Three Dice Trick - Numberphile
HTML-код
- Опубликовано: 13 окт 2024
- Ben Sparks with another trick - can you guess how it works before he explains it?
More links & stuff in full description below ↓↓↓
This is the second of a trilogy of dice tricks with Ben Sparks... More to come...
Martin Gardner called this trick "Guessing The Total".
More dice videos from Numberphile: bit.ly/Dice_Videos
Ben Sparks: www.bensparks....
More Ben Sparks on Numberphile: bit.ly/Sparks_P...
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumb...
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoun...
And support from Math For America - www.mathforame...
NUMBERPHILE
Website: www.numberphile...
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberph...
Videos by Brady Haran
Patreon: / numberphile
Numberphile T-Shirts and Merch: teespring.com/...
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanb...
Sign up for (occasional) emails: eepurl.com/YdjL9
With special thanks to these patrons:
Ben Delo
Jeff Straathof
Ken Baron
Yana Chernobilsky
Andy B
Michael Dunworth
James Bissonette
Jubal John
Jeremy Buchanan
Steve Crutchfield
Adam Savage
Ben White
Andrei M Burke
RAD Donato
Matthew Schuster
Nat Tyce
Ron Hochsprung
Mitch Harding
Ubiquity Ventures
John Zelinka
Gnare
Tom Marshall
Sakkiko
Michael Tulskikh
Robin
Jordan W Oja
Tracy Parry
Ian George Walker
Arnas
Bernd Sing
Valentin
Alfred Wallace
Charles Southerland
Kristian Joensen
Bodhisattva Debnath
Alex Khein
Kermit Norlund
That Asymptote
Mirik Gogri
7σ 
Наука
![CHILE vs. BRASIL [1-2] | RESUMEN | ELIMINATORIAS SUDAMERICANAS | FECHA 9](http://i.ytimg.com/vi/5ObJt_71AYc/mqdefault.jpg)
All tricks are usually simple, its obfuscating the simplicity that makes it cool. This one is very cool.
Not really, there are some complicated card tricks where the deck ends up shuffled in an unexpected way. See for example Matt Parker's video on a perfect Bridge deal.
You clearly not familiar with trick construction. Self-working and semi-automatic tricks are simple, but at the most, it uses a years of sleight of hand practices and presentational refinement to make it less obvious for a lay person.
@@Vlow52 or you're over thinking their comment a little
Less obfuscated if you use a radix seven numeral system.
Obfuscating.... Hmmmm
Regarding the non-reversible dice (d8), some dice are designed to have subsequent numbers next to each other. These are generally called spindown dice, and are used when the dice is needed to represent some value that needs to be changed often. Having subsequent numbers next to each other makes that easier, and they are still sufficiently random. The main use is a d20 for life totals in Magic the Gathering.
The d8 shown in this video can’t be a spin down dice because consecutive numbers are on opposite faces
In addition, d8 are usually done in a way that oposite pair of faces sum the same values as the pair of faces in the other side of the dice. If you look to any 4 faces view of the dice, this faces are suposed to sum up to 18. Some nice dice tricks can come from this also =P
But it is well balanced in the sense that each set of four numbers that share a vertex sum up to 18
+
There's probably some dice randomness paper somewhere that can explain why the "vertex sum" of 18 is better than any arrangement with the consistent opposing sides sum.
This may be the first time I got the trick before the explanation. And now I'm so happy :)
You and me both! I feel so smart, even though I blank at most of the other videos. lol
same here
??
These types of magic tricks are the ones that, at first, looks very impressive! But when we dig deeper, turns out to be much, much easier than I thought. It's still cool though!
I would say most magic tricks are that way. Unless they involve some really technical sleight of hand, you need only be told where the misdirection was, then it seems easy.
@@bobby_tablez Exactly. That's why a magician never reveals their secret. Otherwise the magic doesn't feel as impressive anymore and people start thinking, "I could have done that!".
@@bobby_tablez yep, i dont know how to do magic, but love to see it, and its always funny how people come up with complicated solutions to do a trick, when is always the simplest thing
I instantly got it because I have played probably 500 games of Parcheesi. Using the top and bottom of the dice when you get doubles is part of the game so I already know about the "always 7".
??
I like that this video is 7 minutes long
magic.
That definitely means it has been edited down from 14 minutes.
Long(er) than expected I'd say, regarding the usual audience.
??
thanks for all the free beer I'm gonna get at the pub now
You could build "difficulty" by setting up the first round so that you know which one was rolled twice, then on the next round you tell your victim that you will sacrifice this knowledge to >koff< make it harder on yourself.
You say that but it would require the person to add at least 5 numbers together correctly, which definitely won't be guaranteed a couple drinks in.
??
The top and bottom of a 6-sided-die always total to 7. There. That's like 95% of dice tricks.
And most of us learn that as children
yeah I was gonna say surely it's not that hard... I figured it out straight away
@@scottllewellyn8221 to be fair, they had the dice addition showing on the screen and in the moment without that visual aid, it would've been harder to figure out
@@cybersoul3371 mate it’s simple arithmetic where the highest number is 6… with or without visual aid, the math was the easy part. but it’s not hard to work out regardless
I knew that but I still did not get it until it was explained.
Its amazing how it comes together all of a sudden. As soon as he said at 2:35 that adding 7 to the sum of the number gives the final number, it all clicked into place for me.
As soon as he said at 0:07 that he had a blindfold, I knew what the trick was going to be.
I can't believe he got the 7 trick, but then couldn't figure it out. Because I had no idea how he was doing it until he told me opposite ends add to 7, but then it became obvious.
But these things on the camera is more pressure!
For me as soon as he brought the bottom of the die into play I was watching for it. Once you know that fact about 7 most of these fall apart if you're going into them with a puzzler's mindset.
@@viliml2763 As soon as I saw the video title I knew what the truck was going to be
Brady's gasp was precious.
Always love new videos from the resident "Maximus the Mathematician". You have to admit he looks like Russell Crowe
Lol I was just thinking that!
false.
Only mathematics and TTRPG players have those dice. Im thinking he is both
CCG and TCG players as well, Dice are important. I have D20s D12s D8s D6s D4s and I have D2s D3s D5s D7s D9s D10s D11s etc as well.
You might wonder how those dice could be fair... but D2s are easy you just have a D6 and the numbers 1,3,5 are 1 and 2,4,6 are 2.
D3s are 1,4 for 1, 2,5 for 2, and 3,6 for 3. D5 now that's an interesting dice, it's a D6 but the 6 is reroll. D7s now we're into complicated Bullcrap, it's a fair D8 with 8 being a reroll, D9s is the same with a D10 dice, sure it's not a fair dice to begin with, but still. D11s are D12s with one side being reroll. However for higher rolls than that, Using Pseudo-random number generators are way better, after all, using dice isn't exactly fair in the first place, it only takes 2 hours of practice to roll a single dice to any digit of choice, consistently.
OR, a simpler explanation, is that he's a WARLOCK
Dungeon Keeper intensifies!!
His patron is Michael Stevens
@@illusionist1872 A suspiciously normal name.
@@jansenart0 Vsauce. I was referring to Vsauce.
This is fantastic! It is the first time I have seen any of your videos. I'm a 66 year old retired school teacher. You are a brilliant teacher - clear, concise and very interesting to listen to. Your manner, style and presentation are so very engaging. This would be fantastic for teachers to use in the classroom with their students - and the students can then go home and enjoy fooling their parents. Thank you so very much for bringing us this video. I just subscribed.
Imagine having this guy as your GM
I think that d8 is a roll down dice used for MtG and RP games for health totals and such. Comes in various configurations. You can also get them as "normal" dice as well.
If they come in a different configuration then the correct one, they are considerate loaded. Every die must keep the 1+n on opposite sides, and growing in a specific direction.
In a d20, 2 must always be near 20 and 18, which must be near 4 and so on.
Probably is for ignorance of the manufacturer, and that comes from cheap dice.
@@IIARROWS spin down dice aren't made for rolling, they are meant to keep track of numbers and in that case you want consecutive numbers next to each other for ease of use
this has nothing to do with ignorance, they are just made for another use case
@@Caribbeanmax OK, when have you ever seen d8 or d12 sold for spin down?
I only saw d100 or d20.
Because they make sense.
Often the manufacturers don't know about this small anti-cheat measure, this is a fact.
Also: that d8 is a very bad spin down, as consecutive numbers are not adjacent. For example, 4 is on the opposte side of 3. And 2 is not near 3 either, and 2 is on the opposite side of 1.
When he's demonstrating in the video that the d8 doesn't have a consistent sum on opposite faces, he does so by showing that 5 is opposite 6, which means it can't be a spindown. (I've never even heard of a spindown d8.) Apparently, d8's are just made this way, with the important sums being the four faces surrounding a vertex, rather than opposite sides.
My favourite is still the card trick I saw on here some time ago. A cool use I found for it was very quickly checking if I have a complete deck as the trick doesn't work without one. This is a fun little trick though, definitely going to use it.
It's the "do you remember what happened in the middle" part that is the actual magic.
oh my god my dad used to do this trick ages ago when i was like 9 at family reunions and i had completely forgotten about it until now
If you're familiar with dice enough to know about the relationship between opposite sides this is one of those times where you can feel all smart and go "I know how he did it!"
I'm familiar enough with dice that I guessed what the trick was going to be before I even started watching the video, just from the thumbnail. I'm surprised that the guy trying to work out how it works takes so long after stating that opposite sides add up to 7-I would have thought it should be immediately obvious if you know that.
If you can do this in pub, that means you need more drinks.
I'm proud to say that I actually figured out the trick before the reveal!
Russell Crowe's tabletop-dice-trick videos are a really good follow-up to Gladiator and Master & Commander. Looking forward to the 2-hour cinematic version of these.
I'm much more impressed by how quickly they can both add the numbers up.
Toujours dans l'originalité et la bonne humeur ! Chaine extraordinaire pour nourrir la curiosité et la soif d'apprendre des plus jeunes et des plus agés 👍
For those who don't speak french, to translate in few word : Amazing content as usual , big up from France !
Signé /from: un modeste prof de math ( a modest math teacher )😘
I do not speak French, but I can read it;) That is a very loose translation:)
Martin Gardner was an absolute treasure! This version is a simplified handling. The original version of this routine involves turning over two dice and re-rolling them. This makes the procedure feel even more random and makes it a touch harder for the audience to deconstruct. Also, with re-rolling two of the dice, your range of possible totals is larger, allowing you to repeat with less of a chance for the same total to occur. Oh, and the original version of this routine was published in a book in France in 1584, so imagine someone was performing this at least a decade before the premiere of Romeo and Juliet!
Thanks for the insight! Which book is this trick from? I saw he has lots of books, but I'd like to learn more like this.
btw:
The dice are typically designed that way so they represent a variable in a table-top game.
Because small change = small rotation.
These variants are often called 'tick-down' dice.
You do get d20 and d8 with the same property.
Although, I'm surprised at the inconsistency with the bag you bought...
Spindown D20s are used for MTG, but they aren't used that widely for tabletop games. (Some games use them, some don't, but most people use D20s designed for rolling anyway, which means opposite faces sum to 21.) They are used as counters much like a doubling cube in backgammon. The D8 here is also for rolling and has a different property: the sum of four faces meeting at any vertex is 18.
There are also D20s that do not have this property, as they are predominantly used in Magic: The Gathering and other like-games for counting health totals (and so go from 20 to 1 in sequence across the faces).
They’re not typically rolled, though, are they?
@@ragnkja not usually, but if they're shaken well they're theoretically just as fair as an opposite-sum-21 die
For M:tG, you can use a spindown d20 to randomise who picks who plays first. I prefer to do "odd or even" for the simulated coin flip rather than "high or low" because all the high numbers are on one hemisphere, with all the low numbers on the other.
I accidentally bought one of these the other day. I was wondering what it was for.
@Numberphile watching your video it occurred to me that you could have them "repeat the stage where you add the bottom of the dice and roll it again" many times, just add +7 for every re-roll.
However at the pub it may become increasingly difficult to count how many re-rolls!
Pausing at 3:46 to say, it’s because you’re eliminating the significance of the original result of the rerolled die by adding the bottom to make 7. So of course the answer is going to be the new result of the rerolled die + the two results of the other dice + 7 = the total sum
Edited for typos
You could turn it up a notch by asking if they would like to repeat the 2nd and 3rd steps (add opposite side and re-roll). You would just keep adding 7 each time. This would give the illusion that they're making choices. However, it may also allow them to figure it out sooner.
1:58 "Good" - ah yes, satisfied magician's face. I know you well.
i love the slow infiltration of D&D into Numberphile ...
Before long we'll have a live play series: Discriminants & Divisors
We cannot play this trick with others, coz you've huge fan base here in India 😊
@@screenoholic especially on Delhi girls lol
i'll be using this one on my students. Great video!
Saw through this pretty quickly. He alsways has you add both sides of a die and knows all other info.
lets goooo, early to the new numberphile video, +7 gang
This is so cool. I can't get over how much I like it.
This is gonna be fun in the next D&D session
Cool trick, I'll try this with my kids and see how long until they figure it out.
I'd say it depends on if they already know that opposite sides of a dice always add up to 7.
I’m planning on blowing some of my nieces and nephews minds tonight
Let me tell you being a kid from this generation….they definitely will
It's quite fun if you think about it, because they can reroll as many dice as often as the want. You just need to know how often something got rerolled and the trick still works.
You're just adding 7*n to the sum, since you take out the 7 every time you reroll
The thing in the top right keeping track of the dice made the trick easier to a lot figure out
the real question is; if we could do it with 'n' number of dices.
the general case would be much more amazing!
Sum of all visible dices + 7*number of rerolls.
As long as the dice used all share the same number of faces, and opposite faces sum in a predictable manner.
I mean you can add up as many dice + opposite sides as you want and reroll. It's just that the more you do it, the more obvious to the other person how the trick works since they'll all add up to 7. And once you know that, the trick is really simple how it works.
In love with every Ben Sparks video because Ben Sparks
I actually understood this one pretty much instantly! Lots of free beer will be had!
Martin Gardener is an absolute legend.
Awesome! Ok, so I was compelled to pause the video and figure out why this works before you revealed the answer. Thanks to you for highlighting this fun Martin Gardner trick! 😊
Great stuff. To really misdirect people, the person doing the trick should, after working out the number, reroll the dice, then pretend to think for a moment, and then call out the number.
Easy if you know that the numbers on opposite faces add up to 7. So you're turning the first value of the dice that you re-roll into a 7 and the result is just the sum of the 3 dice at the end plus 7.
As usual, this channel is amazing.
the sum of the opposite faces of any evenly distributed die is the biggest number on the die +1. I mean it's not hard to pick two random opposite faces and add them up, but this is nice and easy and elegant, it's similar to Gauß's idea with the 1+20, 2+19, 3+18, ...
typically, for any die where the number of sides are even, the sum of opposite sides is d+1, where d = number of sides (excepting that pesky d8). this is generally the case, when the die manufacturer uses the flip-turn method of assigning die faces, that is starting from 1, you flip the die over and turn one face in the left or right direction, until you reach face number d. these are considered "fair" dice, as the distribution of high and low numbers is scattered across all faces, rather than clumped around a common vertex for lows, and opposite for highs
this will hold true on most dice all the way from a d2 (essentially a coin where heads/tails is replaced by 1/2) all the way to mathsgear's d120 (don't recall if they've developed a d240 or not)
The reason why a lot of dice might not have the same sum for every set of opposite sides is that when a die is made for the purpose of random number generation it's more common to make sure that similar numbers are never next to each other. So, for example, 1 will usually be next to the highest or second highest number, while two will be on or near the opposite side. This means that even a talented throw will have much more difficulty landing the die on a certain desired roll.
Alternatively, some players just roll hard enough that it's clear they aren't picking and choosing their results. Still, it's nice not to have to worry about stuff like that.
Who cares about the trick, Ben Sparks plays D&D. I kinda wanna see an all-Numberphile-guest game now.
I respect this guy's dice collection.
The problem with trying this trick on people is way too many people will fail to follow the instructions correctly and end up with the wrong mental number, which will make the prediction seem 'wrong'.
That took me a while to understand. Great trick!
It's amazing when you realize that the first two dice don't even matter
It is so painfull when you see it straight away but the video is still 6 minutes long...
i knew the 7 thing, most people do, but it was still surprising. because you could choose which to reroll. took me a minute to realize the 7 thing was all that mattered
"I'm impressed that you are impressed" best quote ever
I saw it the first time so I don't think it will work reliably if I'd try to do it
I paused the video and solved it successfully. Felt amazing 😂😂
It is surprisingly gratifying that I instantly understood the trick when I saw it, without yet hearing the explanation. It probably doesn't really merit much pride, but perhaps a tiny ego boost is forgivable.
Finally new video out!!
I'm impressed by that he could do the math so quick while talking
This is the first Numberphile video I figured out before the explanation. Yay me!
Yeah I could see it after the first couple of rolls. You pick a dice, add on the 'bottom' of it - so that's 7 - then you re-roll it. So the 3 dice now showing are the two unaltered ones, plus whatever is now showing on the re-rolled dice; and the total in your mind is the two unaltered ones plus 7 plus whatever is now showing on the re-rolled dice. Simple yet cunning!
Even with d6s, they aren't always reliable - I loosely classify the d6s I've encountered into 3 categories: there's the standard d6 (opposite faces sum to 7, and if you hold it with a corner toward you so you can see 1, 2 and 3, they go anti-clockwise around that corner) which is substantially in the majority; there's the mirrored version; and there's the smallest category of "others" where the opposite faces don't (or some pairs don't) sum to 7.
And that's before looking at dice which aren't numbered 1-n.
Only the first two (which I consider to be equivalent) are considered standard.
@@ragnkja Since I'm stuck in three-dimensional, locally-approximately-Euclidean space, I distinguish between the dominant and minority enantiomorphs
I once knew a guy who had a few sets of dice where opposite faces were not determined by the number, but by the weight of material removed to carve that number in as they were trying to make the most balanced die possible. The chaotic numbering made me irrationally upset to look at, I'll take my unbalanced and numerically pleasing dice every time
At that point why not just paint the numbers on or something
Wouldn't be hard to just cut the numbers to depths inverse to area. Or do like Vegas dice, filling the grooves with a similar density material. Clearly, more balanced than the method you describe is possible, so they failed.
@@patu8010 even paint has mass
@@jursamaj I feel like if you carved all the numbers to different depths you'd end up with a really ugly die
@@Bloberis I don't see why, but that was only 1 solution.
the d8s made by a Polish dice producer - Q Workshop - are designed so that they follow the rule of opposite sides
You talked tae my class on Monday, and will be doing it again emmrow
Oooohhh, I am so proud of myself. I think I got it after the second example in the introduction.
You don't know which number was picked, turned around and changed.
However: the sum of 2 opposite sides of a d6 is always 7.
So whatever is the end result of the dice, add 7 and you have the answer.
Am I the only one that immediately recognized that you just add the 7 that is always added to the current total?
I believe some dice have numbers arranged so that the carved out part to display the number impacts the roll minimally. i.e. the carved out numbers aren't creating an unfair die.
You can actually do this with most of the other dice armed with this fact: all the opposite sides add up to the sum of the highest and lowest possible outcomes (on a d10 the 0 would be treated as a 10). The only die that you can't do this trick on is the d4 due to its very shape.
It can't be done with some d8s since apparently their faces aren't always lined up in the right way.
a lot of D20's don't necessarily have this opposite rule either
I knew it had something to do with 7 but didn't get it until you explained it.
When person see the 3 dice its missing the 7 you make with 1 of them in previous steps
Some dodecahedral dice (d20's) are made to be used as counters for games like Magic: The Gathering, so they won't be consistent, like the d8 in the video.
icosahedral* (a dodecahedron has 12 sides)
The d8 in the video isn't a spindown die though, as he shows that 5 and 6 are on opposite sides. That's just how standard d8's are made, apparently. I guess someone decided it's the most fair way to do it, but I have no idea why. 🤷♂️
i was never surprised by it
The only opposite side sun for things such as a d12 or d20 is always the number of faces + 1
I'm proud that I got it before it was explained. Yay!
@Numberphile I've got you.
'coutdown' dice are made so adjacent side are 1 number apart. You can get countdown dice in d8 d12 d20 d30 and d100 basically everything except d6 and d4. they are very common and come in games where the dice are used as counters rather than a RNG, for example magic the gathering or D&D.
At 3:00, I'm like "Ohhhh!! That's one of the coolest trick ever."
A great trick to impress 2nd graders and anyone else who has never seen a 6-sided die.
Pick any 3 numbers. Now add 7 to it and think of that number, but don’t let me know what it is.
Now show me the 3 numbers you picked and I’ll magically tell you the number you’re thinking of.
Think of the year you were born. Now add your age to that number. Now, if you haven’t had your birthday yet, add 1 to that number, if you had your birthday, add 0. Think about the new number without telling me. Now, without me knowing if you’d had a birthday or not, I will magically guess the number you’re thinking of.
Pick any number between 1 and 100. Write that number down. Subtract 100 from that number and think about that number, don’t tell me. Now show me what you wrote down and I’ll magically guess the new number you’re thinking about.
Most polyhedral dice do follow the numbering where the opposite sides are always equal (1-8; 2-7 etc). Spindowns are the exception. So you got a die from a bad batch or cheap manufacturer is all.
The real magic would be in telling the person what the original number on the die they re-rolled was...
In any case yeah, they just add 7 to whatever was there because whatever number is on the bottom is added to the total and whatever on the top would mean that the bottom+top numbers add to 7 then you're just adding 7 to whatever number is presented. Note, I figured this at ~2:00 in. So yeah, fun stuff. (I do regularly use dice and probability so this wasn't super hard to figure, trying to reverse figure the original number rolled would be a interesting feat indeed!)
I guessed the trick at 1: 58. The sim le squat to 7 (sim or toi opposite faces on a dice) + the sum of three dice (the remaining dice)
Happy to have figured it out on the second run :)
This is such a fundamental property of d6 dice that it's incorporated into a lot of board games and tricks. I'm more surprised that anybody is surprised by this these days.
I was confused originally thinking the idea was to tell which dice was rerolled but that is only possible to get 100% right if they are unique in the end, not to tell you the number they arrived at, phew. I suppose that is one way to extend the trick, force reroll until they are unique then you tell them which 1 of the 3 got rerolled.
OMG I FINALLY GOT ONE BEFORE THE EXPLANATION! I've peaked, all is well now.
This is BRILLIANT
Is it possible to do a similar trick with different dice? I think not because you wouldn't know what to add to the final top faces but maybe I just didn't figure it out
You could do it if you flip and reroll all the dice, but you couldn't do it if you don't know what size dice have been rerolled.
I love videos with Ben! Please do more. :D
Heya. It's funny you mentioned the d8. I collect D&D dice and the majority of d8's aren't made with opposites adding up to 9. I have a few that do, but they're very rare. And I've always wondered why that is.
I have one of the odd 8-siders ... the opposite sides are sequential, but the 4 numbers around any point total 18.
This trick is so simple but still a little complicated to throw someone off.
gotta admit u got me on the first one! nice trick
Stopped before it got too far along.
My analysis: The three dice at the end have a sum, and the sum of the re-rolled die before re-rolling and it's inverted value will always be seven, so the end value will always be the sum of the three dice at the end plus seven.
Brilliant, cheers for this :)