Non-transitive Dice

[114Freesoul]

7:23 ONE DIE

[heyandy889]

That is remarkably great shit. I'm imaging situations where I could have friends choose a color . . . though, I think they would catch on pretty quickly that I was screwing with them. Eventually, I fear they would challenge me to a true game of chance, and that's not what we what, is it? I guess it would be time to go, at that point!

[LudicrousPlatypus]

The singular of dice is die... I just thought you ought to know.

[xxSichaye]

Hi there, I was wondering how you designed these dice. Did you do it by trial and error or did you have a method? Thanks :)!

[boumbh]

I love the red die from the Efron dice set. It's like it's been designed for fatalists.

"Ah, you misthrown again! Could you be a bit more careful?"

*rolling*

"Three."

[decom1885]

amazingly smart. wow

[PEZenfuego]

I like a die with four 5s and two 1s, a die with four 3s and two 4s, and a die with two 6s and four 2s. The odds work out differently, but the same rules apply with both sets of one and two dice. I wonder how many different sets of these dice can be made.

[Jonsoncao]

rock paper scissors lizard spock!!!!!!!!!!!!!

[tmaduct5]

THE SINGULAR OF DICE IS DIE!!!

[Kingjay144]

red?? not orange??

[jlspma]

6:29 And here was me thinking that Zac Efron was the one they were named after....=D

[MissTrillianAstra]

Rock Paper Scissors Lizard Spock.

[GetMeThere1]

1) Is there a real world aspect (beyond the games themselves) of investigating and classifying transitive vs non?

2) Single, one direction; pair, opposite direction. What happens with triples, quadruples, etc. ?

[singingbanana]

@GetMeThere1 1. I'm really bad at justifying things using 'real life', but you can think of nature as a non-transtie chain. It is something we want to avoid in elections. There's probably something really convincing I can't think of.

2. Patterns don't hold for triples etc. It's quite a balancing act, and these were carefully designed so a pattern held when you doubled the dice. But it's delicate so there's no particular pattern to what beats what after that.

[ChikoWhat]

Wow adding an extra dice flips the cycle. And you turn that into a game. It's amazing how the numbers really fit together, after alot of designing for a 5dice game let alone a 3 dice game.

Great work

[GoodLegoInventions]

Damn, missed the Like button and pressed Unlike! :(

sorry

[tjv323]

@GoodLegoInventions you can change it

[Horinius]

Very interesting, indeed! :)

Two questions: I understand that you created the last set of 5 dice. But the first set of 3 dice, was it created by you as well?

And how much time did you spend on conceiving the set of 5 dice?

[singingbanana]

@Horinius The set of three dice go way back to the original paper on the subject in the '70s. I spent some time designing the set of 5 to do what I want it to do. That is a tricky balancing act.

[Horinius]

@singingbanana

OK.... This time I've read through your article carefully and I've found a

*little* note written in *little* characters at the end of it 8-)

Gardner, M. "Mathematical Games: The Paradox of the Nontransitive Dice and

the Elusive Principle of Indifference" Sci. Amer. 223 , 110-114, Dec.

1970.

Is this the one you're talking about?

[singingbanana]

@Horinius That's one of the early references that put the idea in the form of a game. The idea that such thing exists goes back a few years earlier.

References: The Paradox of Nontransitive Dice, Richard P. Savage, Jr. The American Mathematical Monthly, Vol. 101, No. 5 (May, 1994), pp. 429-436 and;

S. Trybula, On the paradox of n random variables, Zastos. Mat. 8 (1965), 143-154.

[Horinius]

@singingbanana

Thank you :)

[gzierer]

It may take time, but I make the dice using normal playing cards. Mismag822 has a tutorial on how to do it.

[Chessmaster777]

@ 7:56 hey its a pentagram

[xXextraslastaXx]

I calculated the possibility of victory of the red on the green when the dice are 4 (2 red and 2 green):

Red = 671/1296 ---> 51,77%

Green = 625/1296 > 48,23%

Great game! ;)

[kkriegg]

This is amazing! I'm going to have to make all these sets you showed. One question, though... if you start rolling doubles of dice, you start getting bell curves. Does the probability of one set of dice beating the "lower" set increase with the more dice you use in the set?

[singingbanana]

@kkriegg No it lowers! And with the three set of dice the probabilities reverse order so if A beats B with a greater than 50% probability, two As beat two Bs with a less than 50% probability. I wrote an article with more details linked in the description.

[rg0057]

This video seems to fail at its goal, particularly with the probability calculation.

The exact probabilities are irrelevant. What we are interested in is how to construct non-transitive dice, which you invited us to do, but provided absolutely no clue how to do it. (And is blank zero or wild?) The probability calculation suggests a brute-force trial and error approach, which is a waste of time.

Non-transitive dice should have some properties that can be communicated. What are they?

[singingbanana]

@rg0057 Aren't you a grumpy-drawers. The constructions for 3, 4, and 5 dice sets are on the screen. If you want a general construction for n dice, there's quite a dull one that would work for up to 6 dice, but I don't think that would add anything to the sets I've already shown you.

I do not know of any other general construction of non-transitive dice - which is why I don't mention any, they are not easy to construct, which is why finding the set of dice I describe is interesting.

[AdderSIG]

@rg0057 By using straight algebra and a spreadsheet to calculate all the probably outcomes of each game, you could make a set of x n-sided dice... I think. Not sure how to solve if possible.

[DonAlonzo]

Dice of satan!

[Borat711]

Dice is plural for die.

just saying...

[zserf]

I did some calculations, and with the one dice example, he had a 4/9 chance of winning on any roll, with the 2 dice example he had a 155/324 shot of winning on any roll. He had larger odds than either of the other players, so in the long run he should win.

[zserf]

While interesting, I wonder what rules you actually have to play with to win the 3 person game. It seems like it makes you more likely to win a 1 on 1 game with either of them, but I imagine you're odds of winning against both of them are less than 50%. In fact, it might be possible that if you just give a point to the highest out of any of you, that you aren't even the favorite.

[gregarious24]

This guy looks like a combination of Thom Yorke, Travis Pastrana, and Bill Nye the Science Guy.

[ryazbeck]

So you just draw your die out of a bag and keep it hidden. Don't reveal til you both have your die. Then it becomes rock, paper, scissors.

[IB112]

I can't seem to find any Efron dice online. Where did you get yours?

[singingbanana]

@IB112 A website called Grand Illusions sell them.

[IB112]

@singingbanana thanks man, keep up the cool mathematics.

[Artonox]

that is awesome.

I dont know how to design these games, but surely if you can do a 3 player system, you its probably possible do a 4 player system or an n player system?

[illustriouschin]

This dice game reminds me of the manga Gamling Maverick Kaiji which I feel is pretty clever.

[chupan]

nice video! btw: Spiegel = mirror, Halter = holder, so Spielgelhalter = mirror holder... it's German,...

[depewny]

Please tell me how to buy the Efron dice. Brad Efron is my uncle.

[Everyvideo123]

I saw a lecture by David Spiegelhalter today :)

[djbiggyb]

so this is what bill murray has been up to for the lat decade.

[thenosa87]

I honestly don't know why that professor had to do a probability tree to find the R>Y ratio. Suppose dice R has all 3's, the R>Y chance would be 1/2. Each 3 has a 1/2 chance of winning, when the 3 is changed to a 6, it will have a 1 chance of winning. Thus P (R>Y) = 1/2 + 1/6 * 1/2 = 7/12. Ditto with Y>G, it's symmetric, so I hope he didn't do a tree on that.

[singingbanana]

@thenosa87 He was trying to teach people how probability works. It isn't a competition.

[Corporatist]

@singingbanana haha. Yes, seeing that diagram made the basics of probability finally click!

[Brothington]

I think it was more to demonstrate to the less mathematically minded people out there such as myself to make the knowledge more accessible.

[dahjelle]

Is it significant that, in the case of the original 3 transitive dice, that all 3 dice have sides that add up to 21?

[dahjelle]

Is it signficant that, in the case of the original three dice, that the sides of all three dice add up to 21? This doesn't appear to be the case for the other games presented.

[shikamarusgirl17]

Whoa... This is really cool...

I might make these dice sometime... If I get the chance. ^^

[Saruman1000]

I wish to one day be as smart as you, well done!

[Hr75]

0:27 guy wasnt impressed with your buisness card joke

[CogitoErgoCogitoSum]

The Owl is hoo? Professor of what?

[theboombody]

This is an interesting case of natural properties defying immediate intuition. It's tough to argue that the counterintuitive non-transitivity is false while immediate intuition is true. But lately I've been arguing that Cantor's non-intuitive work may actually not be as correct as it is accepted to be. I made a video titled "Does Counting Exist?" to illustrate this point. It might be a good idea for legitimate mathematicians to correct any errors in the video.

[andyroo24601]

Owl eats dice. Owl wins :)

[shirankao69]

'tis witchcraft I say, look at that pentagram!

[wasteland44]

The green dice vs the red dice is the most interesting when you throw two of each. As the green dice has 5 fours and the red dice has 5 threes so it seems intuitive that green will usually win. However because red will win if green rolls any ones or if red rolls any sixes the actual odds of red winning are 1 - (5/6)^4 = about 52%.

[singingbanana]

@wasteland44 Yup.

[crax83]

I believe I saw this on Scam School a while back. Nice vid anyway. :)

[HConquer]

1. He spelled the singular of dice right!!!

2. It's orange

3. He's a genius

[darkdudironaji]

in...wain lol

[weldmaster80]

but, us geeks dont have TWO friends, its hard enought ot find one that'll play with me

[singingbanana]

@weldmaster80 Hahaha :)

[Gnomeslayer778]

@weldmaster80 I think the greater Feat would be to actually memorize which dice beats which >.<

[singingbanana]

@Gnomeslayer778 I've tried to fix that problem with the Maths Gear version. Using the colours, one chain is ordered alphabetically, the other chain is ordered by word length.

[Gnomeslayer778]

@singingbanana Oh, wouldn't have occurred to me to think of it that way Lol.

[livedandletdie]

@weldmaster80 poor geeks of yesteryear don't have friends while all other nerds do.

It's important with friendship it will make you have something to do when not doing homework and someone else than your chainsmoking mother to entertain you while sick.

[AutosuggestionJD]

Rock, paper, scissors, lizard, Spock!

[crazyguitarist953]

where can i get these dice?

[Tolstoievsky]

da-te batut daca nu stii barbut

[Error081688]

This is fascinating! Also, I miss David Spiegelhalter! I hope he posts some more in the future.

[yalg22]

I always love your posts. I have 3 years left of undergraduate in statistics left. I'm unsure whether I want to be an actuary or go for a PhD. I have the same passion for math that you have..Take care.

[Bloodfox610]

definitely orange dice.

[SkitMan86]

Turn on the Closed Captions.

[Berntisso]

Interesting ...

[MrBoyuki]

You know, it was this sort of thing that inspired me to study Maths at university. It's been a couple of years since I graduated. Maybe it's time to get back in the saddle and apply for that PhD.

[singingbanana]

@MrBoyuki If you want to chat about it let me know :)

[mujijibu]

Very interesting video, very good :)

[1handkamehameha]

definitely trying this. my friends are the brightest bunch haha

[1handkamehameha]

@1handkamehameha arent*

[squaltch]

lol the british way to remember the rainbow is much more valiant than the

"Roy G. Biv" of america.

[singingbanana]

@squaltch Yeah, "Richard of York gave battle in vain" is more poetic! :)

[fabiomist282]

@singingbanana Hahaha Thats is an awesome way! I'm gonna start using that in the US :)

[candideguevara]

@singingbanana

You suggest to play ten games, but I tried this out en ten games seems not enough therefore I now play 20 games which is better. However I wonder how many games I should play to be 95% certain to win?

[wishmastter2]

Interesting :O

[tomnotass1]

yellow is my favourite color too

[TheKrazykool809]

3 dice game???

[Moorich]

so now we have three players lol gotta make those dice so I can beat someone whenever I need to fix my mood

[pirsquared99]

Scratch that. I just noticed the note next to the dotted line.  It appears that this one is closer to 50-50.

[pirsquared99]

Just thought I'd post that I requested this a while ago after seeing the ScamSchool episode about non-transitive dice. Thanks for taking the suggestion in such an awesome way! Could you please explain why there is a dotted line instead of an arrow between the white and the red in the "Two Dice" diagram near the end of the video?

Thanks!

[singingbanana]

@pirsquared99 That's right. I had a few requests for this, especially after the Scam School episode - which is very good, people should check that out too. Yes, as you saw, the dotted line means it's about 50-50, the chances are slim in that case.

[dammilo]

your game is the dice version of rock-paper-scissors-lizard-spo­ck!!! that's awesome

[singingbanana]

@dammilo It is :)

[fulvo]

@dammilo yeah, and it's a version with a twist, so you can always win, if u can choose the rules ( 1 or 2 dices)

Math Rules =)

[Vonsen08]

Brilliant video! (Also, nice waistcoat.)

[anubisxdmj0]

I think I'm going to show this in my math club

may I?

[singingbanana]

@anubisxdmj0 Yes please.

[FHomeBrew]

'Die' is is the word for a single 'die'. 'Dice' is the word for other amounts of 'dice'. (zero and more than one).

Hope you take note of this in future video's :-)

Loved the vid!

[singingbanana]

@FHomeBrew Dice may also be used as the singular. Especially in casual conversation. So ner! :)

[paunchyjoe]

@singingbanana i think home brews right i dont think you can refer to dice as singular.

[knuckaclo]

@paunchyjoe You actually can use Dice as the singular as well. (Depending on where you are in the world is why most people think not, in other places to say Die is not proper)

[FHomeBrew]

@singingbanana Sorry, I'm just a grammar Nazi :p

[Cazicten]

This is incredible.  Do you ever tour the Americas? I'd definitely come see your tour in say Oregon/Washington area.

[Roshkin]

David's acting skills are #WIN

[WhiteDragonTile]

is this the dice I asked you to make?

[singingbanana]

@WhiteDragonTile Yeah, sorry, full credit to WhiteDragonTile who challenged me in the first place (this is an updated version of the dice, these are better).

[WhiteDragonTile]

@singingbanana yes I've noticed, you fixed them so that the last two dice aren't equally matched. :)

[dave597]

this is interesting game theory, where A beats B which beats C, and C beats A, a bit like rock paper scissors in dice form! :)

[singingbanana]

@dave597 That's right, have a look at the full article in the description :)

[Jargonaught]

you know eric personaly!??

[Supreme4321]

orange = red

[singingbanana]

@Supreme4321 That's right, red is just an easier word to say when speaking quickly.

[TheCyber96]

Ouch

[markcallaway4ever]

Nice explaination! I think they hadthis on scam school too.

[draconamous666]

i have never been happy to get a lecture before and you sir are a genuine master of making the most advance stuff seem interesting

[norrisonthespot]

Very interesting. Thank you. It has got me thinking!

[ericsurf6]

This is absolutely mind blowing...I've never seen anything like this..Thanks for sharing this Jim ~ !

[singingbanana]

@ericsurf6 Glad you like it Eric. This should be right up your street. Try it out, they're easy to make or buy.

[leungclj]

invent a game in which it doesn't require you to pick to rules of the game, so u can win every time

[singingbanana]

@leungclj I might have done, but you didn't say please.

[leungclj]

@singingbanana awwww, plzzzzz

[singingbanana]

@leungclj haha, have a look at the article in the description. I mention a game for three players that uses seven dice. But it's a trade, if you try to do it with fewer dice you'll have to add something in elsewhere, like I did with my extra rule.

[supermonkeyballboy]

Cool game! It's the perfect game to play in Study Hall!!

[Mandrake1942]

all my friends will fall asleep before i finish explaining the rules

[singingbanana]

@Mandrake1942 You mean "pick a die". You need to get some better friends.

[snakeddj]

@Mandrake1942 they dont nerd any rules...they just pick you just think and then pick the better one...and win.....what he told to us is something your friends should not know -.- how stupid are you...

[Mandrake1942]

@snakeddj Shut the fuck up troll i didn't watch the whole video the first time you stupid fuck . 

[snakeddj]

@Mandrake1942 it doesnt mater if im a troll ...cause you are a fucking moron ...id much rather say you are the troll ..you are the one who is making stupid instuilting comments on the internet....looks like that is the only thing you enjoy since that comment was so full of passion ....now go get a life or just easier go kill yourself you fucking moron

[Mandrake1942]

@snakeddj why would i kill myself #LOL ? you dumb fuck , and as for the insulting comments on the internet you started that with your first comment where you called me stupid i just like sometimes to reply to retard apes like you 

[snakeddj]

@Mandrake1942 i called you stupid cause you are....read your first comment and you should see...oh i forgot...you are stupid you dont understand that...i feel sorry for you ...so ill just leave you to argue with yourself ...

[ICE1ICE2ICE3ICE4]

amazing!

[incunabulamagialtema]

This is brilliant!

I bet you've thought about many combinations of the numbers.

I'd like to send a message if I figured a new puzzle.

[charleybucketcdp]

if there are three dice, willl it flip again?

[alewisgb]

coolm ni knew how it worked but hey ho

[08firthf]

That's quite cool. However, I usually love games like this where I will always win but this one I think is too much trouble to remember and to get the dice. But as I say, well done, it's all very clever!!!

[KR1Nk]

This is awesome and educating at the same time , be me teacher when school starts again please : D

[TheConstipatedcamel]

I Love You Singingbanana!