What are these strange dice? - Numberphile
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- เผยแพร่เมื่อ 21 พ.ย. 2024
- Featuring Henry Segerman. See part 2 at • What are these strange... ... See brilliant.org/... for Brilliant and 20% off their premium service & 30-day trial (episode sponsor)... More links & stuff in full description below ↓↓↓
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WOO
Are you able to change the view count in the description of the video "why TH-cam views stop at 301" I'm very curious. Thank you.
Can you recommend books on higher math skills but for gifted kids?
This is great
I really like those cursed dice. If the cursed 20-sided die could be unfairly skewed towards low numbers, or perhaps both extreme ends, the unfairness of the odds could be explained through the lore. Could be a cool aspect of a campaign.
I'm a simple man
I see weird dice and Henry Segerman, I click to watch it
With the "spinning top" dice, the levelness of the table plays a part. Also the roughness/smoothness of the surface.
Brady with the statistical linguistics vocabulary, dropping "corpus" on the spot like that. Absolute pro. Next we're gonna talk about Zipfian distributions and some hapax legomena.
I think it's safe to say that the nerd score of this video is off the charts.
I'd still like to see a 40+ sided countdown dice in this style, MTG Commander starts at 40 life points not 20 and there are a few ways to go up from there, but I'd understand that it's kinda hard to do 40 without it being rollable... a 5 point sphericon might be better than 3 but you're the expert Henry
I just use d10's for everything including counters. At 40? A 4 and 0. Go over 100? Add a die. Have four thousand Scute Swarms? 4 dice does it.
1 big dice to handle it would indeed be fun. If dividing by 3 still helps, 42 sides would be great for those 'gain 1 life' lands
Imagining the dystopian future game where MTG has become POTUS for life. MTG, Commander
@@mudmug1 Don't bring that evil even to *concept!* Monstrous.
He is definitely one of my favorite Numberphile guests so far.
Segerman's great, lots of curiosities and interesting stuff on his TH-cam channel.
For anyone wondering, the countdown dice at 7:33 that follows a single line and then abruptly stops, Might actually not just be so that the numbers add up to 21 or a bad design choice.
In older versions of DND they had a condition called 'bloodied' which is half or below of your health points.
It could affect certain monsters' and players abilities.
This could be a small detail that let players know they were bloodied. Perhaps if the die were coloured red on the lower number side that could even be a bigger indicator.
That might explain a weird die we had as a kid: it was an icosahedron, but numbered as a D10 (0-9, twice), and with one side painted red (the other half was white).
I like to collect dice and I've definitely seen some weird shapes before (in fact uncommonly shaped dice are my favourite!) and while I've never seen that d6, I've definitely seen dice shaped like that "spinning top" d20, and as you show it's also the common standard size for d10's and percentage dice. One of my favourite "irregular shapes" is when a d4 is made out of an octahedron, but if you imagine it as a square bipyramid then the top pyramid is a little stretched, while the bottom pyramid is a little squished.
Those warped dice should absolutely be included with Call of Cthulhu. That's brilliant. 😂
Instead of a countdown die, how about a peg in something like a cribbage board? That would be more stable, and would make countdowns of more than 1 a bit easier.
Dice are more portable than boards. You make a fair point otherwise.
@@reillywalker195I bet you could make a board that folds to the size and shape of a deck of cards, which would be larger than dice, but pack better for playing card games than something close to round. Cribbage boards are usually pretty big, but they're also counting 121, so a board that only went up to 20 wouldn't need to be that big.
I bought most of these a little while back. Love em. Favorite is the skew d4, fantastic for marking numbers.
so now i really want to know the "fairness" of the ancient greek knuckle dice
So happy to see Mathartfun featured on your channel! From them I got all my odd dice for my collection. I use the same dice for Dungeon Crawl Classics. Super lovely buying from them.
Unfortunate that the shipping costs to the UK are so high, would be great if a store this side of the pond could bulk buy and resell them here
“C-H-O-E-Z”. My longest word would be, “Echo”.
Same here.
I got curious, so I did some working out - if you have 5 different letters, the number of different strings you can make from using each letter up to once is 326 (or 325 if you don't count the empty string) - 120 five letter strings, 120 four letter strings, 60 three letter strings, 20 two letter strings, 5 individual letters, and 1 empty string.
Totally just ordered a set of 4 60 sided letter dice! Love it!
Z is used more often in Canada and the United States than in other Anglophone nations. I wonder which dialect of English was used to inform the letter distribution of 60-sided letter dice.
Without even checking, I'd guarantee there will be only one Z per die. There can't be any justification for having 1/30ᵗʰ of the faces (or more) with a Z.
1:23 there is an advantage. Since these dice do not have as many symmetries, they will be easier to manipulate. Further, the output can be more drastically influenced by the way the dice is held and the surface on which you are rolling, and since there are less symmetries the outcome will be "fenced" into certain groups based on starting conditions more easily, so repeated rolling by the same person with similar starting conditions may not be as evenly distributed as would be the case for maximally symetrical solids. In other words, under real-world, sub-optimal conditions, they are less fair. It's the same reason that you cannot create a fair 3 sided dice, allthough the more faces the less pronounced the bias will be.
I know it's not strictly an ad for the dice, but I did go and buy a set of the skew dice as a Chrissy present for two of my Call of Cthulhu playing friends :)
Why not treat yourself.
If you've ever played Scattergories, it uses a letter die. It is used to select the letter for each round.
as an avid player of TTRPG's like D&D, We are exposed to all kinds of dice shapes, but some of these are quite unique and new to my brains
Do different dice with unique shapes bring new gaming experience or are they the same at the end because they just generate random numbers?
@@mananself there's a whole culture around dice, they don't change anything in-game but there is definitely a psychological element to dice selection
If dice makers don't know whether to use dice or die, I don't think I'll ever know 😂
I looked it up. The plural is "dice" and the singular can be either "die" or "dice" and it doesn't really matter.
"Dice" is correct when dealing with multiple dice or an unknown number of dice, or when speaking casually or colloquially. "Die" is correct when dealing with what you know to be a single die and addressing an audience containing at least one pedant.
Well, die makers are still human and it may be that this one never really learned it either.
Perhaps he doesn't care about this degree of accuracy in his conversations about dice.
As a pedant myself, I appreciate you standing up for us.
The one that ends in the "s" sound is plural just like most english words.
I would have been more impressed with a 26 sided dice with weighted faces to the letter. RSTLNE having bigger faces than Z for instance
The first twelve letters in frequency order are the nearly pronounceable ETOAINSHRDLU.
I guess the probabilites of a letter is dependant on the other letters. For example if the first letter is a Q, the second letter will often be a U
@@stigcc Yes, if you look at letter pairs (or longer sequences) you'll see additional structure on top of the individual letter frequency. CH and TH will also show up a lot while things like KK are very rare.
What 11 letter word has 6 consecutive consonants and only 2 vowels?
Or modify the inscriptions to weight the object physically to produce an uneven distribution. Then you could have a mold that has the same object shape but with different (for example) letter depths based on the letter occurrence frequency for different languages.
They’re back! Loved the last video! Can’t wait to watch this one
I'm fascinated that he uses "dice" as singular (0:05), but "dies" as plural (0:48).
Based on the thumbnail in their subscription feed, 80% of your viewers instantly assumed this was a new video from one of their D&D-related channels.
Your spot on, my DM had a lot of these and almost gave the same tutorial, but they were a math major 😂 to be fair.
🤓
Wouldn't have been far off the mark
I sent the video to my DM less than 5 mins in 😂
They are doing their funny handshakes with their ‘d&d’ (dungeons and dragons) and DM (dungeon Master) talk.
Ahahaha. That leg stepping on a dies animation! 😂
one of my favourite Scrabble words was available on those letter dice:
ZHO!
The "top" dice, or the one created from two pyramids can be used to make fair dice with 2n number of faces for n=3 or more.
If we want to make a fair die with as many faces as we want, (for n=>3), we can make a long, rod-like prism whose bases are polygons. Each face of the die would then be thin rectangles, their number depending on how many sides the polygon bases have. You don't include the polygons in counting the faces of the die.
If you set one face to be "reroll", you can technically have the odd numbers above 1 as well. Also, 2 is possible if your two halves are conical, but it'd be fairly easy to roll your desired number compared to a coin flip if it's too skewed in either direction.
If you use a rugby ball (prolate spheroid) shape, you can make as many sides you want
@@stigcc That's exactly what the OP was describing...🤦🤦🤦
@@HiddenWindshield Right, had to read it many times before I understood haha. Not exactly the same since the rugby shape prevents it from landing on the two ends
I am an avid D&D player and MTG player, and those spin down dice would be pretty awesome. To Brady, it actually is easy to knock over, but more often than not, all players involved tend to pay a good bit of attention and will generally be able to set it back within a matter of seconds - typically immediately.
Dice are cool!
"what is the point of these dice"
Oh hey! I bought dice from this guy! Love my set but I couldn't get their d9 in the color I want. I still love my goofy dice set. Keep up the good work!
The advantages of countdown dice seem primarily to do with situations where you take 1 damage per turn. If somebody fireballs you for 6, you're pretty much back to looking for the number all over.
To a degree, but 1 thru 6 are small changes, so the result won't be far away.
I've been collecting oddly-shaped or "cursed" dice for several years now, and will certainly add several of these to my connection. In related news, I have two more d20s to show Henry-there's a couple other tricks people have come up with to make fair d20s in very unusual shape
I would be interested to see them!
@@henryseg I'll send some pictures later! Been collecting for a while, so might have a few more novel ones
I like playing different games with these kind of dice and I enjoy rolling them also to see what the numbers add up to, etc
You are not helping my chronic dice addiction... I'm a dice goblin who is ready to be irresponsible with my money for a ttrpg game that doesn't exist
Sorry - but there are worse addictions
@@numberphileboo! this is a real problem man. you don't know anyone with 500 bucks worth of dice? you must not be playing D&D
11:04 - They could have choze what letters he rolled by filming multiple takes, and using the optimum.
I see what you did therewith CHOZE - but we would never fake a dice roll. We have too much integrity! :)
@@numberphileNo time for retakes - Brady needed to get to his tennis match!
@@numberphileWell spoken. You wouldn't want it to be a Parker Roll.
@@numberphileI found ECHO. Still no Z but all the other letters are used
I remember discovering as a kid that that sort of right-isosceles faced triangular bipyramid (which I had easy access to after finding a pleasingly simple fold pattern to make them in an origami book) don't neatly fit together to fill space and it felt like something wrong with the universe, because (A) it felt like they should and (B) it was such a small gap leftover when you tried
Interesting concepts, and great to see Henry Segerman talking about novel dice!
I love the dice videos! I've used the "go first dice" in many a tutoring session for my kids and I'm very interested in getting some dLX alphabet dice - plenty of possibilities there
Henry Segerman is so awesome, always love his videos and videos with him
gives me the same feeling as the most efficient 17 square packing
If you want to maximise a die's "tipping angle", I suggest making it hollow, then filling some of the hole with a relatively heavy "flowing" substance - tiny lead balls, for example.
I was hoping the d20 would lead to a talk about d2n vs d4n double pyramids. See this d20 vs your usual d10
When deciding how many of each letter to put on a die, there's always the Scrabble distribution.
How you would distribute them across something other than a D100 (e.g. a set of 5xD20, 3 copies of the distribution spread across 25xD12 or 5xD60, etc.) is a different matter, though.
With all the words available, I can't believe he choze "HE".
the fact that the first set dont pack perfectly is actually a benefit, because it means they wolnt suffocate when huddled together.
Okay, the foot stepping on the dies had me rolling, no pun intended.
Don't mess with the d20, you monster!
What a fascinating topic. I'm already into the next part.
I see Henry, I click.
This is probably a small nitpick, but I thought it was important to mention that, currently, every U.S. state has a large enough population as to avoid the problem mentioned in this video. The smallest state, Wyoming, would ideally be apportioned ~0.76 seats, which (given the populations of the other states) would get rounded up to 1 in basically any fair apportionment method
I'm glad someone with a lot of 🎲 and is a native speaker doesn't know whether it's die or dice.
Seriously, how can this be this interesting? Probably a topic for a different channel's video.
This was unexpectedly fascinating and enjoyable ! GG Segerman. 👍
Thanks for making and sharing.
Please send these to Persi Diaconis as quickly as possible.
Another way to make a 20-sided dice that is fair is make one with more faces than 20, and just blank some of the faces / i.e. "roll again"
If you handed me that, I'd hand it right back. I have a d20 I can trust after just one roll. And honestly, that should be our design goal for a die. You roll it, you get a result you can trust, and nothing else required.
The problem with this is the case where you have to roll the dice infinity times before you get a value.
in fact i like the distorted d4 more
Oh, Etaon Shrdl[c]u. I was taught Etaoin Shrdlu. It's such an amazing character name, so much so that Etaoin is my island's name in Animal Crossing New Horizons.
7:33 you def made me have to go grab a WotC spin down and double check if the numbers are contiguous XD
I knew they are without checking (except 1 and [symbol] are opposite, so you don't get the closed loop). Assuming they haven't changed the design (aside from the set symbol) since I last got one about a decade ago...
The 4th column from the left in the table shown at 13:40 ought to be right-aligned instead of centered so the digit places line up neatly in the same visual columns and the negative signs stick out in the same visual column. A regrettable lapse in the quality presentation of the channel's videos. I say this while acknowledging the glorious animation of the foot stepping on the pointy dice.
that's clearly a production document, not a visual produced for the video. it's got henry's name right on there so you're gonna have to take it up with him, not the editors. unless you're expecting them to meticulously re-type or photoshop the whole thing, to make it a minuscule bit easier to parse some specific numbers that aren't actually important for viewers to be able to understand the point of the video
You could balance it more by having two letters on some sides. So the least common letters share a side.
Screams in Blender topology.
Could you alter the weight distribution of the 20d very precisely to compensate for an odd shaped die?
"Do we call it die or dice?" - for clarity, "die" is singular and "dice" is plural, and when there's room for either, "dice" is correct. You can also use "dice" as singular but it's less correct to do so.
Also "coze" is the longest word you can make on that roll of the letter dice.
You're welcome.
The bipyramid d20 is the only die so cursed and difficult to read I stopped using it.
I really enjoy all the rest of the skew dice though
Die is the singular, dice is the plural.
14:28 DICE ... QuBE
I’ve taken to just using “dice” as both the singular and plural. A sheep, a dice.. two sheep, three dice..
How about creating dice with the normal distribution? SOme numbers more likely than others, according to the normal distribution curve?
Someone can correct me if I'm wrong, but isn't that what already happens? You can roll the die a bunch of times and graph it. I've never done that, but I have rolled dice hundreds of times and averaged it and that result is pretty solid, at half the faces plus 0.5. Suggests to me that a graph of these rolls would probably come out in a roughly normal distribution.
@@muddro420That is the law of large numbers, yes. The sum of many variables will always be normal, regardless of the distribution of each individual variable
magic the gathering / DND / numberphile crossover... thank you sir!
Great video! Seeing so many cool dice is pretty interesting
That "spinning top" one was pretty dicey
I use a cube dice 1-6 For picking winning Greyhounds !
It works a treat 😁
I love the Congressional connection.
9:27 oh lawd he WALKIN
10:22 The forbidden "Caine" dice, used to generate names such as "XDDCC" or "POMNI".
I remember the dLX video. My comment on that video is gone now, I believe, because I like to clear out my comments (people responding to comments from over 10 years ago can get frustrating), but I have a small point of pride that at the time I was the one who pointed out some of the linguistic issues that hadn't initially been taken into account (but which fortunately didn't turn out to change the accuracy of the distribution anyway, which was a good thing, because the dice were already made).
Essentially, Mayzner's work is outdated and it didn't use a large enough sample size for the purpose of finding true letter frequency (only a few thousand words; the same problem in Lewand's list). Peter Norvig updated this by using a corpus of hundreds of billions of words, which is a much better order to go by (which is a different one than shown in this video, and the dLX video). But even though the _order_ of frequency is different, fitting it to the D60 gives the same distribution in the end. To that point, the dLX matches the _use_ frequency of letters in English (a good monkeys-on-a-typewriter distribution), rather than the root or variant frequency (both being "dictionary" frequencies, the former only counting root forms of words, and the latter including different forms of each word, for example increasing the frequency of S due to plurals).
Those were the only two issues. The first wouldn't change the dice, and the second would change the dice based on how you wanted to use them. These dice would be good for something like sentence anagrams, but another distribution would be ideal for something more like Boggle, where you want to get random single words in isolation.
Y'know, I do love being a linguist sometimes. Especially when it steps into my avocational love of mathematics. I really do love this stuff.
Do I get a prize for spotting the word "dice" at 14:25
Since some of those dice are engraved, does that theoretically change the fairness of the dice, if even slightly, since the numbers take different amounts of volume?
"What is the point?' right to the audience that is math resistant.
The point is IMO to roll them and use them to count ! 😂❤
Although the sides are all the same some of these will clearly not tumble in a way that all the numbers have the same odds of coming up. like the 4 sided one that's too flat. or the 20 sided that close to two cones. its more likely that you will only get odds or even numbers.
The d4 is clumsy, to be sure, but there's nothing inherently unfair about it. It's up to you to make it turn over in the air before it hits the table, but it'll be fine if you do. The d20 is less clumsy, but more in line with a solid d100 in that there is potential for it to roll on and on. But beyond that, I see that as essentially two dice rolls in one. First, the coin flip of which of the two sides it will land on, then the d10 roll of which of those ten faces it will land on. I don't see a fairness issue there. Either one of them could be tested in salt-water for balance, and if they're in balance then there shouldn't be any issues that aren't about user error.
The word DICE appears (backwards) on the dice at 14:26.
It seems clear that it is easier to throw that 20 to a desired result than an icosahedron, in that you can give it flat spin so that it at least lands with your preferred major side facing up. Some of these other shapes seem similar in that regard. I don't understand why you would call them fair, in a die-throwing context.
You can make any die give you the result you want by holding it a millimeter above the table and dropping it flat. Perhaps a better word would be “unbiased”: that over all possible throw positions and velocities, no one outcome is favored over another. Symmetry gives you that.
@@henryseg I do not readily sense a clear distinction between "fair" and "unbiased" but i think symmetric dice, where all angles between faces are equal, are clearly fairer and more unbiased than many of these examples. (Not to say these aren't interesting in their own right.)
I'd have gone for "chez" as in "Chez Paris"
Gonna use these for my next DnD game
This video seems to be like something Matt Parker should be doing 😅
Matt's book was included, as a hat tip.
If the numbers are painted onto the face of the die, then the weight will be slightly different
1:31 😨caltrops!
Would be interesting to instead optimize the character dice geometry to approximate occurrence of each character.
The letter dice are from a game called Scattergories
Any chance we could get the math behind the distribution if you rolled the countdown dice? Really curious how they would vary from fair dice and how you would calculate that!
4:56 You could've done a trapezohedron for the cursed d20. Then it wouldn't even have a clean top face.
i am horrified after that foot animation
You should've just added sides until an ideal distribution would give every letter at least 1 side.
I dont know what the shape is called or how common/uncommon it is, but I have a d20 that is cylindrical in shape with two cones on the the end of the cylinder, and the cylinder itself is made of 20 stretched out triangles. If that makes any sense.
6:16 that is so clever omg
Instead of two 10-sided pyramids glued to each other as a skewed d20, why isn't a dice with two 5-sided pyramids sandwiching two 5-sided rectangular rings possible as a skewed d20?
It might work if the surface area of all the sides is equal, but it's questionable. I'm expecting it would probably favor one of the pyramid sides. Probably if you try to balance test it, there could be a problem there too. It might be possible but it would take a lot of trial and error, I think.
It wouldn’t be isohedral.
@@henryseg I agree it isn't a skewed isohedral, but it would be a skewed d20 I would prefer over the double 10-sided pyramid d20 dice in the skewed Dungeons & Dragons dice set, if it is feasible of course. :)
@@henryseg last night I thought of two alternative skewed dice (because insomnia).
The first is a skewed d10 of two square frustums glued to each other, which is kind of isohedral when skewed.
The second is another skewed d20 alternative of two hexagonal frustums sandwiching a 6-sided rectangular ring. I know it is not pretty and not isohedral, but in case the skewed two 5-sided pyramids sandwiching two 5-sided rectangular rings d20 doesn't work, I would then still prefer the two hexagonal frustums sandwiching a 6-sided rectangular ring over the two 10-sided pyramids glued to each other as a skewed d20.
I just realised I really dislike pyramids for some reason and I do not know why...? o_O