Non-transitive Dice November 30, 2019 Tags:Brad, brad efron, Bradley, bradley efron, david, david spiegelhalter, deventer, dice, die, efron, game, grime, james, james grime, M. oskar van deventer, math, mathematics, maths, non-transitive, nontransitive, oskar, probability, problem, Puzzle, spiegelhalter, statistics, transitive Related Posts Top 10 Decade Defining Rap Songs of the 2000s Laff Mobb’s Laff Tracks – Hotel Rooms Are Disgusting ft. Gina Yashere | truTV How to Play Roulette – Straight Up Bets & Zero Bets About The Author Kameron Okuneva 100 Comments Reziik 7:45 HOW DID I KNOW IT WAS GOING TO GO AROUND IN A STAR??!!?!? December 10, 2014 Reply D-Sheep 1:13 January 8, 2015 Reply Count_Butter I root for the Cambridge Professor of Ornithology. January 11, 2015 Reply PSpurgeonCubFan first game – no ties. Luck? or did you edit out the ties? January 13, 2015 Reply Unconventional Wisdom Two professors one doc DO NOT WANT. January 23, 2015 Reply Sam McInturff 7:50I never thought i'd hear James Grime saying "2Chainz" February 17, 2015 Reply Sydney Talapov Its orange not red.. March 2, 2015 Reply dropagemonem I understood, but what if i choose first time before my friend? March 4, 2015 Reply Cooper Gates I finally saw that 50-50 part of the two-dice version for the five-die set lolz April 17, 2015 Reply Horror Versions So cool. April 29, 2015 Reply Nayuta Ito How about the sum of three dice? Will the chain broken? May 2, 2015 Reply deadlypendroppingby Spiegelhalter looks like he thinks James should do less YouTube and more research, LMAO May 30, 2015 Reply deadlypendroppingby 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. May 30, 2015 Reply phantomcruizer So what's the practical purpose for all this ? May 30, 2015 Reply Thomas Hirons 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. June 17, 2015 Reply Nulono "a dice"? July 3, 2015 Reply Girish Manjunath 02:33 So, it's like Pokemon starters… The second one always gets the better choice. July 21, 2015 Reply Zane Dobler That diagram looks like a pentagram… July 28, 2015 Reply LogikEngine Loved the video. Just one small thing: the singular of 'dice' is 'die', so you pick one die, not 'one dice'. August 6, 2015 Reply Username The singular of dice is die 🙂 August 11, 2015 Reply Username 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 😉 August 11, 2015 Reply ben rider 0:45 I don't have two friends :') August 11, 2015 Reply The Awesome Fish What would happen if you played the five-dice game with two dice of two different colours? August 24, 2015 Reply BigBen Hebdomadarius 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 waiting for the odd occasion when it's appropriate to use it. August 25, 2015 Reply Izzo Mapping This looks a bit like rock-paper-scissors-snake-spock September 21, 2015 Reply fedos White is not one of the colors of the rainbow. September 27, 2015 Reply Generic Internetter 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. October 2, 2015 Reply bnumber8 WHERE ARE THE DAMN BILL MURRAY COMMENTS? October 13, 2015 Reply liverpooler1997 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) = 3.5Yellow dice: 3*(5/6) + 3* (2/6) = 3.5Green 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? October 26, 2015 Reply Noel Walters So who would win with three players using the first set ? October 28, 2015 Reply jturner7771 And I thought Rock-Paper-Scissors-Lizard-Spock was confusing. 🙂 November 3, 2015 Reply jimpozcaner Spielgelhalter gives a funny look at 1:24. I wonder why. Could it be that Grime is calling an orange die red? December 2, 2015 Reply Alec Craig 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 December 7, 2015 Reply deserado11 ?! December 31, 2015 Reply Alfonso Esteves 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? January 7, 2016 Reply Henk-Jan Bakker So how do you calculate the actual chance when rolling against two players? January 21, 2016 Reply Joe Adams Oskar Van Davender did this ages ago and with far more dice xD January 23, 2016 Reply Christian Hildebrandt 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! January 24, 2016 Reply trexpaddock Die, die, die, die, die!! The singular of dice is die. January 25, 2016 Reply Noah Peachey 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. January 29, 2016 Reply Peter Müller What happens when you throw all three die? Which will win in the long run? January 30, 2016 Reply Shock n'aw thanks very much, and for explaining it February 9, 2016 Reply Nils Eriksson if you don't have dice you can use a deck of cards and choose between AK, J10, 22 February 10, 2016 Reply Ashish Barnawal Beating your friends is not okay. #noviolence February 15, 2016 Reply Thomas Fucking Jefferson 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. March 15, 2016 Reply Hannah Palma Percy Weasley March 16, 2016 Reply chinareds54 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. March 19, 2016 Reply Mixa 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%. March 25, 2016 Reply Yuriy Gordeyev David Spiegelhalter looks like Bill Murray's doppelganger in some shots. April 3, 2016 Reply sugarfrosted Using the plural as the singular is ear scraping. June 9, 2016 Reply Daniel Wood Damn it, I thought he was gonna say Bill Murray. June 15, 2016 Reply Jenn W but how did you come up with these dice??? how long did this take you? July 13, 2016 Reply Oaky Oak Umm, Dr. Grime? Mr. Spielgelhalter? That "red" dice is orange… September 19, 2016 Reply Michael S As a former grammar Nazi, it bugs me when people say "a dice" (the singular is "die"). October 6, 2016 Reply 樊哲齊 【小樊】 Good October 31, 2016 Reply Anirudh Chinta Ser Davos, is that you? November 2, 2016 Reply Jakharr Vinta/VoryoMTG Spiegelhalter? Doesn't that mean mirror holder in German? lol November 9, 2016 Reply Cameron I shouldn't play this with my sisters… it would piss them off pretty bad… But very cool! Thanks for the video, Dr. James! November 21, 2016 Reply Doug Jones 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. December 7, 2016 Reply Jaydon J. did any one else see a pentagram of crosses at 7:40 February 22, 2017 Reply Orange Juice Has anyone tried picking two different dice? March 20, 2017 Reply Blackmark52 Blank sides on the dice seems like a cheat to me. Zeros are for funky RPG dice only. March 24, 2017 Reply Tristen Roddenberry The five dive is a devil's trap March 26, 2017 Reply Patrk38 that's orange dice, not red! April 8, 2017 Reply Stray216 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) April 12, 2017 Reply drmedwuast So cool that you have Bill Murray in your video May 9, 2017 Reply McPeeperson Smith I'm actually trying to get a paper published on this subject! not that you'll read this. May 10, 2017 Reply Zed Dash 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. June 15, 2017 Reply TheDruidKing What started out as a board game with James quickly escalated to a scene from Scanners. July 20, 2017 Reply tru jay it took me 2 datys to understand.. July 24, 2017 Reply Overkillius I saw a diagram of the Chinese elements for the first time and this video INSTANTLY popped to mind. The resemblance is uncanny. August 9, 2017 Reply Mickey Rube 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? August 22, 2017 Reply RichTheWolfGaming Rock paper scissors lizard spock August 24, 2017 Reply Asther Phoenix is this pokemon? August 28, 2017 Reply MumboJ 7:08 "Richard Of York Gave Battle In …Wayne" October 1, 2017 Reply Albert warren So James' new game is like a dice version of Rock Paper Scissors lizard Spock. January 1, 2018 Reply tlhod 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! January 22, 2018 Reply eighteen animation #diesquad March 2, 2018 Reply Pc 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. March 10, 2018 Reply Steve B. 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. March 25, 2018 Reply Oleh Gults 02:37 "As you have seen", three crosses pop up "There was some witchcraft involved." April 14, 2018 Reply Practical Mediocrity Die April 24, 2018 Reply wassupkop Rock Paper Scissors Lizard Spock!! August 13, 2018 Reply Jaycee Kim 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. August 21, 2018 Reply FRM5993 what about pairing two different dice? November 10, 2018 Reply Doctor KILLEE 7:40 see the pentagram? Satan was way ahead of us November 11, 2018 Reply Noi3skill 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. December 29, 2018 Reply Menko I love this I love this I love this! February 15, 2019 Reply wello987 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 February 19, 2019 Reply Eragon7 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 chanceThe 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] February 20, 2019 Reply Stefan Lopuszanski I know there are non-transitive dice containing 7 different dice. Is there an upper limit to this? Has that been explored? February 25, 2019 Reply Dead Light And this is how quantum entanglement works February 25, 2019 Reply Dead Light Which one is Spock in the 5 die game February 25, 2019 Reply zsolt levente i think i need a phd to master the game you invented 🙂 March 7, 2019 Reply Dana Adalaide His name means "mirror holder" in German. March 8, 2019 Reply kailomonkey 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! June 16, 2019 Reply Alex King For the one person who sees this I just want to tell you That God loves you ❤️ June 23, 2019 Reply Nik Blackwell @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? July 9, 2019 Reply Lajos György Mészáros So Pokemon is a non-transitive game. I see. July 25, 2019 Reply John Hales As a professor of ignorance on this matter what has color to do if anything? September 16, 2019 Reply Add a Comment Cancel reply Your email address will not be published. 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