Since Matt gives alot of speeches I'm sure he knows how to hit a certain time after rehearsal, although maybe not to the second. But that's not so important, because that's not the only way. Would you have minded for example if the 1:18 were hit at the end of the sentence instead of right when he said "1:18"? I guess you would have though as well "how did he manage to finish right at that time?". With video you have even more options, like having a second or two at the beginning of the video so you can cut it to the approriate length. He could even drop or duplicate a few frames of the video, if that still wasn't enough. So it was definitely an effort and attention to detail, but not that hard.
+ZipplyZane He also first said 31 at 31 seconds. Whether that was planned or not (i.e. within a 6sec window, depending on the total), we may never know
I've known the 7 trick for the longest (years of playing Parcheesi as a kid). The rest was very interesting. (And also made me feel vindicated for refusing to allow someone to roll their MTG spin down a few years ago for a random number.) Also, thanks for the Patreon shoutout! I'm not sure you could have picked a better video to add my name to. :D
Well, at least Platonic solids won't work: the only Platonic solid with even number of faces around a vertex is octahedron, but the only combinations for a vertex if we want face balance on it are 1+4+6+7 and 2+3+5+8, which is not enough to fill six vertices.
I find it cool that you mentioned how most dice have opposite sides add up to one plus the number of faces. I noticed this a long time ago when I got my first set of DnD die and noticed that property. I always have referred to it as the "n+1 property of dice" myself.
VINDICATION! I had learned about the d(X)+1 = opposing face addition when I became a D&D nerd many years ago, and I loved being able to do little teasers wherein I would roll a random set of dice using 1d4's to 1d30's and then could automatically tell them the opposite face without looking on any of them. SO happy to see a fellow mathematician using this as a topic for video discussion.
As for question #4, why do dice have the property of its opposite faces sum being one higher than the total number of faces is due to want, really the necessity, of appearing to be relatively random when rolled. I use the term "appearing" because a properly rolled dice has a random tendency regardless of number orientation; but in this case, you wont have strange pairings like 19 being opposite 12, with subsequently 9 now opposite 2 (on a standard d20), due to the possibility that this can somehow alter the chance of any particular number group being rolled more or less often. On another note, Magic The Gathering has d20's in which the 20 is by the 19, the 19 is by the 18, etc. in what is known as a "Countdown" die. Despite that you can move from one number to its sequential with only one move, it STILL adds up to 21 when you add the opposite faces. I find it somewhat arbitrary though, in that one hemisphere of the die contains all its high numbers, and the other all its lows; might not make for the best randomized D&D d20.
Actually I was thinking dices would be the active verb for dice i.e dicing an onion, but apparently dice is not dices which breaks even more English conventions than the fact at the noun dice is plural for die. So we get two homophones first die the noun and die the verb (interestingly does include the active of dies). The second being dice the noun, as the plural for die, and dice the verb. Yet for some reason while dies is a word, dices is not... so weird.
New to your channel, July 8 2020. I am not a mathaholic, but I am fascinated with it's properties, and have occasionally watched numberphile and a few other channels. The content is great and now I have a party trick with dice! - Cheers
Man, I just love what you do... Correct me if I'm wrong but this seems to be that kind of thing that anyone would say "Why do you spend time with this?" and the answer would totally be "Because we CAN and it is interesting!". The joy in your face while you go along is fabulous and reminds me of my physics teacher xD. Endearment for knowledge is quite the idea. Keep up the good work.
I have a Dice Labs D20, and I am crazy enough to do 1000 test rolls with it apparently. Turns out it's very imbalanced, the 12-face only turns up 24% of the time! Upon closer inspection, the 9-face is noticably smaller than the other faces, itself turning up only 65% of the time. However, the average of all rolls still ends up being 10.375, a mere 1.2% deviation. So it works! ;)
13:19 I thought about that arrangement during the video but instead of thinking of vertices, I was thinking about the sides being balanced. Because we use dots instead of numbers, a bigger number has more dots and since dots are made by little "valleys", they have less material (at least according to my hypothesis). So if you pair 1 with 6, the side with the number one has a lot more material compared to its opposite, and the same goes for 2 and 5 though the difference is less. Having 1 with 2, 3 with 4 and 5 with 6 keeps the difference at a constant minimum of 1.
John Chessant Genuine question, as you seem far too knowledgeable to make such a typing error, how does 'verticee' relate to 'vertex' and 'vertices'? Google did not lead to much of any help in regards to the terminology so I figured I'd do the seemingly unlikely of things on the Internet and ask.
I imagine dice have that property because if one pair of opposite faces has a lower (or higher, depending on what's convenient) sum total, you could make it roll around the axis perpendicular to those faces so you're guaranteed better than average results.
Just for reference, if anyone's curious, the spin-downs are from New Phyrexia (blue), Mirrodin Besieged (green), and Premium Deck Series: Fire & Lightning (red).
Yes! Got one of your signed dice. Thanks. I will be thinking of you every time the weight of your signature has me throw a 6 (and a little bit less so every time someone else throws one).
I have researched dice a fair bit, and i was ready to hop in the comments to add something that matt missed, but he pretty much nailed it. The only thing you might add, is that there is a different style of dice where your dice is shaped like a bumpy log, and you just roll it like you might roll a tiny bumpy log. These tend to still do opposite faces, but i don't trust them!
Well the funny thing about this video , to me, is that I watched it about a year ago and forgot to 'like' it Today I rewatched it (thinking I hadn't watched this one) and when Matt mentioned that the 'sum of the hidden faces is 31' and showed the top face , I had immediately calculated the whole procedure and the rest of the video became pretty darn pointless (although I can never get tired of Matt's videos) Coming from a guy who couldn't apply the order of operations in simple equations without incurring a cardiac arrest amongst all onlooking math-lovers , I'm very glad to have found Matt's channel and have started enjoying mathematics heaps more~!
weesh ful You mean truncated as opposed to a non-truncated tetrahedron? I could imagine stacking the latter might be somewhat difficult and the definition of face-up in regards to the sum of which may be slightly gray. I'm going to need my morning cup of coffee now, thank you.
i was thinking about a d4 with faces in a square arangement to each other, similar to this die: s-media-cache-ak0.pinimg.com/originals/e6/72/80/e6728091c996d20a8aabc930560efacd.jpg except, instead of distinct edge surfaces, you would curve and taper the 4 sides to a point. You'd have 4 curved sides, but also a solid building surface to stack on top of. by setting 1-4 opposite, 2-3 would be opposite, and a total of 5 would be hidden on each die that isn't the top.
weesh ful Ah. I like the idea but, by definition, that is not a tetrahedron. I didn't watch the whole video but I think it's fair to say any polyhedron does not necessarily fit the bill (; I thought you were talking about a truncated tetrahedron such as this thedicelab.com/d4TruncatedTetWhite.jpg
In 2021, Magic came out with a set that actually involved rolling 20 sided dice. Instead of spindowns for that set, they used normal d20s. With some sleight of hand, you can control whether you roll high or low on a spindown
A word about D6: If you orientate a dice that you look at vertex between 1, 2 and 3, there are 2 ways to number them: clockwise and counterclockwise. If the numbers count clockwise, we call the dice "lefthanded", otherwise "righthanded". Western dice are usually righthanded, eastern dice are usually lefthanded.
From what I understand the original property of the faces matching is because classic d6's are done with pips, so numbers correspond to weight. And having opposite faces pip-balanced means that all 3 axes have the same moment of inertia, making it not tend towards any given axis when spun... Although having it more vertex balanced keeps the center of mass closer to the center, which is also probably desirable.
I am mostly impressed by the 1:18 prediction... did you do that explanation before, timed it and then did it again? For the D6 I often see them "physically balanced" by the amount of material being remvoed for each side being the same, making the 6 dots pretty small and the 1 dot quite giant
The reason you want the opposites to add to a constant is if you are concerned with a vertical spin. That way every angle of vertical spin would have a fair number revolving to the top. Large dice like d30, d60, and d120 tend to be rolled and develop a vertical spin. Of course if you need any number that is not 1, create a vertical spin with the 1 and maximum values on the side.
You got me. I just dropped nearly £100 on Maths Gear. Turns out the hook for this DnD nerd to buy your book was that I could get it alongside loads of weird dice. Cheers!
You can do better for the d20. You just implant weights (or change the shape of the die) in the cube to balance out the imperfections of the distribution of the numbers. You can also do the same trick with the dice even if the don't have opposites adding to the same number, it just takes longer to compute (and even longer if each die has a different numbering scheme).
From previous vides, it's basically an icosahedron, but each face is then split into 3 with a sort of really flat pyramid (now 60 faces) and then each of those faces is split again into two, thus giving 120 faces =]
Because of this video I actually bought a d20 and a d4 from dice labs. Pretty good dice! Love the truncated tetrahedron for the d4. Rolls much better than a normal tetrahedral d4 and you read it off the top.
The reason they have the property of having opposite numbers add to a consistent total is because they want the numbers which are adjacent eachother to be very different so that it is hard to try to intentionally roll a good or bad number
they have that property because a long time ago people used to make six sided dice for gambling that didn't have all the numbers. it was quite simple to replace a number with a different number and it go relatively unnoticed. to prevent this all "regulation" dice had to have opposite sides add up to equal 7. That is easier and faster to verify than it is to hunt down all six values.
Strangely, I have a polyhedral dice set where each die has the opposite faces adding to the same number, except the d8 which has all the numbers around each vertex adding to 18. When I watched the 3 dice trick Numberphile video, I saw that Ben Sparks also has a d8 like mine. The reason that opposite faces on most dice always add to the same number is that sometimes 1 dimension on a die is shorter than the others. Say a die might be 1cm x 1cm x 0.9cm causing a pair of opposite faces (the pair that the shorter axis runs through) to come up more than the others - lets say the pair with 1&6 - then the average for the pair is (1+6)/2=3.5, and the average for the other faces is (2+3+4+5)/4=3.5, so the average stays 3.5.
If anybody is wondering, the spindowns are from Magic the Gathering products. More precicely New Phyrexia prerelease kit, Premium Deck Series: Fire and Lightning, Mirrodin Besieged prerelease kit.
The standard is actually the most mathematically balanced in my opinion. If you start at a side and wrap around counting the four sides it will always equal 14. So if you lay out a dice in the "T" shape the 4 row will equal 14. I just spend 20mins trying to figure out one that would be balanced just to find out the one I came up with was the standard. I do like your videos though cause I love finding random maths in odd places.
For the first several minutes of the video I was thinking something along the lines of, "Well yes, obviously." But of course standupmaths doesn't stop at the simple analysis, but goes for a general analysis that makes things interesting!
~7:30 now explain me the difference to a regular dice. 4, 5, 6 all lie around one corner. 1, 2, 3 do too. ok now i get it. nice explaination +matt and +Emrys Smith
So .. if you turn it around, you could play the trick "Rain-man" style.. - You give 6 dice to your friend. Then tell him, take any number of dice (1-6), cast them, dont rotate them, and stack them properly. - Then you just casually look over all dice pretending that you quickly glance over all sides of the stack, all in less than a second or two. - Then you tell your friend that you were able to quickly calculate all the dots on the outside facing sides (which would be number of dice that were stacked x 14 + whatever value is on the top) The added choice (select 1-6 dice) plus the varying top value will make it maybe harder to quickly de-code your math skills (and will leave the impression that you simply can add up all those values impressively quickly)
I have been trying to get one of these dice. There a chance to get them them on some of your other vids, but I'm always too slow. However, I finally got one. Thanks Matt
So can some argument about random bubble distribution in dice be used to work out which is a bigger deal, bad vertices or bad faces? Or, for that matter, which of the fifteen pairs gives the best compromise?
What gives RUclips!? Thanks for not putting this video in my sub box, jeez, making me wait like that. What a Parker Square effort youtube, you need to up your game.
I feel like the layout that prioritizes vertices over faces would be more perfectly fair because each opposing side would have the closest possible amount of material cut out so the center of gravity will be moved the least.
12:30 - "Always the same arrangement, or the mirror-image"... Fun fact: something like 99% of d6 also have the same chirality. In my life I've only ever seen a handful of dice that are the mirror image of the standard arrangement. Specifically: if you look at the vertex with the 1, 2 and 3... you can rotate it so the 1 is on top, the 2 is below it on the left, and then the 3 is on the right. They're in normal English reading order, going top to bottom, left to right. The net highlighted in the figure at 12:40 is actually the mirror image of this.
Hello, standupmaths I don't know if someone else has noticed, but I couldn't help to notice that the method described in the video doesn't work. When the first stack of 5 dice is shown, it is mentioned that they should add up to 31, however I counted the numbers when the stack of dice was turned side by side, and they add up to 74!. I'd suggest the following formula for simmetric dice: [ n ( [(m-2)(m+1)] / 2 ) ] + T = the sum of visible numbers Where: n = the number of dice, m= the number of faces in one die, and T=the number on the top. Best regards!
Finally I can show my family a "professional" explanation. My family never wanted to believe me that the die we use is the least fairest die I could ever imagine! However they never found out I'm playing with a biased die all the time - I mean _I_ would never do that.... :D
The reason it's done now is mostly just tradition. The tradition got started because, at the time, it made it much more difficult to build loaded dice with the particular loading patterns that were useful for craps.
The moment, when Matt says "You can get the very items used in the video if you're fast", and you know full well they've run out. And you're still disappointed, when you find that inded they're all gone.
I think I remember this correctly (don't have dice to check)... If you are to look at any d6 dice where you see "1", "2", "3" vertices of the dice. The "1", "2", "3" vertice will be in ascending order counter-clockwise... I don't think there are any d6 dice where "1","2","3" vertice is in ascending order clockwise.
When you started with the d20s, I thought about how most of the ones I own are, in fact, spin-downs - and lo and behold, you talk about spin-downs! You know your audience XD
The faces of a D6 always add up to 7 because the numbers are represented using pips. This means that each pair of faces taken together should (in theory) have the same amount of material in them.
The most impressive part about this video is how you got the 1:18 seconds mark right
Li tleydxdy but he said at the beginning that it would be 1:18
Yeah, rehearsal.
Since Matt gives alot of speeches I'm sure he knows how to hit a certain time after rehearsal, although maybe not to the second. But that's not so important, because that's not the only way.
Would you have minded for example if the 1:18 were hit at the end of the sentence instead of right when he said "1:18"? I guess you would have though as well "how did he manage to finish right at that time?".
With video you have even more options, like having a second or two at the beginning of the video so you can cut it to the approriate length. He could even drop or duplicate a few frames of the video, if that still wasn't enough.
So it was definitely an effort and attention to detail, but not that hard.
I would guess that he used a combination of rehearsal, an off-camera timer, and possibly a very subtle post-production time stretch.
+superdau Maybe it wasnt on his first try. Thats why there exists a thing like bloppers :).
The trick that astounds me is knowing how long the explanation will take. Even if you practiced and threw out bad recordings, it's rather impressive.
Or you can have a countdown timer in front of you and pace yourself to make it in time :)
Alex Taradov
Well, yes. But it's impressive he could do that.
+ZipplyZane He also first said 31 at 31 seconds. Whether that was planned or not (i.e. within a 6sec window, depending on the total), we may never know
@@andymcl92 he does a lot of this, like tripping over a root when he says “square root”
"Three and a half..." Best line in the video. You never fail to impress me, Matt!
"5 x 13 is, in this case, 65" I'm very interested to know what 5 x 13 is in other cases
5 x 13 in hex: 5F = 95
Commenting Creatively You have lived up to your name.
71.3
42. It's always 42.
5x13 modulo 64 is 1
How can a video talking about things like that be SO interesting ??! Good job !
+wgolyoko What can I say: maths is interesting.
It's Matt Parker doing maths. Do I really need to add anything ?
maths*
Peter LeRoy Barnes
Classic mistake, thanks.
***** No problem. Grammar [and Spelling] Nazis are always willing to help out, even in the world of maths.
I've known the 7 trick for the longest (years of playing Parcheesi as a kid). The rest was very interesting. (And also made me feel vindicated for refusing to allow someone to roll their MTG spin down a few years ago for a random number.) Also, thanks for the Patreon shoutout! I'm not sure you could have picked a better video to add my name to. :D
+Caitlinm007 Hurray! Glad it was an appropriate video!
props for using Phyrexian spindowns.
"Ash is our air, darkness our flesh."
16:40 Matt looks up "I should have enough of a clearance"... I loved it!
17:11 He makes a Parker Stack
and he's giving away Parker Cubes
Least creative Parker Square comment I've seen.
Bit of a Parker Comment.
"I suspect a few people into tabletop games watch my videos", most reasonable hypothesis I've heard all year.
12:20 there is a mistake... 3rd 'net' across on the top row has got 2 '5's in it. Great video as well by the way!
Yep saw that too. Came in the comments to see if anyone else did
I am constantly amazed how much I enjoy these videos. I think he has truly awoken my inner nerd.
I'm surprised you didn't ask and answer this in the video, but what is the minimum size of die that can achieve both a face and vertex balance?
Well, at least Platonic solids won't work: the only Platonic solid with even number of faces around a vertex is octahedron, but the only combinations for a vertex if we want face balance on it are 1+4+6+7 and 2+3+5+8, which is not enough to fill six vertices.
A coin.
Jerry Nilsson
Hah, that's an interesting solution.
I find it cool that you mentioned how most dice have opposite sides add up to one plus the number of faces. I noticed this a long time ago when I got my first set of DnD die and noticed that property. I always have referred to it as the "n+1 property of dice" myself.
The more videos I watch, the more I realize how much I love math.
I'm not looking for fairest dice. I'm just looking for dice. A lot of them. I just love dice.
Chris Pi leisure suit Larry 7 must've made you jealous.
VINDICATION! I had learned about the d(X)+1 = opposing face addition when I became a D&D nerd many years ago, and I loved being able to do little teasers wherein I would roll a random set of dice using 1d4's to 1d30's and then could automatically tell them the opposite face without looking on any of them. SO happy to see a fellow mathematician using this as a topic for video discussion.
As for question #4, why do dice have the property of its opposite faces sum being one higher than the total number of faces is due to want, really the necessity, of appearing to be relatively random when rolled. I use the term "appearing" because a properly rolled dice has a random tendency regardless of number orientation; but in this case, you wont have strange pairings like 19 being opposite 12, with subsequently 9 now opposite 2 (on a standard d20), due to the possibility that this can somehow alter the chance of any particular number group being rolled more or less often.
On another note, Magic The Gathering has d20's in which the 20 is by the 19, the 19 is by the 18, etc. in what is known as a "Countdown" die. Despite that you can move from one number to its sequential with only one move, it STILL adds up to 21 when you add the opposite faces. I find it somewhat arbitrary though, in that one hemisphere of the die contains all its high numbers, and the other all its lows; might not make for the best randomized D&D d20.
Question #7 was the most burning one in my mind. I'm glad you answered it.
3 and a half stacks sounds like the most difficult to achieve using whole dices
A year late but, is it really dices?? (shouldn't it be just dice? If so, did no grammar nazi come across my comment yet?!)
its probably dice
Die is singular, dice is plural. You're lucky you didn't get ganged by grammar nazis. lol
Actually I was thinking dices would be the active verb for dice i.e dicing an onion, but apparently dice is not dices which breaks even more English conventions than the fact at the noun dice is plural for die. So we get two homophones first die the noun and die the verb (interestingly does include the active of dies). The second being dice the noun, as the plural for die, and dice the verb. Yet for some reason while dies is a word, dices is not... so weird.
It's like base 12
New to your channel, July 8 2020. I am not a mathaholic, but I am fascinated with it's properties, and have occasionally watched numberphile and a few other channels. The content is great and now I have a party trick with dice! - Cheers
Hearing Matt say "vertisee" so much for the singular of "vertices" broke my heart a bit. A true Parker Pronunciation.
I looked at this, blinked, and remembered the word vertex. Now that'll drive me nuts.
"Any non zero whole number of dice" Damn, I wanted to use e^2 dice.
I wanted to use 5.4×sqrt(6)+3×pi×i
Glad I can still use my 3i sided dice!
Man, I just love what you do... Correct me if I'm wrong but this seems to be that kind of thing that anyone would say "Why do you spend time with this?" and the answer would totally be "Because we CAN and it is interesting!". The joy in your face while you go along is fabulous and reminds me of my physics teacher xD. Endearment for knowledge is quite the idea.
Keep up the good work.
2:28 "...a normal DICE?" Bad Matt, bad!
He also said "vertice" as the singular of "vertices" rather than "vertex", which is something I'm not sure I've ever heard anyone say
I have a Dice Labs D20, and I am crazy enough to do 1000 test rolls with it apparently.
Turns out it's very imbalanced, the 12-face only turns up 24% of the time! Upon closer inspection, the 9-face is noticably smaller than the other faces, itself turning up only 65% of the time.
However, the average of all rolls still ends up being 10.375, a mere 1.2% deviation. So it works! ;)
Is it a fluke in the die you have or does it apply to all the dice they make
I'd be interested to see the full distribution if you still have that data. In particular, the 1 and 20, since those mean special things so often.
13:19
I thought about that arrangement during the video but instead of thinking of vertices, I was thinking about the sides being balanced. Because we use dots instead of numbers, a bigger number has more dots and since dots are made by little "valleys", they have less material (at least according to my hypothesis). So if you pair 1 with 6, the side with the number one has a lot more material compared to its opposite, and the same goes for 2 and 5 though the difference is less. Having 1 with 2, 3 with 4 and 5 with 6 keeps the difference at a constant minimum of 1.
9:13 "I'm now checking my D"
-Matt Parker, 20/12/16
The trick was great... when is the ironing board coming back or is it gone forever?
+Domen Bremec It's still around! Sadly too wobbly to balance dice on though
standupmaths If you iron the dice it would be much easier.
So what you are saying is things get a bit Dicier when you are Dealing with friends who play magic the gathering.
Oh dear...
Anonymous Person So about half my school.
Honestly the best trick in this video is that he said it was going to be 1:18 seconds before showing the dice trick.
Verticee? That's a bit of a Parker singularity.
John Chessant Vertex?
Yeah, but Matt said 'verticee' throughout the video. (Otherwise, great video!)
He did say vertex at least once.
Stephan da Silva Ya, he did at 10:58
John Chessant Genuine question, as you seem far too knowledgeable to make such a typing error, how does 'verticee' relate to 'vertex' and 'vertices'? Google did not lead to much of any help in regards to the terminology so I figured I'd do the seemingly unlikely of things on the Internet and ask.
I imagine dice have that property because if one pair of opposite faces has a lower (or higher, depending on what's convenient) sum total, you could make it roll around the axis perpendicular to those faces so you're guaranteed better than average results.
Just for reference, if anyone's curious, the spin-downs are from New Phyrexia (blue), Mirrodin Besieged (green), and Premium Deck Series: Fire & Lightning (red).
Yes! Got one of your signed dice. Thanks. I will be thinking of you every time the weight of your signature has me throw a 6 (and a little bit less so every time someone else throws one).
Matt, the singular of vertices is vertex.
I have researched dice a fair bit, and i was ready to hop in the comments to add something that matt missed, but he pretty much nailed it.
The only thing you might add, is that there is a different style of dice where your dice is shaped like a bumpy log, and you just roll it like you might roll a tiny bumpy log. These tend to still do opposite faces, but i don't trust them!
Well the funny thing about this video , to me, is that I watched it about a year ago and forgot to 'like' it
Today I rewatched it (thinking I hadn't watched this one) and when Matt mentioned that the 'sum of the hidden faces is 31' and showed the top face , I had immediately calculated the whole procedure and the rest of the video became pretty darn pointless (although I can never get tired of Matt's videos)
Coming from a guy who couldn't apply the order of operations in simple equations without incurring a cardiac arrest amongst all onlooking math-lovers ,
I'm very glad to have found Matt's channel and have started enjoying mathematics heaps more~!
I can do this same trick on 4-sided-die.
Impressive!
i could see how you could...unless they are traditional tetrahedron d4s
weesh ful You mean truncated as opposed to a non-truncated tetrahedron? I could imagine stacking the latter might be somewhat difficult and the definition of face-up in regards to the sum of which may be slightly gray. I'm going to need my morning cup of coffee now, thank you.
i was thinking about a d4 with faces in a square arangement to each other, similar to this die:
s-media-cache-ak0.pinimg.com/originals/e6/72/80/e6728091c996d20a8aabc930560efacd.jpg
except, instead of distinct edge surfaces, you would curve and taper the 4 sides to a point.
You'd have 4 curved sides, but also a solid building surface to stack on top of.
by setting 1-4 opposite, 2-3 would be opposite, and a total of 5 would be hidden on each die that isn't the top.
weesh ful Ah. I like the idea but, by definition, that is not a tetrahedron. I didn't watch the whole video but I think it's fair to say any polyhedron does not necessarily fit the bill (; I thought you were talking about a truncated tetrahedron such as this thedicelab.com/d4TruncatedTetWhite.jpg
I wish math classes in school would have been this enjoyable.
In 2021, Magic came out with a set that actually involved rolling 20 sided dice. Instead of spindowns for that set, they used normal d20s. With some sleight of hand, you can control whether you roll high or low on a spindown
A word about D6: If you orientate a dice that you look at vertex between 1, 2 and 3, there are 2 ways to number them: clockwise and counterclockwise.
If the numbers count clockwise, we call the dice "lefthanded", otherwise "righthanded". Western dice are usually righthanded, eastern dice are usually lefthanded.
Love your shirt man. My PB is 13 seconds for 3x3.
From what I understand the original property of the faces matching is because classic d6's are done with pips, so numbers correspond to weight. And having opposite faces pip-balanced means that all 3 axes have the same moment of inertia, making it not tend towards any given axis when spun...
Although having it more vertex balanced keeps the center of mass closer to the center, which is also probably desirable.
Finally these d120 have been released !
You still manage to amuse me in every single video Matt, thanks a lot and merry chistmas *
+NAMEhzj Thanks! Merry christmas to you as well.
Please stack the dodecahedra and icosahedra in the same colour-order... You're excused, just remember it next time :P
+ugabugasuga1 I'm just glad I got them balanced!
Yeah, good job, almost perfect, but the mismatched colours makes it a bit of a Parker Square.
standupmaths Matt, you have a lovely personality! That expression of wonder and pride near the end when you got three balanced was the best
I am mostly impressed by the 1:18 prediction... did you do that explanation before, timed it and then did it again?
For the D6 I often see them "physically balanced" by the amount of material being remvoed for each side being the same, making the 6 dots pretty small and the 1 dot quite giant
i must admit I kinda giggled at 6:04 when he held up the life tracker dice from magic the gathering
The reason you want the opposites to add to a constant is if you are concerned with a vertical spin. That way every angle of vertical spin would have a fair number revolving to the top. Large dice like d30, d60, and d120 tend to be rolled and develop a vertical spin. Of course if you need any number that is not 1, create a vertical spin with the 1 and maximum values on the side.
You got me. I just dropped nearly £100 on Maths Gear. Turns out the hook for this DnD nerd to buy your book was that I could get it alongside loads of weird dice. Cheers!
You can do better for the d20. You just implant weights (or change the shape of the die) in the cube to balance out the imperfections of the distribution of the numbers. You can also do the same trick with the dice even if the don't have opposites adding to the same number, it just takes longer to compute (and even longer if each die has a different numbering scheme).
why not just write the name on the sides of a fair d20, rather than carving out material?
weesh ful That's not the point. The point is if there is a natural bias in the dice it is biased to spread out numbers rather than just high or low.
The only mistake I see is in the description: "I deliberately day dice" ... umm "say" ;-) Happy Tuesday.
+Wordsnwood (Art Mulder) Well spotted! Fixed.
Wow, that ending was quite the Parker... 120-sided solid? Help me I don't know math
According to the Dice lab site, it's a kind of triacontahedron.
From previous vides, it's basically an icosahedron, but each face is then split into 3 with a sort of really flat pyramid (now 60 faces) and then each of those faces is split again into two, thus giving 120 faces =]
Because of this video I actually bought a d20 and a d4 from dice labs. Pretty good dice! Love the truncated tetrahedron for the d4. Rolls much better than a normal tetrahedral d4 and you read it off the top.
16:41 - Wow, Matt started to balance the D120s with lots of ambition.
The reason they have the property of having opposite numbers add to a consistent total is because they want the numbers which are adjacent eachother to be very different so that it is hard to try to intentionally roll a good or bad number
they have that property because a long time ago people used to make six sided dice for gambling that didn't have all the numbers. it was quite simple to replace a number with a different number and it go relatively unnoticed. to prevent this all "regulation" dice had to have opposite sides add up to equal 7. That is easier and faster to verify than it is to hunt down all six values.
Strangely, I have a polyhedral dice set where each die has the opposite faces adding to the same number, except the d8 which has all the numbers around each vertex adding to 18. When I watched the 3 dice trick Numberphile video, I saw that Ben Sparks also has a d8 like mine. The reason that opposite faces on most dice always add to the same number is that sometimes 1 dimension on a die is shorter than the others. Say a die might be 1cm x 1cm x 0.9cm causing a pair of opposite faces (the pair that the shorter axis runs through) to come up more than the others - lets say the pair with 1&6 - then the average for the pair is (1+6)/2=3.5, and the average for the other faces is (2+3+4+5)/4=3.5, so the average stays 3.5.
How fascinating! The dice I never knew I needed.
It must be such an exhausting invigoration, an enlightening burden, to be a close friend of Matt's.
the ending made me giggle, which is good bc today i'm feeling sad. thank you matt!
If anybody is wondering, the spindowns are from Magic the Gathering products. More precicely New Phyrexia prerelease kit, Premium Deck Series: Fire and Lightning, Mirrodin Besieged prerelease kit.
The standard is actually the most mathematically balanced in my opinion. If you start at a side and wrap around counting the four sides it will always equal 14. So if you lay out a dice in the "T" shape the 4 row will equal 14. I just spend 20mins trying to figure out one that would be balanced just to find out the one I came up with was the standard. I do like your videos though cause I love finding random maths in odd places.
A fascinating video! Your channel made me appreciate math a lot, Matt!
I guess it is a parker cube...
"Don't play a game unless your dice have been numerically balanced"
That's probably the best nonsexual advice I've ever heard
Matt, Matt, Matt, a geometry nerd and stickler like you should surely know that the singular of vertices is vertex and not vertice...
10:00 The Bottom sum suddenly switches from 343 to 363, what a real Parker presentation ;)
Great vid, but It would be awesome to see you try to stack D4's.
Question 8: If you had a blank cube to start, what would the numbers on the faces need to be in order to be the most fair dice possible?
Most D20 are not made for count down, so they actually work
Found a little error in the video. There's a die without a 4 and with two 5's in the d6 schemes. It's the middle one of the top row.
For the first several minutes of the video I was thinking something along the lines of, "Well yes, obviously." But of course standupmaths doesn't stop at the simple analysis, but goes for a general analysis that makes things interesting!
That was impressive prediction of how long it would take you to explain the trick!
~7:30
now explain me the difference to a regular dice. 4, 5, 6 all lie around one corner. 1, 2, 3 do too.
ok now i get it. nice explaination +matt and +Emrys Smith
thats a good enough starting point for the world record for most 120 sided dice stacked.
seriously , I hold hundreds of records.
So .. if you turn it around, you could play the trick "Rain-man" style..
- You give 6 dice to your friend. Then tell him, take any number of dice (1-6), cast them, dont rotate them, and stack them properly.
- Then you just casually look over all dice pretending that you quickly glance over all sides of the stack, all in less than a second or two.
- Then you tell your friend that you were able to quickly calculate all the dots on the outside facing sides (which would be number of dice that were stacked x 14 + whatever value is on the top)
The added choice (select 1-6 dice) plus the varying top value will make it maybe harder to quickly de-code your math skills (and will leave the impression that you simply can add up all those values impressively quickly)
I have been trying to get one of these dice. There a chance to get them them on some of your other vids, but I'm always too slow. However, I finally got one. Thanks Matt
So can some argument about random bubble distribution in dice be used to work out which is a bigger deal, bad vertices or bad faces? Or, for that matter, which of the fifteen pairs gives the best compromise?
I had the same thought.
What gives RUclips!? Thanks for not putting this video in my sub box, jeez, making me wait like that. What a Parker Square effort youtube, you need to up your game.
I feel like the layout that prioritizes vertices over faces would be more perfectly fair because each opposing side would have the closest possible amount of material cut out so the center of gravity will be moved the least.
12:30 - "Always the same arrangement, or the mirror-image"... Fun fact: something like 99% of d6 also have the same chirality. In my life I've only ever seen a handful of dice that are the mirror image of the standard arrangement.
Specifically: if you look at the vertex with the 1, 2 and 3... you can rotate it so the 1 is on top, the 2 is below it on the left, and then the 3 is on the right. They're in normal English reading order, going top to bottom, left to right.
The net highlighted in the figure at 12:40 is actually the mirror image of this.
I love my D1 - just keeps on rolling
Hello, standupmaths
I don't know if someone else has noticed, but I couldn't help to notice that the method described in the video doesn't work. When the first stack of 5 dice is shown, it is mentioned that they should add up to 31, however I counted the numbers when the stack of dice was turned side by side, and they add up to 74!. I'd suggest the following formula for simmetric dice:
[ n ( [(m-2)(m+1)] / 2 ) ] + T = the sum of visible numbers
Where: n = the number of dice, m= the number of faces in one die, and T=the number on the top.
Best regards!
so do the one exactly in between, minimizing the problem with both
Happy Winter Solstice Matt
Finally I can show my family a "professional" explanation. My family never wanted to believe me that the die we use is the least fairest die I could ever imagine!
However they never found out I'm playing with a biased die all the time - I mean _I_ would never do that.... :D
As a magic player, I can say that it is possible to rig the outcome of a spin down. The opposite faces makes it much harder and more obvious.
gets even more intricate if you take the weight (or absence of weight) of the numbers. a 1 is going to leave a smaller hole in the material than a 20.
New Phyrexia, Mirrodin Besieged, and Fire and Lightning spindowns from MTG. Is there a guilty pleasure you want to tell us about?
Can someone please teach Matt the singular form of "vertices"? "Verticē" is a real Parker noun. Love you, Matt!
Signed,
A pedant
The singular of vertices is vertex
Just yesterday I was suggested by youtube to watch the video with the 3 indistinguishable dice that resulted in you signing 97 red dice to give away!
The reason it's done now is mostly just tradition. The tradition got started because, at the time, it made it much more difficult to build loaded dice with the particular loading patterns that were useful for craps.
The moment, when Matt says "You can get the very items used in the video if you're fast", and you know full well they've run out. And you're still disappointed, when you find that inded they're all gone.
i love how the spindown was new phyrexia
I think I remember this correctly (don't have dice to check)...
If you are to look at any d6 dice where you see "1", "2", "3" vertices of the dice. The "1", "2", "3" vertice will be in ascending order counter-clockwise... I don't think there are any d6 dice where "1","2","3" vertice is in ascending order clockwise.
When you started with the d20s, I thought about how most of the ones I own are, in fact, spin-downs - and lo and behold, you talk about spin-downs! You know your audience XD
I did this trick with 3 dice for a fifth grade magic show. The principle was absolutely amazed. XD
The faces of a D6 always add up to 7 because the numbers are represented using pips. This means that each pair of faces taken together should (in theory) have the same amount of material in them.