# Non-transitive Dice

November 30, 2019

100 Comments

Skip to content
##
Massy Circus Festival

# Non-transitive Dice

#### Add a Comment

Types of Gambling

November 30, 2019

100 Comments

7:45 HOW DID I KNOW IT WAS GOING TO GO AROUND IN A STAR??!!?!?

1:13

I root for the Cambridge Professor of Ornithology.

first game – no ties. Luck? or did you edit out the ties?

Two professors one doc

DO NOT WANT.

7:50

I never thought i'd hear James Grime saying "2Chainz"

Its orange not red..

I understood, but what if i choose first time before my friend?

I finally saw that 50-50 part of the two-dice version for the five-die set lolz

So cool.

How about the sum of three dice? Will the chain broken?

Spiegelhalter looks like he thinks James should do less YouTube and more research, LMAO

I have a question. At 6:04.. how come the "doubled" red dice is better than the "doubled" green? The 3s will likely become 6s but the 4s will become 8s. Of course there is still a chance for them to become 9s and 5s (still smaller than the 6s). But on the first look it seems counter intuitive that red would win.

edit: Okay, I did the math. Because green can only win when it rolls two 4s and red no 6, there is a (5/6)^4 or 625/1296, ca 48,23% chance for green to win.

So what's the practical purpose for all this ?

Watched this video and proceeded to punch my friend in the face. I didn't believe it, but it really did help me beat him.

"a dice"?

02:33 So, it's like Pokemon starters… The second one always gets the better choice.

That diagram looks like a pentagram…

Loved the video. Just one small thing: the singular of 'dice' is 'die', so you pick one die, not 'one dice'.

The singular of dice is die 🙂

The lottery is still played in the UK, even in Cambridge, so I'm wondering how good he is at helping the public understanding of risk 😉

0:45 I don't have two friends :')

What would happen if you played the five-dice game with two dice of two different colours?

Allow me to pick a nit here: the singular form of the word "dice" is "die." Granted, we don't usually use the singular, because dice generally come in pairs, like scissors. But it is worth remembering that there is a grammatical form just

waitingfor the odd occasion when it's appropriate to use it.This looks a bit like rock-paper-scissors-snake-spock

White is not one of the colors of the rainbow.

D&D and WarHammer tabletop players just got their minds blown with this video. I guess.

Also, I'm just wondering… Isn't there a simple calculation that determines the 'force' of the die? Perhaps by adding up the dots? As a layman, my instinct would be to add up the number of dots on the dice to determine how 'powerful' each one is.

WHERE ARE THE DAMN BILL MURRAY COMMENTS?

mmm I did understand the logic in this video, but I had a question…

I was calculating the net winning of rolling each dice:

The red dice: 5*(3/6) + 1*(6/6) = 3.5

Yellow dice: 3*(5/6) + 3* (2/6) = 3.5

Green dice: 5 * (4/6) + 1*(1/6) = 3.5

All of the dice have the same expected gain… how come some dice beat other dice?

So who would win with three players using the first set ?

And I thought Rock-Paper-Scissors-Lizard-Spock was confusing. 🙂

Spielgelhalter gives a funny look at 1:24. I wonder why. Could it be that Grime is calling an orange die red?

Was any other American viewer dumbfounded when he said, "Richard of York Gave bat…."?

Never heard that. I know all about Roy G. Biv though

?!

even if your dice is better than your friend's dices (7/12 chances of winning), to first beat one and next beat the other has (7/12)*(7/12) chances of wining, equals to 49/144 which is 34%

and if the 3 of you throw the dice at the same time, I believe the chances are even smaller. (I'm lazy to do the 3 levels tree)

am I missing something?

So how do you calculate the actual chance when rolling against two players?

Oskar Van Davender did this ages ago and with far more dice xD

This does not quite seem to work out!

4, 4, 4, 4, 4, 9 seems to beat 0, 5, 5, 5, 5, 5 in the two dice version of this game, as if the order on that chain had flipped. But the order of this chain is supposed to remain the same on the two dice version. How am I supposed to beat my 2 very clever friends now, even if they let me choose whether to play with 1 or 2 dice?

More importantly: Is there actually a set of 5 dice that has all the qualities advertised in this video? If so, I would rather buy that!

Die, die, die, die, die!! The singular of dice is die.

Quick question, at 8:18 there was a caption that said that white vs. red was about 50 50. Reds sides were 4,4,4,4,4, and 9, and whites were 5,5,5,5,5, and 0. With those numbers it seems that red only has a 2/6 or 1/3 chance of winning. I may just be missing something, but it looks that way.

What happens when you throw all three die? Which will win in the long run?

thanks very much, and for explaining it

if you don't have dice you can use a deck of cards and choose between AK, J10, 22

Beating your friends is not okay. #noviolence

At 0:32 the little text that pops up should be "Take that, Dog on a Skateboard!"

When I read it, I thought you were suggesting I take a dog on a trip with me using a skateboard for locomotion.

Percy Weasley

That five dice double chain diagram looks really familiar… Hmm.. Yellow cuts blue. Blue covers red. Red crushes green. Green poisons white. White smashes yellow. Yellow decapitates green. Green eats blue. Blue disproves white. White vaporizes red. And as it always has, red crushes yellow.

In a 1v2 game it should be still more expected that you win one player but lose to the other, because the die advantage probabilities are so close to 50%. If the whole set winning probabilty doesn't exceed 70,7% for you, then it is likely that you will lose to at least one of the players since the probability of winning them both drops below 50%.

David Spiegelhalter looks like Bill Murray's doppelganger in some shots.

Using the plural as the singular is ear scraping.

Damn it, I thought he was gonna say Bill Murray.

but how did you come up with these dice??? how long did this take you?

Umm, Dr. Grime? Mr. Spielgelhalter? That "red" dice is orange…

As a former grammar Nazi, it bugs me when people say "a dice" (the singular is "die").

Good

Ser Davos, is that you?

Spiegelhalter? Doesn't that mean mirror holder in German? lol

I shouldn't play this with my sisters… it would piss them off pretty bad…

But very cool! Thanks for the video, Dr. James!

These dice have intrigued me for a few years now. I need to either make or order a set. These would be fun as just to have around.

did any one else see a pentagram of crosses at 7:40

Has anyone tried picking two different dice?

Blank sides on the dice seems like a cheat to me. Zeros are for funky RPG dice only.

The five dive is a devil's trap

that's orange dice, not red!

Now Spiegelhalter sounds like a funny profession. I'm a professional Spiegelhalter myself. (Spiegel -> german for mirror, Halter -> german for holder/thing that can hold stuff)

So cool that you have Bill Murray in your video

I'm actually trying to get a paper published on this subject! not that you'll read this.

If you pick yellow, you can't beat both white and blue because they only interact on the second loop and yellow is in the middle of the path.

What started out as a board game with James quickly escalated to a scene from Scanners.

it took me 2 datys to understand..

I saw a diagram of the Chinese elements for the first time and this video INSTANTLY popped to mind. The resemblance is uncanny.

Why dice instead of die in the singular? Some other math guy on you tube does the same, admittedly stubbornly. I always thought he did this on purpose because he learned of "die" at an late age and refused to change. But hes a brit too. hmmm. Is it proper British English to use dice ib the singular? In American it is bad grammar. Die is proper. Is die actual wrong is British? Are they equally valid? like dreamed and dreamt?

Rock paper scissors lizard spock

is this pokemon?

7:08 "Richard Of York Gave Battle In …Wayne"

So James' new game is like a dice version of Rock Paper Scissors lizard Spock.

Check out cindicator.com. They are using Hybrid Intelligence, a combination of AI and the wisdom of the crowd to predict prices of assets. Seems to be highly successful, and profitable!

#diesquad

I just googled it for you to save time: Spiegelhalter does not mean "mirror-holder". "Halter" comes from "Halde" which means hillside. There is a German name called "Winterhalter" meaning "the one living on a hillside, facing north and not getting lots of sun". The Spiegelhalter lived opposite to this on a sunny hillside.

No wonder Mr. Spiegelhalter is very bright.

The winning bias in these non-transitive dice is significant over several trials, but not such that it guaranties a win on every throw. For a MUCH more dramatic demonstration you can construct a "Lucky 7" non-transitive gambling wheel as follows.

Outer ring is simply in alphabetical order:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Inner ring increments by 7 mod 26 (except 26 instead of 0) 1-8-15-22-3-10-17-24-5-12-19-26-7-14-21-2-9-16-23-4-11-18-25-6-13-20

As a set up, you tell your victim that the numbers are jumbled up between high and low so the person spinning the wheel can't control whether a high or low number comes up next to any particular letter – and just to make doubly sure that it's fair, they can pick first and spin the wheel themselves. What ever letter they pick, you just look at the wheel and just as they spin, choose the letter that is currently next to the number that is one, two, or three higher than their letter. If you choose the letter that is next to the number one higher then the number next to their letter as they spin, your chosen letter will beat their chosen letter by ONE about 25 times out of 26. If you choose the letter that is next to the number that is TWO higher than the number next to their letter as they spin, you will beat them by TWO about 24 times out of 26, etc. Unlike the dice in the video above, these are punishingly one-sided odds, which quickly make it crystal clear how something that LOOKS FAIR (after all I can't predict the future can I?) can actually be very, very, unfair. The increment by 7 mod 26 pattern, and letting them spin and picking just as they spin is to delay them catching on, as they would if the wheel was laid out A-Z and 1-26.

02:37 "As you have seen",

three crosses pop up"There was some witchcraft involved."Die

Rock Paper Scissors Lizard Spock!!

I played 5 non-transitive dice game with my family, my mum and my brother Josh.

Mum selects a 4, 4, 4, 4, 4, 9 dice, Josh selects a 0, 5, 5, 5, 5, 5 dice and I selected a 1, 1, 6, 6, 6, 6 dice. After 10 games, I realized that I won most amount of times than two members of my family. The result is, me 6, Josh 3 and mum 1.

what about pairing two different dice?

7:40 see the pentagram? Satan was way ahead of us

Good afternoon, I have a program that calculates all possible sets of non-transitive dice for any number of faces and I was wondering if you would like the results.

I love this I love this I love this!

I'm now stuck; knowledge of rock, paper, scissors, lizard, spock in die form, without the ability to purchase said pack of die. Where's my < favorite > Klein bottle distributor when I need him? @Cliff Stoll

In the 2nd loop of the 5 dice problem, [so when you are using 2 dice.] The Red dice has approximately a 51.77% chance to beat the White dice. Its approximately 50% but the red dice actually WINS.

The probability of the red dice winning is the probability that either the 9 face of ANY red dice is rolled or that the 0 face of ANY white dice is rolled. Any other combination not including one of those faces results in a white win so we dont have to calculate them.

So the probability of the first red dice being a 9 is = 1/6 chance

The probability that the 2nd red dice being a 9 and the first dice not being a 9 is = (5/6)x(1/6)

The probability of the 3rd being 0 and first 2 not being 9 is = (5/6)x(5/6)x(1/6)

The probability that the 4th being 0 and the first 2 not being 9 and 3rd not being 0 is = (5/6)x(5/6)x(5/6)x(1/6)

You can stop calculating probabilities once you hit a 9 or a 0 because every branch on those paths lead to a Red victory so the entire brach is just a red win so calculating the further probability isnt necessary. [Thats why we stop at 1/6 for the first red dice but the 2nd we count the 1st red dice missing and then stop when the 2nd rolls a 9 etc for the other 2 dice]

Thus, the probability that Red beats White is equal to the probability that either at LEAST one 9 OR 0 is rolled which is equal to

(1/6)+[(5/6)x(1/6)]+[(5/6)x(5/6)x(1/6)]+[(5/6)x(5/6)x(5/6)x(1/6)] = 51.77% [about]

I know there are non-transitive dice containing 7 different dice. Is there an upper limit to this? Has that been explored?

And this is how quantum entanglement works

Which one is Spock in the 5 die game

i think i need a phd to master the game you invented 🙂

His name means "mirror holder" in German.

When you say the inner cycle swaps as opposed to the outer cycle as with the previous dice… It really depends which order you pick first to call the outer cycle… The other way round these basically flip the outer cycle but not the inner… I've tried buying these but they're always out of stock!

For the one person who sees this I just want to tell you

That God loves you ❤️

@singingbanana have you worked out a proof of what is the maximum number of dice this can be done with? Also, did you look at it for any of the other Platonic solids?

So Pokemon is a non-transitive game. I see.

As a professor of ignorance on this matter what has color to do if anything?