a d12-within-d12 and a d20-within-d20. They don't roll very well due to the inner dice bouncing around causing weight-based screwery but they're still cool.
I bet you could make like a box thing that you would but on top of the golf ball that has a window on the exact middle, and wherever the window was is the side it landed on.
did you actuly roll the dies like 500 times just to get those 3 1's? or was that actully random luck? i ask becuse statisticaly ods of getting those 3 1's is about 1.15 in 1,000,000
i imagine the prototype d120 isn't machined perfectly and is biased. the more sides the more precise the thing needs to be manufactured. Any flaws will be more easily magnified.
Imagine Twenty One Pilots! Against the Disco you relise that I said 1.15 right? further I said about . so my numer is correct.my number is only .0000000074 less then yours. in probability you try to simplify things and so by rounding .0000001574 as .00000015 to make it easier to read and understand that works. in truth I should have said 1.16 to make it slightly more acurret but I was doing it in my head at the time and must have been off by .000000003.
Because the problem of different number of pips on each side of a die the official Las Vegas casino dice have filled spots and the density of the fill material is exactly the same as the rest of the die.
You climb a small tree to get a better vantage point of the path to the tower that is your destination. You grab out your binoculars. You roll to see what you see, you critically failed your d60 roll. The DM is feeling nice and doesn’t want this to be too much of a trouble, so you simply drop your binoculars. You reach for them to catch them, but you roll a 1 on a d120 and fall off the tree, you try to land safely and roll another 1 on a d120. You have such bad luck, that the binoculars somehow land and break in a way that acts as a spear, impaling you through your back, for you were in such shock that you could not change your position mid-air. You have died falling 10 ft off a tree.
One solution to the alternate version of the D60 would be to make it transparent and have the numbers on the inside, if you get what I mean. Then you can see the number on the face that the die is resting on.
+antiHUMANDesigns Neat idea but, you'd still have to see through two numbers and the edge (with all the reflections and refractions going on) to see the number.
CraftyF0X Yeah, I wonder if it'd work out well or not, in practice. Refractions can likely be avoided by using the right material, and perhaps reflections could also be dealt with. And perhaps there is a way to make text only visible clearly from one side.
Or just roll in on a glass table with a camera underneath. I mean...we all have cameras in our pockets anyways. So all you need is a glass/clear table.
Fair d100s exist as well. I owned one before I fell on it (a lot of practical d-bignumber dice have small pellets inside to slow down the roll faster) and cracked it in half.
I think it would be interesting to see a 6 sided dice made in a what such that rolling it by itself is completely unfair, and it would seem totally useless, untill you realise that rolling 2 of them makes it completely fair. So when you have 2 of them, each number from 2 to 12 has an equal chance.
Unfortunately that's impossible (for 2,3,4,5,6,7,8,9,10,11,12) to have the same probability. There are 11 possible outcomes here, but with 2 dice, you have 6*6=36 combinations. 11 doesn't divide nicely into 36, so it can't work.
awesomepancakes381 simple, if you get a 2, its a 50 percent chance of being a 2, and a 50 percent chance of being a 1. now there are 12 outcomes. getting snake eyes simply needs to have twice the odds of every other outcome.
+martinshoosterman How would you go about implementing a 50% chance of 1 and 50% chance of 2? If you are rolling the same die twice, (or two identical dice), you still need an external device to determine the last 50/50, which breaks the rule of the equal chance being solely from the design of the die.
awesomepancakes381 Thats simple, use orientation. If the die are both facing the same way, then its a 1, if they are facing opposite direction, then its a 2.
This got me thinking... What about actually unfair dice? Like dice where the chance of rolling higher numbers is proportionally lower (still somehow fair)? For example 1-23%, 2-20.5%, 3-18%, 4-15.5%, 5-13%, 6-10%.
The 60 sided skew die DOES work. What you have to do is roll it on a glass table and look at the die from below the table. Whatever number is flat on the table is the number you rolled
I've ordered some of these skewed dice - this is awesome! For other Europeans ordering these - the Dice Lab site does offer to send it to Europe even though it's not in the drop down. And only if you order a single die Maths Gear is the cheaper option, otherwise ordering from Dice Lab is cheaper. (£6.5*D+£3)*1.248=($3*D+$13.95)*0.8764, so D = 1.5.
At around 4:50 when he described the 'less symmetrical' d60 with non-parallel faces did anybody else think of a d4? Because he totally could have just done what you do with a d4... (For those who don't know what a d4 is or how they are used - it's a tetrahedron and you just use the face that landed down or, if you will, the point that landed up).
I imagine a cubed dice is not perfectly fair because the center of gravity is not the center of the cube. Since the 6-side face has 6 holes in it, it has more mass removed compared to the 1-side face. So the center of gravity is shifted very slightly towards the lower number sides. When it hits the table, this slight difference causes the dice to prefer bouncing towards the heavier sides (the lower numbers). Of course, the bias is probably less than, say, the levelness of the table. I wonder if anyone actually has ever done the calculation to determine this ...
Some D6 have the dots "painted" on them, so the mass difference is even smaller, to the point where it's negligible, making these dice *almost* perfectly fair
rolls 1 on a d60 -> your character tries to push open a door but it is a pull door -> you don't notice it so you push and push until your arms break -> from the shock you stumble backwards and fall down the staircase -> your character breaks his neck roll a d20 to see weather you are still alive or are just paralized from the neck down.
bless you for calling it a d6. And if I recall correctly one guy in our D&D group had a 1 die D100, was a ball with a weight in the middle that would rest of center. not sure if it was a d100 but pretty sure "critical fail" aren't we a happy group of nerds together.
+12Rman21 I still have one as well. Yeah, there is another ball inside as a weight to help it settle rather than roll forever; mine rattled as it rolled.
Faladrin the inside ball helps settle it and keep it from rolling forever. The die is rolled as in dropped/tossed like other die. These things are notorious for rolling off tables across rooms bouncing off things because of how light and how small the die surfaces are--the smoother the surface is the easier it rolls. That is why there is a weight inside, Of course if you literally roll it, which isn't what you are trying to do (this is not bowling), yeah the momentum of the inner ball would assist in keeping it rolling. I'm not even sure it is a ball inside. Could be some other shape, i've never broken one open, they aren't that cheap. But yeah, they are usually light plastic with a bearing or something inside, sometimes just more plastic that is more dense. it isn't a huge weight. Yes, we also do not know what the surface texture is inside the die either. might have honeycomb or nodules anything like that.
Faladrin when you toss a die it isn't rolling smooth, the inside ball would be bouncing around inside the die slowing down it's rolling motion. The weight is only added to the die's momentum if the die and inside ball are moving at the same velocity in the same direction. The inner weight and die are not the same weight or density. You can roll them yes, and they will roll, not as well as without the loose weight inside. They are meant to be tossed/dropped. That is how physics supposed to work. You would be correct if the weights weren't loose and moving independently from the die.
I play DnD and am quite familiar with how dice roll. Your description seems to not completely answer the problem though. You pick up a die and toss it down. The inner die will be moving with the outer die (the object as a whole was tossed together). They might not be moving precisely in sync and it may be that some of the momentum of the inner die would negate some of the momentum of the outer die. I doubt however that somehow you would ever toss it so that they cancelled out resulting in a die that hits the table and literally just lands there without any further rolling (and of course your not saying that). So that partially answer the question, and maybe that bit if different in their initial trajectories is all there is the answer. What happens as the inner die bounces around though doesn't seem to matter. It will strike the inner wall of the outer dice and when it does it will rebound in a new direction, but no energy is lost doing this (beyond heat generated from the impact and friction or converted to sound). Any change in direction of the inner die will have an equal and opposite affect on the outer die.
Faladrin They would be acting upon one another and friction from rotational differences (speed/direction). The inner object is skidding around if rotating with the die at all. I figure that is where most of the drag is, the other being the drag created from surface the die is contacting on the outside. But we aren't sure of the surface area inside the die either. Or the surface area of the weight for that matter. Friction/drag is the only thing slowing down die rolls anyways. Any difference in the surfaces that contact one another creates that drag, as with air. I don't think air resistance plays much part in drag on a rolling die though. I am assuming negligible unless there is wind. Air pressure would account for more of the drag than air resistance i'd think. I mean at this point we are speculating completely how the weight and the die are interacting with one another... hypothesizing... spose we could just look, because you know someone else has had to of torn one apart lol.
Interesting, especially for a DM! I got a set of, as they were called, "High Precision dice" back in the day and they serve me well so long as I use my dice tower, but they came with a few extras beyond the usual 4/6/8/10/12/20: a d3, a d5, a d14, and a d24. I was shocked at the d5 especially; it's a triangular prism (oh please memory of high school don't fail me now) . 1 and 5 on the top/bottom triangles, 2/3/4 on the rectangular sides. I couldn't believe it was fair until I started rolling it. Now I feel like getting some novelty dice like these... provided the usual D&D set are all accounted for.
+Cooper Gates I was thinking that with so many faces, (and this being numberphile) that he could design a die where you add all of the numbers that meet at the apex.
Rippertear AKA SDL Benjii TGPASOTSISAPROA(THR)STTLOYTYVMDFTBYTBCTSAASPIYH Let me see. Hmm seems I rolled a 420. Oh never mind that was a joint not a d120.
Those skewed 6-sided dice are amazing! It's almost like watching a rotating 4D object in 3D. Also, with the 60-sided one with minimal symmetry, couldn't you somehow draw the areas with corresponding numbers ignoring the actual faces, over the edges and all? Some extremely weird shape that would be the actual way to decide what did you roll? Maybe I miss something important here though and the question is completely silly... my mind is still a bit skewed right now.
@@Anonymous-df8it Yeah, that would work! You can even choose between top and bottom with such D60 too, the bottom version would come with a small overhead projector.
I was always to understand that the normal 6d was trusted b/c it was balanced not because each side looks the same Also my favorite die has always been the 100 sided
Each side has to look the same or it isnt fair. And what do you mean by "balanced"? Because relative to its center its the least balanced die besides a d4
you can make the skewed d60 have a clear top by, pun-ily enough, having a transparent acrylic outside layer with the results in colored acrylic in the inside layer below. if each material is the same density, it will be fair.
Well, it's not just symmetry, but the right amount of symmetry. Imagine a die that has a big square on one side and a smaller one on the other. In a lot of ways it will be symmetrical, but due to the way it's shaped, one side will be heavier. Heavier die on one side, means it will fall with the lighter side up more often. That makes it unfair.
The d120 looks like a dodecahedron with the midpoints of each edge raised and then points in the center of each pentagon raised such that 10 edges go up to each of those points. You should get this guy together with one of the people who talked about higher dimensional polytopes and figure out what sort of skewed or increased-sided dice can be constructed based off the 4-dimensional d5, d8, d16, d24, d120, and d600. Or what you can do to modify the (n >= 5)-dimensional d(n+1), d(2n), and d(2^n).
Holy cow, I was just asking a few days ago if these kinds of dice existed. I felt that they couldn't exist because with dice with corners of varying angles, they would catch differently in the hand as they are being released.
Ive had a 100 sided die for 20 or so years. Its mechanical though. Its a plastic shell with 100 flattened round spots on it. The numbers are printed inside, and there are ballbearings inside to help it stop rolling.
Numberphile is like a collection of videos put together when all your friends hang out for a bunch of drinks and some smokes and there's that one friemd who's always recording,but in this case it's mathematicians and physicists
I'd say that 'just enough symmetry' may be better, as it could be harder to master skewed rolls on such thing (especially if you just switched from one to the other :P).
You say in the video that this is the minimum symmetry required for a fair die, but I can go one further. Take a pentagonal pyramid, say, with the numbers 1-6 on its faces. If it's very tall, there's roughly a 1/5 probability for each of the five identical faces. If it's very flat, it approaches a 1/2 probability for the base face and 1/10 for the other faces. In-between those extremes, you must be able to get a fair d6 (you have to look at the face which is down, like with a tetrahedral d4) with unlike faces. The precise answer probably requires computer modelling, but you can approximate it by ensuring the solid angle around each vertex is fairly divided between the faces (if you add up how the vertices are divided over the solid). Maybe more sixty symbols than numberphile, but it's a thought.
+Bruno Barton-Singer See "Dungeons, Dragons and Dice" by K. Robin McLean, The Mathematical Gazette, Vol. 74, No. 469 (Oct., 1990), pp. 243-256. On p252 to 253, the author discusses a 2D example that makes it clear that once a die is not symmetric, the probabilities unavoidably depend on how the die is rolled, the surface it is rolled on etc. So the intermediate value theorem doesn't really help you, unless you can control precisely how the die is rolled etc.
![BLACK BAG - Official Trailer [HD] - Only in Theaters March 14](http://i.ytimg.com/vi/Du0Xp8WX_7I/mqdefault.jpg)
*rolls dice once*
"Yeap. That looks fair to me. "
Well he had 2 that were the exact same shape but came up with different numbers. So yeah
says the guy who only ever rolls 1
🤦🏻♂️
you calm it down. I can attest to the fairness of at least the d120s. I am the worlds foremost dice collector and I trust The Dice Lab wholeheartedly
@@JonYodiceI highly doubt that
Presents this to the Sharks as a new invention; a "New Fair Dice".
Keeps rolling 1's in front of the investors.
+White Razor Kevin: "But how can i make any money?"
@@adrianbornabasic7499 get them to roll 7s?
Well, yes, the normal models are perfectly fair, this one just happens to have been cursed on the way out of the factory
@@theonlymrcat638 "I can show you with this other one"
*rolls some more 1s*
"..."
Rolls a D120 twice and gets a 1 both times. Lmao... he's getting killed...
+iluvatar003 Getting killed? Nope. Rolling a 1 on D120 twice would be like your DM would say "You tried to swing your sword in a dungeon underground, but your character jumps off of a building head first into concrete and gets stabbed 4 times on the way down.
+James Revan Unless you're playing Second Edition on an ability check!
+iluvatar003 Shadowrun, critical glich, he be ded.
+iluvatar003 In my group, the gm would just have your attack or whatever hit yourself, then your pants fall down.
+TheRancidMarshmallow it's all depends on a system. There's a fair number of those that favor smaller rolls (like GURPS as an example)... so... mb that was a crit hit?
> Hammering a nail in a board
"rolling 120 for success in hitting the nail"
> Rolls 1
"rolling 120 for crit"
> Rolls 1
"You attempt to hit the nail on the head but utilizing your otherworldly clumsiness, you critically fail and manage to let the grip of the hammer slip from your hand, at which point it just so happens to be traveling fast enough to smash open a notorious dictator's window and land on his missile launch button. You end up killing off an entire country, the death count totaling to 300 million."
Why is this not the top comment?
yeah why is this not the top comment?
If i was this guy, in fact i would be very impressive with how much luck i have to do so much rare unluckiness in just a single event. I think i'm an unlucky person, so i feel it precisely.
Trump kills us all
So I got 300 million kills? That's a lot of XP
I'm pretty sure your player character has been eaten by a Dragon by now.
+Nukestarmaster not even that epic, probably just a goblin or something
+Geoffercake slipped on the way out of the boat and drowned in 3 centimeters of water right on the shore.
Tripped and got a rock lodged in their windpipe
Got killed by his own dice... twice
was killed by a squirrel or rat
Rolling a 2 or 3 on a D60 is a critical fail.
Rolling a 1 is an epic fail.
+I'm Very Angry It's Not Butter (#WTFU) And here I am rolling 1 for critical success.
+FuckYouGooglePlus Well aren't you a sassy little scamp.
3: Critical fail
2: Epic fail
1: Epicly Critical fail
Anything greater than 1 can still hit if ya got the skill but that damned 1 with my +360 no scope still fails. The list of doom is fun or funny when ya drop you weapon and it shatters like a grenade killing everyone but you in the party. Leaving you weaponless and easily captured for a life of slavery and torture. The remains of your allies, creature snacks. Family back home wondering why you don't write as the end of their world slow creeps upon them.
The dice may be fair, but life unfortunately is not.
+Physics Videos by Eugene Khutoryansky Deep stuff man.
(Love your videos btw)
+Physics Videos by Eugene Khutoryansky It is fair in a way. It is at least effectively U(1)×SU(2)×SU(3) fair.
+true reality
Certainly, the laws of nature govern everyone indiscriminately. But that's not what anyone is refuting when they complain that "life isn't fair," so making that argument in response is kind of irrelevant. instead, I think people are generally getting at the problems I described in my initial comment, which is more of an indictment of our society than it is a misunderstanding of the laws of nature.
+KlaxonCow
Thank you very much!
I wouldn't necessarily disagree with your characterization of reality as "solid lines through 4D spacetime," but I don't think we can call fairness "illusory" just yet. Without the ability to perfectly predict where these solid lines will end up in the future, we can't exhaustively say that they will never end up in a configuration that might be described as "fair."
Honestly, if nothing else, the eventual heat death of the universe will remove any possibility of unfairness, so boom! de facto fairness! at least there's that to look forward to.
I just checked out this guy's physics videos, they are amazing :D
Trys to explain why these are fair, only shows footage of them rolling 1's.
good job.
I think this might be best described by the term "successful fail"
1
Well... if you have a die that always comes up as 1... i guess it's fair. If everyone gets 1 all the time, it has to be fair.
I think their definition of "fair" is what is generally considered to be random, not necessarily everyone getting the same roll.
+Cristi Neagu Communism in a nutshell
+Gavin Warner Fair means equiprobable.
+Sage Says
+Sage Says Bernie Sanders in a nutshell.
Rolls 1 on d60.
Rolls 1 on d120.
ROLLS 1 AGAIN ON d120.
The critical fail is so intense, it wraps around the entire multiverse and becomes an epic legendary win. You become an immortal agent of entropy and order; the world is your biscuit.
He then rolls 36
@@AlexzanderWickham "so close, man!"
@@AlexzanderWickham too late tho
A crit fail on a d60 is a curse for life on all future D&D characters
+Sam Spain and a D120?
+Sam Spain That's before you roll 1 with a d120.
I would love to see these interesting dice used more in math classrooms, would make for some fun experiments.
g
+MindYourDecisions Hey! small world
Paul Ngo beat you to it.
"Is there a bigger a bigger die?"
"yes! a D120."
*gets biggest die around. rolls fail twice*
"oh.... ummmmmmmmmmmm...."
I don't think these dies are as fair as you think they are...
as long as all the faces are the same, and are all arranged in the same way, those dies are fair... i think so, atleast. maybe there was a balance problem in the die itself ?
Still triangles though.
@@Anaklusmos42 If there were unbalanced enough to make it roll a 1 twice on purpose
It would be unbalanced enough for it to be noticable while it's rolling
@@thehiddenninja3428 yeah true. I'm not an expert with weighted dice, but I would believe you're right
These dice are designed to cause arguments. Used exclusively if your opponent is better at the game than you.
+Dan S Or for games, especially roll-playing games, where a larger number of sides may be required. (Because rolling multiple dice and adding them up actually results in a bell curve of results, and rolling a separate die for, say, multiples within the largest possible number, may add unneeded complication)
+HaniiPuppy "roll-playing"
slowfreq Hah xd Seems like an appropriate typo.
+HaniiPuppy Oh, I get that. Been playing wargames and TRPGs for over 40 years. Old school way is to use two ten sided, and discard any results higher than the desired range. So if you need random 64, roll two ten sided until a result 64 or less is obtained.
Also should add that if the rules are designed around a bell curve (from multiple dice), you NEED the bell curve.
+HaniiPuppy Agreed. As you probably know, usually the simplest solutions are the best. Less conceptualizing, and more gaming.
This guy must have the worst luck in D&D
+spaceLem It depends on what you're checking.
Attributes (Strength, Intelligence, etc) are checked under your score.
Thaco, a 1 is a critical miss.
+Canadian Bacon You attempt to cut the orc in half with your axe, and only succeed in making yourself cry. The orc takes pity on you and lets you have another go.
+Canadian Bacon He rolled the ones out of the system, so they don't show up when it matters in D&D :)
+0vesty My hobby is casually making the gambler's fallacy and seeing if anyone catches me out.
+Canadian Bacon Shadowrun only uses d6s, and apparently my luck with them is better.
This guy needs to put some skill points into luck, immediately.
Well it would appear you must roll for these aditional skillpoints..... which would appear to be an issue
rolling a one in a D120? my dice aren't getting anywhere near this guy.
Must be touched by Wil Wheaton.
Fun Fact: He became a numberphile after he determined that his very short lived D&D career wasn't going to pan out.
natural 1s on a d20 is a fail, d60 critical fail, d120 everyone in your party dies in a fiery explosion.
It's only fair
Wait! I also get a saving throw! Oh...
His entire universe implodes
He rolled it twice on the 120
Must be hilarious to play D&D with you... xD
With a D6?
He rolls a 1 on a 120 sided dice and the dungeon master dies in real life they just explode into fire or something.
They see me rollin...
Crit failin'...
+tehjamez trying to catch me hittin dirty
+lian armstrong or, Trying to catch me throwin' twenty.
Makis Metaxas they hating
No control in their dice as they be rollin dirty.
"Okay, roll the die and get anything but a 1"
Okay, those last two 1s had to be scripted, but was the first one, on the d60, planned as well?
+Rabbit Cube not rigged. Henry's first two rolls of the prototype for me were 1s.... he later sent me some non-1s to show the D120 wasn't faulty and one of them was included at the very end of this video.
+Numberphile 2 1's ... trhats 1 in 14,400 probability (about 0.007 %)
+Numberphile You can make the die fair as much as you want. But if the rolling is not fair, it's all the same.
+Stritt Faiter Alfa Plusse
It got 1 two times. That doesn't mean it always gets 1.
+Rabbit Cube It's not scripted he's simply channeling his inner pen and paper rpg player. No point in playing if you don't slip on a wet cobble stone and ram your own sword through your abdomen at the first roll, am I right?
Critical 1 on a d60, wow, sir, you should go and play lottery, right now! :D
+MrSerrrg88 he'll just lose the most amount of money you can possibly lose
Tanmay Nandanikar I would say, in mathematics, there is no such thing as critically "unlucky", even in your "unluck" you are critically lucky :)
+MrSerrrg88 Yeah
he did have a very low probability of getting those ones but I was implying that getting a one is generally considered unlucky and although maths does not have a concept of 'luck', in this analogy he will be 'unlucky'
That just makes your analogy ambiguous though, doesn't it?
Also, I did say generally..
But whatever
who cares..
Tanmay Nandanikar either way it was funny to watch :)
"I want to cast a spell!"
"Which spell... Oh! It's you... never mind then, your character catches fire!"
Okay, so don't let this guy make saving throws. :B
Wait, you're falling off a cliff?! Don't worry, I'll save you!
You must now roll to save them.
...
A cool form of dice is one that has a water bubble inside, so it "points" out the top, makes it way easier to identify what you roll on the huge dices.
Also nice, a dice with more dice in it, so you can roll multiple dice with just 1 throw of a big dice (and allways keep them together).
I literally have three dice-within-dice. A d10-within-d10, a d12-within-d12 and a d20-within-d20. They don't roll very well due to the inner dice bouncing around causing weight-based screwery but they're still cool.
You could just label all of the dimples on golf ball and have like a 300-500 sided die.
u could but you wouldn't know what number you rolled.
Why, he said they were labeled. But you might need a vision aid to see them
Yes but how would you be able to tell which one is pointed up?
I bet you could make like a box thing that you would but on top of the golf ball that has a window on the exact middle, and wherever the window was is the side it landed on.
Yeah, you could use microdots, like the espionage tool. And that box idea that the person above suggested.
2 things that the world didn't know they needed. 120 sided "fair" dice and another channel to subscribe to from Brady.
i actually feel as if the oddly shaped d-6 is more fair because it's harder to do a controlled shot with them
did you actuly roll the dies like 500 times just to get those 3 1's? or was that actully random luck?
i ask becuse statisticaly ods of getting those 3 1's is about 1.15 in 1,000,000
+theendofit Yes Brady, answer please!
+theendofit it was not planned - just how the video unfolded.
i imagine the prototype d120 isn't machined perfectly and is biased. the more sides the more precise the thing needs to be manufactured. Any flaws will be more easily magnified.
Actually it's exactly 1 in 864000. That shouldn't be too hard to work out.
Imagine Twenty One Pilots! Against the Disco you relise that I said 1.15 right? further I said about . so my numer is correct.my number is only .0000000074 less then yours. in probability you try to simplify things and so by rounding .0000001574 as .00000015 to make it easier to read and understand that works. in truth I should have said 1.16 to make it slightly more acurret but I was doing it in my head at the time and must have been off by .000000003.
3:40: Thought for a second there was infinity on that die. :-D
+Robin Koch the infinity sided die?
+anion cation AKA "Spehre™".
Wouldn't recommend it, though.
Rolls forever. Hard to read.
+Robin Koch but that crit damage lol
The dents on balanced dice are taken out at different depths, also the paint they put in the holes help rebalance each side.
Those skew dice look like they're from Superliminal.
Because the problem of different number of pips on each side of a die the official Las Vegas casino dice have filled spots and the density of the fill material is exactly the same as the rest of the die.
Brady, remember all those happy hours you spent trying to roll a Yahtzee with D6s?
...
D120 Yahtzee. It's what the subscribers want man.
+AlanKey86 Maybe I'll commission you to do it for me, Alan? Teachers have lots of holidays right?
Rolling 1 on a d60... that is like tying your shoe in a game of D&D, falling over, and breaking your neck.
D6 - _Reroll Your Destiny._
+antenn0 **rerolls into soy milk**
You climb a small tree to get a better vantage point of the path to the tower that is your destination. You grab out your binoculars. You roll to see what you see, you critically failed your d60 roll. The DM is feeling nice and doesn’t want this to be too much of a trouble, so you simply drop your binoculars. You reach for them to catch them, but you roll a 1 on a d120 and fall off the tree, you try to land safely and roll another 1 on a d120. You have such bad luck, that the binoculars somehow land and break in a way that acts as a spear, impaling you through your back, for you were in such shock that you could not change your position mid-air. You have died falling 10 ft off a tree.
One solution to the alternate version of the D60 would be to make it transparent and have the numbers on the inside, if you get what I mean. Then you can see the number on the face that the die is resting on.
+antiHUMANDesigns Neat idea but, you'd still have to see through two numbers and the edge (with all the reflections and refractions going on) to see the number.
CraftyF0X Yeah, I wonder if it'd work out well or not, in practice. Refractions can likely be avoided by using the right material, and perhaps reflections could also be dealt with.
And perhaps there is a way to make text only visible clearly from one side.
Or just roll in on a glass table with a camera underneath. I mean...we all have cameras in our pockets anyways. So all you need is a glass/clear table.
Fair d100s exist as well. I owned one before I fell on it (a lot of practical d-bignumber dice have small pellets inside to slow down the roll faster) and cracked it in half.
I think it would be interesting to see a 6 sided dice made in a what such that rolling it by itself is completely unfair, and it would seem totally useless, untill you realise that rolling 2 of them makes it completely fair. So when you have 2 of them, each number from 2 to 12 has an equal chance.
Unfortunately that's impossible (for 2,3,4,5,6,7,8,9,10,11,12) to have the same probability. There are 11 possible outcomes here, but with 2 dice, you have 6*6=36 combinations.
11 doesn't divide nicely into 36, so it can't work.
awesomepancakes381 simple, if you get a 2, its a 50 percent chance of being a 2, and a 50 percent chance of being a 1. now there are 12 outcomes. getting snake eyes simply needs to have twice the odds of every other outcome.
+martinshoosterman How would you go about implementing a 50% chance of 1 and 50% chance of 2? If you are rolling the same die twice, (or two identical dice), you still need an external device to determine the last 50/50, which breaks the rule of the equal chance being solely from the design of the die.
awesomepancakes381 Thats simple, use orientation. If the die are both facing the same way, then its a 1, if they are facing opposite direction, then its a 2.
+awesomepancakes381 It's not impossible, since the 36 combinations aren't neccessarily equally distributed.
Critical fail with a d60 is actually really impressive
+Ionlymadethistoleavecoments So is a 27 on a d60.
+Kenkojuko MC What.
aeneas6899 .Poteeto Potato The chances of getting any single number on a d60 are the same.
Kenkojuko MC i dont even know what critical fail stands for. Is it d&d related?
+Kenkojuko MC yeah but getting a crit fail is still so unlucky.
Yes! You finally acknowledged the beauty of the deltoidal hexecontahedron. Thank you for that.
GUYS, GUYS! I've found a 1-sided die!
I'll call it...
a sphere!
That's a ∞ sided die
+Jolly Spyder Careful rolling that, Probilator might get you.
What, you don't watch Gravity Falls? Sorry.
A sphere has infinite sides.
Infinite sides, but finite surface area (unless we're using the Banach-Tarski Paradox) and zero edges.
Monohedron!
This got me thinking... What about actually unfair dice? Like dice where the chance of rolling higher numbers is proportionally lower (still somehow fair)? For example 1-23%, 2-20.5%, 3-18%, 4-15.5%, 5-13%, 6-10%.
I guess looking at this from a systems engineering point of view, you'd say that each of the six steady states of the die are equally stable.
The 60 sided skew die DOES work. What you have to do is roll it on a glass table and look at the die from below the table. Whatever number is flat on the table is the number you rolled
So, where's the Kickstarter where I can get these dice?
+Jamas Enright links to get these dice are in the description
I've ordered some of these skewed dice - this is awesome! For other Europeans ordering these - the Dice Lab site does offer to send it to Europe even though it's not in the drop down. And only if you order a single die Maths Gear is the cheaper option, otherwise ordering from Dice Lab is cheaper. (£6.5*D+£3)*1.248=($3*D+$13.95)*0.8764, so D = 1.5.
Why isn't numberphile 2's icon tau?
George M lol
At around 4:50 when he described the 'less symmetrical' d60 with non-parallel faces did anybody else think of a d4? Because he totally could have just done what you do with a d4...
(For those who don't know what a d4 is or how they are used - it's a tetrahedron and you just use the face that landed down or, if you will, the point that landed up).
I imagine a cubed dice is not perfectly fair because the center of gravity is not the center of the cube. Since the 6-side face has 6 holes in it, it has more mass removed compared to the 1-side face. So the center of gravity is shifted very slightly towards the lower number sides. When it hits the table, this slight difference causes the dice to prefer bouncing towards the heavier sides (the lower numbers). Of course, the bias is probably less than, say, the levelness of the table. I wonder if anyone actually has ever done the calculation to determine this ...
Some D6 have the dots "painted" on them, so the mass difference is even smaller, to the point where it's negligible, making these dice *almost* perfectly fair
Casino dice have the pips filled in with opaque resin with the same weight as the resin taken out.
On the pentagonal hexecontahedron, you could just number the vertices rather than the faces, like a traditional d4 is numbered
All we need now is a dr seuss board game to go with them.
rolls 1 on a d60
-> your character tries to push open a door but it is a pull door
-> you don't notice it so you push and push until your arms break
-> from the shock you stumble backwards and fall down the staircase
-> your character breaks his neck
roll a d20 to see weather you are still alive or are just paralized from the neck down.
So where can I buy these?
+Paul Conti links in full description
+Numberphile They're sold out!! D:
+Numberphile What about those numberphile dice exhibited at the end? I loved the handwritten design
Hang on, are these £7 EACH???
This is my Calc 2 teacher this year in college! Great guy!
bless you for calling it a d6. And if I recall correctly one guy in our D&D group had a 1 die D100, was a ball with a weight in the middle that would rest of center. not sure if it was a d100 but pretty sure
"critical fail" aren't we a happy group of nerds together.
+12Rman21 I still have one as well. Yeah, there is another ball inside as a weight to help it settle rather than roll forever; mine rattled as it rolled.
Faladrin the inside ball helps settle it and keep it from rolling forever. The die is rolled as in dropped/tossed like other die. These things are notorious for rolling off tables across rooms bouncing off things because of how light and how small the die surfaces are--the smoother the surface is the easier it rolls. That is why there is a weight inside, Of course if you literally roll it, which isn't what you are trying to do (this is not bowling), yeah the momentum of the inner ball would assist in keeping it rolling. I'm not even sure it is a ball inside. Could be some other shape, i've never broken one open, they aren't that cheap. But yeah, they are usually light plastic with a bearing or something inside, sometimes just more plastic that is more dense. it isn't a huge weight.
Yes, we also do not know what the surface texture is inside the die either. might have honeycomb or nodules anything like that.
Faladrin when you toss a die it isn't rolling smooth, the inside ball would be bouncing around inside the die slowing down it's rolling motion. The weight is only added to the die's momentum if the die and inside ball are moving at the same velocity in the same direction. The inner weight and die are not the same weight or density. You can roll them yes, and they will roll, not as well as without the loose weight inside. They are meant to be tossed/dropped. That is how physics supposed to work. You would be correct if the weights weren't loose and moving independently from the die.
I play DnD and am quite familiar with how dice roll. Your description seems to not completely answer the problem though.
You pick up a die and toss it down. The inner die will be moving with the outer die (the object as a whole was tossed together). They might not be moving precisely in sync and it may be that some of the momentum of the inner die would negate some of the momentum of the outer die. I doubt however that somehow you would ever toss it so that they cancelled out resulting in a die that hits the table and literally just lands there without any further rolling (and of course your not saying that). So that partially answer the question, and maybe that bit if different in their initial trajectories is all there is the answer. What happens as the inner die bounces around though doesn't seem to matter. It will strike the inner wall of the outer dice and when it does it will rebound in a new direction, but no energy is lost doing this (beyond heat generated from the impact and friction or converted to sound). Any change in direction of the inner die will have an equal and opposite affect on the outer die.
Faladrin They would be acting upon one another and friction from rotational differences (speed/direction). The inner object is skidding around if rotating with the die at all. I figure that is where most of the drag is, the other being the drag created from surface the die is contacting on the outside. But we aren't sure of the surface area inside the die either. Or the surface area of the weight for that matter. Friction/drag is the only thing slowing down die rolls anyways. Any difference in the surfaces that contact one another creates that drag, as with air. I don't think air resistance plays much part in drag on a rolling die though. I am assuming negligible unless there is wind. Air pressure would account for more of the drag than air resistance i'd think.
I mean at this point we are speculating completely how the weight and the die are interacting with one another... hypothesizing... spose we could just look, because you know someone else has had to of torn one apart lol.
Interesting, especially for a DM! I got a set of, as they were called, "High Precision dice" back in the day and they serve me well so long as I use my dice tower, but they came with a few extras beyond the usual 4/6/8/10/12/20: a d3, a d5, a d14, and a d24. I was shocked at the d5 especially; it's a triangular prism (oh please memory of high school don't fail me now) . 1 and 5 on the top/bottom triangles, 2/3/4 on the rectangular sides. I couldn't believe it was fair until I started rolling it.
Now I feel like getting some novelty dice like these... provided the usual D&D set are all accounted for.
is there somewhere I could buy any of these squished looking dice?
Description ;)
> Fair dice
> Rolls a 1 three times in a row
i have no idea what this was about, but they should use their skills to find a way to beat the house at craps
I didn't understand the symmetry of the skewed dice. Was it that all the faces have the same shape?
4:43 Read off whichever face has a "point" that doesn't meet with the points of the other two faces.
+Cooper Gates I was thinking that with so many faces, (and this being numberphile) that he could design a die where you add all of the numbers that meet at the apex.
+Reckless Roges To make that yield the numbers from 1 to 61, you might need 0,0,1 and 0,1,1 or 0,0,2 to end up with 1 or 2, could be tricky.
That D120 rolled double 1's in a row. That dice would be the ultimate Dungeons and Dragons dice since you rolled off the 1's so quickly.
For anyone outside the US the dice are not cheap. I might have to find extra investors for my giant game of snakes and ladders involving 2 d120s.
+noodles6669 how high are you?
Rippertear AKA SDL Benjii TGPASOTSISAPROA(THR)STTLOYTYVMDFTBYTBCTSAASPIYH Let me see. Hmm seems I rolled a 420. Oh never mind that was a joint not a d120.
Those skewed 6-sided dice are amazing! It's almost like watching a rotating 4D object in 3D.
Also, with the 60-sided one with minimal symmetry, couldn't you somehow draw the areas with corresponding numbers ignoring the actual faces, over the edges and all? Some extremely weird shape that would be the actual way to decide what did you roll? Maybe I miss something important here though and the question is completely silly... my mind is still a bit skewed right now.
So just like a d4?
@@Anonymous-df8it Yeah, that would work! You can even choose between top and bottom with such D60 too, the bottom version would come with a small overhead projector.
@@Eldorado1239 ???
Video came out 7min ago but I'm already at 7:01
Roman Neill
Joke--->
You
Henry's on Numberphile! So awesome!
I totally want those squished D6. Where did they come from?
Herp, description. Nevermind.
I thought my luck was bad, this guy rolls 1 on a d60 and a 1 twice on a d120
I was always to understand that the normal 6d was trusted b/c it was balanced not because each side looks the same
Also my favorite die has always been the 100 sided
Each side has to look the same or it isnt fair. And what do you mean by "balanced"? Because relative to its center its the least balanced die besides a d4
Rolls one on both 60 and 120 sided dice
_applause_
*rolls once* "So yeah, that looks fair to me."
That's.. not how it works.
+Kotsar Yuriy You're obviously new here. Please allow me to introduce you to... sarcasm.
+Oskar Elek You're obviously sarcastic here. Please allow me to introduce you too...
IcIcyEyes ;)
So awesome to have Henry Segerman on this channel.
I'm afraid I don't understand what the actual problem is that their trying to fix; they didn't actually explain the issue with it being too even.
i seriously love this channel.
So many critical fails... Almost as bad as when I roll dice. I bet if I rolled the d120 ten times, I'd get at least 9 crit fails.
the one time you don't crit fail its a 2
I like the dramatic sound when the 60-sided dice fell into the cup like BOOM IM HERE
You should sell these, I'd buy 10 of each!
you can make the skewed d60 have a clear top by, pun-ily enough, having a transparent acrylic outside layer with the results in colored acrylic in the inside layer below. if each material is the same density, it will be fair.
You didn't explain why symmetry is detrimental to fairness.
It is important for the way the die bounces and rolls.
I understand that but how is it unfair.
Well, it's not just symmetry, but the right amount of symmetry. Imagine a die that has a big square on one side and a smaller one on the other. In a lot of ways it will be symmetrical, but due to the way it's shaped, one side will be heavier. Heavier die on one side, means it will fall with the lighter side up more often. That makes it unfair.
If not symmetrical then some numbers would have a higher chance of being rolled than others.
They say the opposite, most symmetry is what makes a die fair and some symmetry is without effect.
The d120 looks like a dodecahedron with the midpoints of each edge raised and then points in the center of each pentagon raised such that 10 edges go up to each of those points.
You should get this guy together with one of the people who talked about higher dimensional polytopes and figure out what sort of skewed or increased-sided dice can be constructed based off the 4-dimensional d5, d8, d16, d24, d120, and d600. Or what you can do to modify the (n >= 5)-dimensional d(n+1), d(2n), and d(2^n).
Anyone else think the guys head looks like one of those dice ?
I dont know why... But I really want a D120...
Unoriginal joke
Unoriginal reply.
Holy cow, I was just asking a few days ago if these kinds of dice existed. I felt that they couldn't exist because with dice with corners of varying angles, they would catch differently in the hand as they are being released.
HENRYYYYY! I've been following you for yearssss!
You should roll them 10^9 times and watch for the results. This is the only way to be sure enough about their fairness.
Ive had a 100 sided die for 20 or so years. Its mechanical though. Its a plastic shell with 100 flattened round spots on it. The numbers are printed inside, and there are ballbearings inside to help it stop rolling.
Numberphile is like a collection of videos put together when all your friends hang out for a bunch of drinks and some smokes and there's that one friemd who's always recording,but in this case it's mathematicians and physicists
I slapped that like button for that incredible roll of a 1.
My number theory professor from 2008 at UT Austin! He would juggle for us occasionally. If he's on Numberphile he must be doing well! :)
I'd say that 'just enough symmetry' may be better, as it could be harder to master skewed rolls on such thing (especially if you just switched from one to the other :P).
You say in the video that this is the minimum symmetry required for a fair die, but I can go one further. Take a pentagonal pyramid, say, with the numbers 1-6 on its faces. If it's very tall, there's roughly a 1/5 probability for each of the five identical faces. If it's very flat, it approaches a 1/2 probability for the base face and 1/10 for the other faces. In-between those extremes, you must be able to get a fair d6 (you have to look at the face which is down, like with a tetrahedral d4) with unlike faces. The precise answer probably requires computer modelling, but you can approximate it by ensuring the solid angle around each vertex is fairly divided between the faces (if you add up how the vertices are divided over the solid). Maybe more sixty symbols than numberphile, but it's a thought.
+Bruno Barton-Singer See "Dungeons, Dragons and Dice" by K. Robin McLean, The Mathematical Gazette, Vol. 74, No. 469 (Oct., 1990), pp. 243-256. On p252 to 253, the author discusses a 2D example that makes it clear that once a die is not symmetric, the probabilities unavoidably depend on how the die is rolled, the surface it is rolled on etc. So the intermediate value theorem doesn't really help you, unless you can control precisely how the die is rolled etc.
@@henryseg What's the example?
The slow-mo footage looked awesome
The d&d reference made my day
With the 60 sided Isohedron, why not lit the numbers around the point, like on the d4, to get a readable number output?
I love these funky dice so much I'm gonna buy them and add them to my DnD-game through houserules.