You'll Never Win This Game
ฝัง
- เผยแพร่เมื่อ 18 ก.ค. 2021
- The transitive property is ingrained in our thinking. It gives our brains a simple, straightforward way to process the world -- especially with numbers. If one thing is better or more valuable than another, and that second thing is better than a third, you KNOW that the first one is better than the third.
But it doesn’t always work that way. And if you fail to recognize when real life violates the pattern of transitivity, you’re going to run head first into a veridical paradox.
Efron’s non-transitive dice demonstrate that hard and fast rules about value don’t always exist. By toying with relative probabilities, Efron discovered that a die’s superiority or weakness can be relative -- and as the dice values get more complex, it becomes nearly impossible to reason out which die is stronger against the others.
In math, our first impressions are often deceptive. Occasionally they’re just plain wrong. And sometimes a game is designed to deceive you into believing you’re in a position of strength when there’s no way to win. That’s the deception paradox.
Oh -- and if someone wants to play a game with you and they let you go first… run.
** LINKS **
Vsauce2:
TikTok: / vsaucetwo
Twitter: / vsaucetwo
Facebook: / vsaucetwo
Talk Vsauce2 in The Create Unknown Discord: / discord
Vsauce2 on Reddit: / vsauce2
Hosted and Produced by Kevin Lieber
Instagram: / kevlieber
Twitter: / kevinlieber
Podcast: / thecreateunknown
Research and Writing by Matthew Tabor
/ tabortcu
Editing by John Swan
/ @johnswanyt
Huge Thanks To Paula Lieber
www.etsy.com/shop/Craftality
Vsauce's Curiosity Box Store: www.curiositybox.com/collecti...
#education #vsauce #maths
![แม่กลองสองใจ - ซีแกรม โตเกียว มิวสิค [ OFFICIAL MUSIC VIDEO ]](http://i.ytimg.com/vi/GSQfVjcr_f4/mqdefault.jpg)
Rock/paper/scissors is mathematically trivial; its intransitivity is obvious and needs no explanation. Efron's Dice have unequal features with varying average rolls and a transitive/higher number wins aspect to the game. Also, a die's advantage as we add more dice approaches a limit of 3/4, which is pretty interesting. R/P/S has none of this complexity.
I'm sorry that there's so many people complaining in the comments. I found this video a bit interesting even if I did somewhat catch onto the trick early on, and, either way, the video still has value
lol
That just sounds like Rock Paper Scissors with extra steps
I mean your basically sayin I can't win cause I'm goin 1st it's kinda like da thing wit rpgs or pickin a starter Pokémon where they beat each other in a circle
rock paper scissors has none of the complexity, but all the layman parallels.
"Let's play rock paper scissors, but you get the advantage of picking first and letting me know what you picked."
I was thinking the same thing lol
You completely missed the point of the video, it's not rock paper scissors. The rules for winning rock paper scissors are completely non-transitive while the rules for winning this game are transitive. If you roll the A dice and beat the B dice, which beat the C dice, which beat the D dice, the A dice should have the highest number and beat C and D. But it doesn't. But there's a simple explanation for that. That's why it's a veridical paradox, a paradox that seems like a paradox at first, but has an explanation
@@michaelmiller2210 No, the *NUMBERS* are transitive (1
@@unliving_ball_of_gas my guy, the point of my comment went right over your head. I know numbers are transitive and I know the dice aren't, I implied that in the previous reply, you just completely missed it. The point is, rock paper scissors isn't transitive at all, while this dice game seems like it should be transitive at first since it uses a transitive ruleset rather than a non transitive one. It's a veridical paradox, Kevin said it himself in the video. People just think they're smart because they understand that the dice are non-transitive, when they actually just have no clue what this paradox is.
@@michaelmiller2210 Yesh, I understand it, I thought you didn't understand the paradox so I tried explaining it. Well, at least it might make someone else understand.
It’s not choosing the meta, it’s choosing counterpicks
exactly, pick up any strategy game and its core gameplay loop is literally this
omg yes, i thought the same
Clash royale in a nutshell
@@stonyfanatic3785 tru
@@stonyfanatic3785 yes
alt title: Kevin spends 9 minutes explaining how he's going to devastate your A with his D.
hmm... I have a slight suspicion that he is targeting a certain community of people for a certain activity revolving around some certain areas but he is not getting struck by youtube by explaining it with math...
So what happens when you roll all 4 dice in a 4 play free for all? Over time, which one wins?
Ive written a script and it seems like its a _very_ close call with C and D - D is a _little_ better. Then followed by A and the worst is B.
@@leobozkir5425 What about a 1v1 with blind picks where you don't know the opponent's choice beforehand? excluding cases where both players pick the same dice, that's an obvious case.
The overall chart would be 1296 deep, but we can simplify it logically. The following is for the SIMPLER dice.
1. C wins if C rolls 6. This occurs at 1/3.
2. D wins if D rolls 5 and C rolls 2. This occurs at 1/2 x 2/3 = 1/3.
3. A wins if A rolls 4, and both C and D roll sub-3. This occurs at 2/3 x 2/3 x 1/2 = 4/18 = 2/9.
4. B wins if all others roll sub-3. This occurs at 1/3 x 2/3 x 1/2 = 2/18 = 1/9.
Thus, C and D are equal, followed by A, and finally B.
As for the blind picks (a later comment), you simply average each chance of winning.
1. A wins 2/3, 4/9, and 1/3 of the time, for a total of 13/27 (26/54).
2. B wins 1/3, 2/3, and 1/2 of the time, for a total of 9/18 (27/54).
3. C wins 5/9, 1/3, and 2/3 of the time, for a total of 14/27 (28/54).
4. D wins 2/3, 1/2, and 1/3 of the time, for a total of 9/18 (27/54).
So C has a slight advantage, and A a slight disadvantage. This could introduce psychological factors - will you pick B anticipating that I'll pick C?
@@shiningvivian Blind picks are straight-up 50/50. You're just playing Rock, Paper, Scissors.
You gotta write out a complete match-up chart and then it becomes obvious
The line "I'm going to crush you, with my D." crashed my TH-cam app. I hope you're happy Kevin.
Judging by the heart, I suppose he is lol
Seems like his D did crush something
3:07
wow
should've ended the video there to be totally honest
"IT MAKES NO SENSE"
People picking their starter Pokemon: "tell me about it"
LOL.. thats actually a really good example
Just choose a fire starter cause usually fire types are rare in the wild
Yeah, that's actually also a non-transitive example. Good point
Yay pokemon reference
Indeed
I misread the title as "The Decepticon Paradox"
Jerk 🥸
I misread your comment as you misreading the title as “The Deception Paradox” so I reread the title four times always reading it as “The Deception Paradox” and thinking I read it wrong five times in a row, only then I read your comment again and noticed that you misread the title as “The Decepticon Paradox”, that was weird (and also weird to write down)
@@Lagrange00 same honestly
@@Lagrange00 same dude. And because Vsauce videos have (in the past) the tendency to show you something deceptive, I thought there was something extremely subtly wrong with the title. Took me a good minute to realize. Lmao
Heyy big fan bro !!
The most confusing part of this video is you trying to convince us that this is somehow unintuitive.
Yes
yeah, I just looked at the dice, compared the numbers in my head and could easily see which dice were good against the others. It really was obvious when he said "you get to choose first". If this were a true blind pick, then things would be far different. If I told you to play rock paper scissors and that I got to pick after you did, you would say no. That is the real problem here in part. The other part is assuming this is a single game. It is not. He requires a series of games to have absolute victory. If it were a single game, I might still win, even if the odds are against me. But after rolling the dice 20 times I am clearly going to lose more than I win. I'm not impressed if this is the best an award winning statistician comes up with as some sort of mind bending puzzle.
Or Pokemon type advantages, we're taught from a pretty young age to understand this sort of concept...
Maybe Vsauce2 is trying to target, and cater for, a less intellectual audience. ¯\_(ツ)_/¯
Mood
You’re talking (largely) to a generation that grew up on Pokémon. This is more intuitive for people than you may think lol
very true
That is exactly what I was thinking (assuming you’re referring to type matchups)
Yeah
Fire>grass>water but water>fire
Literally exactly where my brain went. Pokemon already taught me how this works, and even without it there's rock-paper-scissors.
VSauce: "It makes no sense."
Me: "You've clearly never played a video game with a weapon triangle."
This.
Math nerd: "Let's play a game, you move first."
You should know that means there's a twist.
except for chess
@@cy_ this mostly happens to games that are 1 choice options
@@cy_ even with chess "proceeds to create stockfish based on mathematical gradation of available by efficiency and positioning"
Imagine playing rock paper scissors but one player chooses first. Yes, they'll always lose
The funniest thing is he said most of the time, imagine losing a Rock Paper Scissors game when your opponent went first, even if it is 1/1000
Also, as the top comment points out:
The way you win rock paper scissors isn't transitive (if it was, this would mean if paper beats rock, and rock beats scissors, then paper must beat scissors) but the rule for winning this game (rolling the highest) number IS transitive (i.e for any 3 numbers, if number a is greater than number b, and number b is greater than number c, then c MUST be greater than a, this is true for all numbers in the entire world). That's why it's weird that the dice you pick do not satisfy a transitive realtion (i.e if one dice out preforms another which out preforms another, the first dice does not nessecairly out preform the last) but the rule (greatest number) that decides if you win the game DOES work like that ( if one number is greater than another which is greater than another, the first number is always greater than the last)
@@noahmanc2 And also you need to point out that, most of the time when one dice wins, it wins by a lot, but when it loses, it loses by a little.
OMG YOU'RE SUCH A GENIUS, YOU DEFINITELY FOUND OUT THAT THERE WAS NO BEST DICE BEFORE WATCHING THE VID!! ALL HAIL THE GREAT GENIUS!!
@@noahmanc2 paper can cut through scissors
I feel like most people don't assume transitivity.
And I don't think the non transitivity is that mind boggling since because a "worse dice" can win small while loosing big and it doesn't make a diffence.
Agreed, he stated the problem then gave a bunch of misleading assumption
Agreed too ... When he stated that dices "battle" are transitive I was a bit shocked, it clearly isn't something to assume from thin air if you did a bit of math in your life.
I’m a very visual person, for the record (which correlates to how I wrap my head around these things). I feel like his assumption of transitivity is based on an assumption that most people will see this (or similar scenarios) very linearly, which isn’t true. Yes, the transitive property is a proven property, and this does qualify as being a mathematical paradox, but it doesn’t need to be confusing in actual practice. He/We just have to change how we see it. Instead of seeing it as a line, see it as a circle. It’s like the game “rock, paper, scissors”, which is structured off of a triangle - rock beats scissors, scissors beats paper, and paper beats rock. That makes sense, we all understand that. This is the same thing - A beats B, B beats C, C beats D, and D beats A. There you go, makes sense. The only difference to understand, then, is that there are no laws of averages. Even though D beats A MOST of the time, we’re still playing with dice. A could absolutely win, just by rolling well. Still a game of chance, in the end.
Also, random thing, but the way he painted D as winning 10 times and A winning 5 times feels misleading (though it might not have been intentional). It paints this very strict scenario where the math will go perfectly, which isn’t true. It’s still just a roll of the dice, in the end, in a game where the highest roll wins.
@@TheUltraUltimatum just a theory, but, and hear me out on this one, maybe that's why he named the video "the deception paradox"?
"How can the best one lose to the worst one?"
"It makes NO sense!"
rock, paper, scissors, an incredibly simple game that pretty much anyone can grasp: Am I a joke to you?
oh yea, now lemme build spirals
how does paper beat a rock?
@@baconheadhair6938 It "covers" rock by wrapping around it. Not really that big a threat compared to being cut in half or shatter to pieces. Never made much sense to me. Honestly seems like it would do more damage to the paper than the rock.
"Rock, paper, scissors, a very strange game. The only winning move is not to play. How about a nice game of global thermonuclear war?"
"I'm going to give you a game-changing hint." *lies*
He never said A beats D though, he just said you may assume that A beats D. It's kinda like rock paper scissors. Plus if you look at the numbers, it would be obvious D loses to A
"I'm choosing D to go against your A"
Go on.
Oh that's a nice one 😏
lmao
"D is stronger than A"
Hmm. Depends on the A...
͡° ͜ʖ ͡°)
At 69 likes so I can’t like it
Well Bulbasaur is strong against Squirtle, Squirtle is strong against Charmander, but Charmander is strong against Bulbasaur.
This all makes sense
Kevin is a Pokémon rival.
@@Depressed_Spiderwhat do you mran
Mean?
@@microwavabletoothbrush the rival picks their starter after you pick yours, giving them an advantage
@@Jzphh ok
Thanks
I feel like as someone who has played hundreds of hours of Pokémon in my life, this concept is familiar enough to something I’ve experienced for so long that it makes pretty decent sense.
While sure Pokémon has been called a traditional “rock paper scissors” for decades, like this game it’s far more complicated. There are 19 types, all weaving in chains and webs of one beats the other beats the other, with some traditional RPS triangles, as well as complex chains where fire beats grass beats water which beats both rock and ground and is resisted by steel, and then that ground is also good against the rock as well, steel and fire which is against fire. It’s hit many complex layers and branches that dictate where something lands on a winning matchup.
Ice for example is one of the worst defensive types with 4 weaknesses, but offensively it crushes dragon, grass, ground, bug and flying.
The first batch of numbers was so incredible easy to work out, it makes perfect logical sense. Should have started with the second set of numbers to make it at least somewhat difficult to work out.
this actually makes total sense. I don't understand how this is a paradox
its just rock paper scissors with extra steps. completely logical
Yeah. It is pretty much the basis of a lot of card games. Not the individual cards, but hands of cards.
Veridical paradox
Because the first player has no way to pick the best choice, in this game whoever's plays first will always lose (if the second player chooses the best choice in the situation)
It's known as a veridical paradox
"because I'm nice I'm gonna let you pick first"
Yeah we know your tricks next time you play a game YOURE choosing first Kevin...
Hey melody, you seem so lonely.
let me be ur bass line?
t. someone who doesn't know what a counterpick is
Ok then let’s play tic tac toe and I am taking the center square.
When it comes to picking, counter picking is an advantage
@@zariftahmidshoeb3487
Not sure how this benefits you. Tic Tac
Toe will always end up a draw unless you are playing against children.
25 years of playing Pokemon, and 20 years of playing tabletop RPGs have made this a very easy concept for me to grasp. The moment I was picking first, I already had a good idea of what was up. I was just like, "oh, this is going to be non-transitive dice... Yep, called it."
3:02 "I'm using D to go against your A, and I'm going to CRUSH you" 😂
transitive property makes zero sense in this example as it's all about matchups. Total value is pointless to look at as well. It's not a paradox, it's just looking at the problem compeltely wrong and then making it out to be more than it is.
Welcome to VSauce2!
I came to the same conclusion. I stopped the video and made my own opinion and found it out in less than 2 minutes max, it's really not that hard to win this dice game.
Yeah, you can work it out just by looking at the dice in the first place without all the charts lol
Its counterintuitive to the most who hear it. Thats what makes it a paradox! Its not a logical paradox, its a psychological paradox (veridical paradox)
@@gianjeffers6200 as long as you pick 2nd, you can win most of the time.
The relative advantage is not adding up the dice but being able to pick AFTER your opponent has chosen.
Title - "the *deception* paradox"
Complaints in the majority of responses "hey, you were deceptive by tricking people into assuming this should be transitive"
yeah, he framed it as a chain of "this is best" but before he even mentioned that, i assumed the last one would beat the first, because thats of course how its going to work.
You can even see it from the number plots, all of D's numbers are better than A's by like, one. cool video puzzle but still, kinda missed a big piece that we the audience arent dumb :P
Except I never assumed that, even when he said why it should...
Ah, so he was using French grammar?
This is the equivalent to telling someone to go first in rock paper siccors
@@moth2910
Yet virtually nobody could be fooled into thinking that Rock Paper Scissors is transitive... where as many people could be fooled into assuming all dice are transitive.
So, not it isn't equivalent. The chances of winning is equivalent, but the chances of deceiving someone isn't equivalent at all.
Which goes back to my comment about this being called the *deception* paradox.
Lmao this is exactly like rock paper scissors and Kevin's like "I'm so nice that I'm going to let you make your move first". 🤣
Not really. If it was like Rock, Paper, Scissors, then you'd be able to choose scissors and be beaten by paper. In the video he shows that he opted to choose the overall statistical weakest in the face of the strongest and still managed to have the advantage.
"Only the Sith deal in absolutes."
-Obi-Wan Kenobi
This seams almost misleading, it is very obvious immediately that D beats A. It makes perfect sense, just look at how many sides on one dice beat the side in the same position on another dice.
Well yeah it's obvious after you compute that D tends to beat A that D tends to beat A.
@@Adamant- Yeah, that's what he said. The point this video tries to make is that it's some big surprise that this is the case, but it isn't. It's pretty obvious just from looking at the dice that they aren't transitive. It's just a weapons triangle or rock paper scissors. So it's 9 minute explanation of an incredibly obvious concept.
This is really the weak part of the video. No one is surprised that D beats A. Anyone who actually sat and thought about it would realize this.
Tbh this wasn’t hard for me to wrap my head around at all, type advantages taught me this kind of logic lol
the part that's unintuitive is *why* it works. it may not be hard to wrap your head around, but presented a different way you could easily fool a lot of people. which is...kinda the point i think. i think, in this case, kevin is jsut a victim of his own success. everyone expects the twist, so they know not to just...go with their instinct.
@sillyking1991 that's not the problem. The problem with this video is he intentionally is deceptive about how it works to force the twist. The dice itself are an interesting way to show non transitive properties, this video is not. Kevin acts as if everyone assumes that "Well #1 beats #2, and #2 beats #3, so obviously #1 always wins." People learn rps at a very young age. The fact that something is nontransitive is not a twist in any way.
Actually C is still the best dice but not just because it has more points and it’s the same for A which is the worst, let me explain :
Let’s evaluate every probability of each matchup :
A wins against B : 2/3
A wins against C : 4/9
A wins against D : 1/3
A wins against a random dice between (B,C,D) : 13/27
B wins against A : 1/3
B wins against C : 2/3
B wins against D : 1/2
B wins against a random dice between (A,C,D) : 1/2
C wins against A : 5/9
C wins against B : 1/3
C wins against D : 2/3
C wins against a random dice between (A,B,D) : 14/27
D wins against A : 2/3
D wins against B: 1/2
D wins against C : 1/3
D wins against a random dice between (A,B,C) : 1/2
So we see that C is the best choice, B and D then, and the worst one is A.
Note : Of course if you’re opponent can choose his dice he will always wins 2 over 3 times but C is better if he can’t choose.
All of the comments on this video are "it's basically rock paper scissors but you have to pick first and show me your answer" or "the strange part is how you're trying to convince us it's unintuitive". It IS unintuitive to people but when demonstrated in such a clear way people don't see how they are still falling into this trap.
Take a game like League Of Legends, look at the sheer amount of tier lists the community has made or how even pro players build the same item build every game because "It's the always the best", things like this fall into the trap. A tier list inherently says S tier is better than F tier while ignoring factors like matchups, meta and etc. an F tier hero can counter an S tier hero and now the tierlist is broken. Despite that we still see it being used by nearly everyone in the community.
Alternately we could look to Magic The Gathering or Hearthstone, what's the best deck? does that deck beat everything? of course not that's essentially this point Kevin is trying to get across here.
I love the quote he uses to sum up the video "We fall into a cognitive trap in thinking in absolute terms when real value is often relative. In this game the concept of better or worse is deceptive, it depends entirely on the situation. Our brains want to find patterns to identify "The Best Choice" and we love ranking things, But life isn't always transitive". the above examples show how the majority of people fall into this trap and while the comment section here say they don't, a lot of us probably do without even knowing it.
3:03 "I'm choosing D to go against your A and I'm going to crush you with my D." O.o
I was looking for this comment
@@kajvanveen5302 same lol
Boy am I glad the “timed” filter on comment sections exist
So basically Rock Paper Scissors, but you get to see what your opponent picks beforehand.
I was about to say that, doesn't seem so special after that, does it.
@@undercatviper I wouldn't say it's not special. It's still a pretty unique mathematical property. But it's not as confusing as it seems at first.
not exactly, because the whole concept of rock paper scissors is intransitive, where as here, numbers are transitive, just the collection of them forming the dice aren't
this is exactly my thoughts put into words, thank you for explaining it so well XD
Ehh just because numbers have transitive properties, that doesn't mean that sets of numbers do.
This is like when no matter which starter you pick in Red and Blue in Pokemon, Blue always picks the pokemon stronger against you. In this scenario, It's actually better to pick your dice after your opponent does.
I just think about it as A>B>C>D and then repeat a little, which gives A>B>C>D>A>B… giving the reasoning on why D beats A. Its more of a pattern than anything else
This game doesnt have an OP meta, just hard counters to everything
The only problem I see is being forced to pick first; if both players picked randomly and revealed at the same time, then it (should) be random who wins.
This whole "paradox" relies upon a nasty mangling of the transitive property.
I understood the system almost instantly. It's just the total number of higher digits on the dies that make the difference. Very cleverly made!
For a simpler version of this game, Imagine you are playing Rock-Paper-Scissors against someone, but you get to see what your opponent is choosing before you choose.
There's no weak or strong, there's only counterpicks
It's funny that "even against going first" implies that by going first we should have a greater advantage, when that was the sole cause of our defeat.
The early bird may catch the worm, but the early worm is who gets caught
@@NerdyTransformed i’m stealing this
@@NerdyTransformed the second mouse gets the cheese
@@Demandes14 "A second mouse doesn't create a new cursor" - Bill Gates probably
@@NerdyTransformed life is then about figuring out if you’re a worm or a bird. If you’re the word go last. If you’re the bird go first.
In this situation, the fact that you pick first actually hurts you, because no matter what you choose, your opponent can choose the better option. It's like playing Rock-Paper-Scissors when your opponent already knows what you're going to play.
The reason a
Suggesting that this is transitive and that the highest number combined means anything is misleading and kinda insulting to viewers who see it is definitely not.
I mean you can easily overlook the transitive part but even a 6th grader won't fall for the sum argument because a 1-1-1-1-1-1 beats a 0-0-0-0-0-9999 83% of the time.
thats why he removed the simple dice and replaced them with ones that were *faaar* less obvious.
you actually were insulted by a logical argument
my god
Seemed fairly straightforward to me when you showed the simpler dice. Yes the more complex dice hide the stats a little, but when you think about the percentage of time each number comes up and how it compares to the percentages on another dice, there's nothing unintuitive about it at all.
So it’s like playing Rock Paper Scissors but with 4 hand gestures and I get to see what they do first. Love it.
In any strategy game with multiple choices, learning how matchups interact and how you can perform in certain scenarios with something will almost always be better then just always picking what might be the objective best. Nothing is without weakness, and if you can abuse their weaknesses, it matters not how weak something is in it's own right. Situational awareness is key.
Anyone who thinks this is a paradox has never played rock, paper, scissors.
Ha
Or most other games, like chess. Your best moves depend on the opponents moves.
pin this damn comment!
YES! that's what i was
thinking
@@SirKingquote If you play strategy game, you'll understand.
So basically this is what it feels like to be a Pokemon.
this is so intuitive and trivial to see I don't know how it can be called a paradox
I feel like this is similar to when your ranking something such as movies and when you compare a certain couple from further up or down the list you realise that it’s not always linear.
They're non-transitive dice. We're just playing rock paper scissors with dice. And you're letting us go first...
That's so smart, letting your opponent go first in rock paper scissors
0:47 Everything makes sense, even at just a glance. It's not mind-blowing at all...
Okay, how about you explain it properly to see if you really understand it?
@@jemangerrit1747 He explained it similar to the way I would have. But even before he did, it made sense.
@@F_L_U_X he didnt really explain it, he just showed it. If you say "at first glance" it implice you didnt need to calculate I feel. So again, what is the reason that the math works?
Im sure you can explain something like why the golden ratio is the way it is, but can you put this into words?
@@jemangerrit1747 The way the numbers are set up. C's numbers are all better than D's, when comparing strongest with strongest and weakest with weakest. B beats C's weakest, which is more likely, while A's strongest beats B. A, however, still has numbers lower than D's. This is just a simple case of rock paper scissors with RNG to it. B is what makes the importance, having only one number to have the loop work.
@@dropthehatantonycraft7516 this is a fair explanation. However I think its a little bit naive to call it a rock paper sciccors game. RPS is purely non-transitive. What makes these dies special is that it works with numbers that are inherintly transitive. I also calculated that C beats A, which isnt on purpose I think, but is that way because of the numbers. Also, the loop doenst work because of B, since in the harder example it has multiple different values.
If A had five 4s and one 0, it wouldnt work. So theres a delicate balance that I cant put into words without straight up calculating it.
And that is why, while not being mindblown by it or anything, I can admit I didnt REALLY understand it "at first glance"
Thanks for not making another "short". I was itching for edited video!
I remember stumbling across the Wikipedia article for nontransitive dice a few years back. It's neat to see these cool dice step into the TH-cam spotlight!
I imagine Fighting Game players would have an easy time understanding this. Plenty of cases where a "strong" character has a really weak matchup against a "weak" one.
This
and then that character becomes the main counter
It's like Rock, Paper, Scissors. Rock beats scissors and scissors beats paper, that doesn't mean rock beats paper. It's not a line, it's a cycle.
Yeah, but it feels less intuitive since the outcome of each roll is based on which number is higher.
Yeah the concept is easily understandable but the thing is that the mathematical total is useless since beating somebody 6-1 is the same as beating them 2-1, so how far apart you beat them doesn’t matter; not crazy to grasp but I see what he was trying to say
Rock beats paper and paper beats scissors?
What i want to know is, does A also lose to C or is it just D? Also, does B lose to D?
I get the A and D part, but he never explained if the whole thing is none transitive or is just the A vs. D that isn't transative...
Please, I need to know! this will keep me up at night!!! Well probably... for like 5 mins or so anyways. I still really wanna know though.
@@raincandy3 You sayin you *don't* play it like that?
Kevin's titles alone will shut down any ounce of self-confidence I've ever had
Your Videos are the greatest they are energetic and they learn us a lot of thing! Keep doing these!!!
I noticed it immediately. Not sure why he's so convinced that it's impossible to see the outcome beforehand; when I looked at "which dice I should choose" I immediately noticed each dice had a strict advantage over another, like rock paper scissors, except you're forced to obviously pick first and tell your opponent (so they'll always have the advantage). Totals never mattered.
Then again, it could be that I'm too used to games where counterpicks/triangle advantages are important, so that's more ingrained in my thinking than the transitive property.
Same
I think it bc u genus
It seemed pretty straight forward. I agree
"My D is still going to win 2/3rds of the time against your strong A, which seems impossible!"
harder
The win rate goes up to 100% when played in prison...
@@McPilch true
Thanks, Kevin. You did a good job not throwing the dice at the camera.
I love non-transitive dice. I made a set of resin cast ones for our local math museum. It's also with raised pips for visually impaired people and they are highly in use.
Mathematikum?
@@petraw9792 yes exactly, the mathematikum in Gießen.
Of course the paradox doesn't make sense if you get railroaded into the wrong lines of thinking like this video does
It's not necessarily the wrong lines of thinking, its the usual one.
But thats the entire point of the video. The video is titled, "The Deception Paradox." He literally admits that it can be confusing not because of the dice, but because of your interpretation.
@@nickhohl3468 ok.
This same phenomenon was explored in TED's "monster duel riddle"
Yes! I enjoyed that vid.
I choose the disk with only 3
This seems like a practical demonstration of the MMA Axiom "Styles make fights".
The dice put most of their eggs in one 'basket' and responding to the move is what's powerful
The thing about this is that the relation isn't transitive. So no paradox
Edit: One more thing to people that say that the higher number wins and that relation is transitive. Yes, it is transitive but Kevin never told us that the higher number wins he just showed some tables and showed A beats B, B beats C and so on. He mislead us by putting A ">" B symbols so that we think the relation is transitive. He should have just said A "beats" B and the relation "beats" isn't transitive.
But the rule to win the game is transitive. (The "greater than" realtionship is a transitive realtionship, if number a is greater than number b, nd number b is greater than c, then we know a is greater than c. Thats a MATHEMATICAL rule). Thats why its "paradoxical" (although not a true paradox). Many people are comparing this to games where the way you win is NOT TRANSITIVE (like rock paper scissors) which is why some people are missing what's "confusing" about this
Exactly my thought!!! He keeps hinting as if the relation is transitive when it's not. For the first 3 minutes of the video, he keeps talking as if the relation is transitive and leading people into thinking that it is, when it's obviously not. The whole thing about A > B & B > C & C > D => A > D is just wrong when the relation is not transitive.
@@IsmailTaleb ...the rule to win is transitive.
You win by rolling a higher number than the other person. That realtionship is most certainly transitive. If a number A is greater than a number B, and B is greater than C, then you know for a FACT A is greater than C.
The paradox arises in that, that the rule to win is transitive but the dices you pick are not. The paradox isn't that they SHOULD be transitive. Its that, a normal human would derive from a game where the rule to win is transitive, that the matchups are also. You would greatly struggle to find another game where the rule to win is transitive but matchups aren't.
Its not technically a paradox, but alot of people are completing missing why its confusing. Its not confusing that its a game of matchups, there is plenty of games of matchups. Whats confusing is DERVING that fact from a transitive rule.
@@noahmanc2 I'm afraid that is not the definition of transitivity my friend. We can take the definition from a math forum or Wikipedia for the sake of this argument : "a relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c".
Now, on this video we have a bunch of relations between pairs: a>b, then b>c, then c>d, then d>a (this last one he doesn't say explicitly, but it's there) but since this relation is NOT transitive, we can never put them all in our relation as a>b>c>d (this one is wrong).
I believe the confusion happens because we consider a, b, c and d to behave like numbers, but they are not, they are dice. So the relation ">" is not the "regular" relation > that we know applies to numbers, this is another relation ">" that we just defined for the purpose of this game. So we should not use it, and I believe that's where people get confused and they think that ">" in this example is the same > we use to say a number is greater than another number. So yes, as Abhjitih S and I said earlier, this new relation ">" is not transitive, unlike the > relation that is transitive when it comes to numbers. There is no paradox.
@@IsmailTaleb dude, I majored in abstract algebra... You're not about to tell me what transitivity means. If you really don't think the integer greater than relationship is transitive you can literally Google it.. its not a hard proof to understand.
Nobdoys saying the dice are numbers. But what decides if you win the game or not IS a number (the number that is rolled)
You seem to think im saying the matchups are transitive. I am not . I am talking SPECFICIALLY about the rule that decides if you win the game or not.
Your missing the point of the video. The point isn't that the matchups should be transitive. Nobodys saying that. The point of the video is realizing that they aren't is counterintuitive (not wrong or illegal, just counterintutive)
And you clearly didn't read my comment, because I specially said a NUMBER A(not a DICE a)
People who play Pokémon: Grass, Fire, Water right? What's so confusing?
And exactly when people ask which is the best Pokémon.... It's not transitive. It entirely depends on what the opponent has and does.
@@DatShepTho Pokémon is often transitive. Stats often beat type match-ups. Each generation to date has had competitive meta choices that have been put in S tier and often been banned for tournament play because they are just considered strong against everything.
Granted, those S tier Pokémon change from one generation to the next, but the point still stands.
@@CrashSable it's not transitive though. There's no pokemon that outright beats every other pokemon in every situation. And if the transitive property did apply, there would have to be one
There will always be a Pokémon with some ability, ivs or moveset that beats a meta pokemon though. Otherwise it's probably banned to ubers
Do you do podcasts? I would love to listen to your content while I’m driving.
It's about the individual match ups for each face against every face, you can have a dice that can win more individual of these match ups of face per face, but still have a lesser total value on all sides
Just comparing the expected values doesn't work for duel games.
Legendary Berkshire Hathaway investor Warren Buffett challenged Bill Gates to play a simple dice game, but Buffett had a set of Efron’s non-transitive dice. Gates was suspicious at being able to choose first, and after looking at the dice, he decided not to play. NOW YOU KNOW THAT.
Never trust dice games.
Second
Smort
But you didn't answer the most important question. How do I win?
excited for the end because 3 minutes in it just seems like matchup spreads in fighting games
The thing that helps me understand it is using a tennis analogy. For example. Person 1 can beat person 2 person 2 can beat person 3 but person 3 has the specific skills needed to beat person 1 so they win.
"By the transitive property A>D." ... this man has never watched NBA, NFL, or even a chess league..
Did you even watch the whole video?
@@system_ai9248 nah he didnt
This one really wasn't hard to grasp.
Its similar to rock paper scissors, but whoever goes last, gets to see what the first person picked.
I think it would be worth mentioning that as much as A>B>C>D is valid, so is B>C>D>A and so on. There might be merit in thinking of the "dominance" as more of a cycle than a chain with definite starting and ending points.
Also, D>A seems to hold just as well for the simpler dice:
1 1 1 5 5 5
0 1 1 1 5 5 5
0 1 1 1 5 5 5
4 4 4 4 5 5 5
4 4 4 4 5 5 5
4 4 4 4 5 5 5
4 4 4 4 5 5 5
I often watch Vsauce videos and leave dumbfounded, entertained, and a bit smarter for the experience. This is the first video in a long time I understood why the "worst" was better than the "best" before the explanation; even with this being the first time I've heard of intransitive dice.
Decades of board game logic has finally paid off!
I'm starting to think that I'm not the target audience for these. I didn't really understand why you would rank the dice in the first place, it was pretty obvious that doing that made no sense.
A has a higher probability of winning compared to B, B has a higher probability of winning compared to C,... and so on so forth. People often associate this model with transitive property since we pretty much use it throughout our lives. For example, a grandmaster has a higher probability of winning compared to an international master, an international master has a higher probability of winning compared to a nation master, a national master has a higher probability of winning compared to a beginner, therefore a grandmaster has a higher probability of winning compared to a beginner. They have the same structure, they both rely on probability and there doesn't seem to be any discernable differences. If you mind doesn't jump to this structure right away then you're mental slow.
"You *Most likely* will not rationalize this paradox" I figured everything out in less time than you took to finish the game....
What makes it intransitive is the fact that what matters is whether it's bigger or smaller, not by how much.
Another term for this paradox: *Rock Paper Scissors Paradox*
So basicly this is "rock, paper, sissors" with 4 choices.
Instead of thinking in straight lines, just think of it as a circle.
Nah look at the pinned comment
no rock paper scissors is circular, what makes it beautiful is that clearly in each match-up the higher number wins but still somehow NOT, it does not make sense EVEN though IT SHOULD, a freaking PARADOX.
@@yashbaviskar6458 rock paper scissors is circular only because it has 3 choices. There is not way doing this non-circular with just 3 choices if you want for every option to be able to win agains at least one other. So it IS just like rock paper scissors, 'circularity' has nothing to do with this.
@@XQgint the problem with this is that this game doesn't have just 3 options. Yes it has 3 dice, but each of those dice have 6 sides, with seemingly random values, for a total of 18 sides. I promise a game could be made in the spirit of rock paper scissors that mirrors this game almost perfectly.
Pokemon is probably the best example, there is no best pokemon, just as there is no best dice.
Also Mario party uses these dice, and allows the player a balanced dice, or a risky dice to move around the board. I opt for the balanced dice, unless I know that dice will not give me a probability of landing on the square I desire, and instead use the more risky dice, hoping for the high or low number depending on distance.
It's just a loop and whoever goes first loses essentially. A>B>C>D>A....... and on and on and on not complicated to grasp at all.
I view this as me having the weakest gear in a rpg game vs an extremely challenging boss and somehow winning.
My IQ goes up by .1 everytime VSauce uploads
Remember, learning makes you dumber
Yes
True
@REPORT BOTS ON YT!!! jeez chill it’s youtube
Soon we can celebrate when you hit 100!
I guess that they just arent transitiv. If a is in a relation with b and b with c than it doesn't mean that a is in a relation with c.
Now let the relation be "wins more often against" and we get "a wins more often against b", "b wins more often against c" but that doesn't mean that "a wins more often against c" because the relation "wins more often against" isn't transitiv.
Edit: I was correct.
This is like playing rock paper scissors, but knowing what the other person picks...
It's like playing rock paper scissors but you know what your opponent chooses before you choose
Me, who has seen Numberphile's video about these dice:
Yeah, I know where this is going.
Also, no one is gonna talk about A vs C or B vs D!?
yeah the correct move would be to compare each combination of the dice choices to see the full picture, rather than making assumptions illustrated in the video
That's what I want to know.
It would be better if A vs C was a 50/50 odds like with B vs D, but it's a hard balance. Also if the video started out with the complicated dice first.
vsauce: Right?
me: oh no not aga- “ok let’s play again”
me: *visible confusion*
He had us on the first half. Ngl
I actually think it was easier to see 'why' with the first set of dice, although the same argument applies for the second set of dice.
Think about it this way.
A vs B:
When A rolls 4, it beats everything B can roll, which happens 4/6 times. 4/6 > 50%. Hence A > B
B vs. C:
When C rolls 2, it loses to B, which happens 4/6 times. 4/6 > 50%. Hence B > C
C vs. D:
If D rolls 1, C automatically wins. This happens 3/6 times = 50%. So 50% of the time, C already wins. Furthermore, D only beats C, when D rolls 5 and C rolls 2, which happens 3/6 * 4/6 = 1/3 of the time. Hence C > D
A vs. D:
If A rolls 0, D automatically wins. A can only win if A rolls 4 and D rolls 1. This happens 4/6 * 3/6 = 1/3 of the time. Hence D > A
"Poor, predictable Bart. Always picks rock."
"Good ol' rock, nothing beats that."
He sounds like my cousin who always ends his sentences by “I’m not crazy right?”
I’m sorry, I don’t see how this is a paradox at all. You keep insisting that there is a best dice and that the relationship between the dice is transitive but you never go into detail as to why we should assume that outside of “our brains kinda naturally want to assume that”. As someone who’s played a lot of pokemon I’d never make either of those assumptions.
It’d be like me saying that charizard is the best because he’s a fire type and his attacks will be super effective against grass or ice pokemon. If you think that charizard beats venasaur and venasaur beats blastoise so therefore charizard beats blastoise, then you are not gonna make it to the Pokemon league.
Just like there’s no best type of Pokemon, there’s no best dice that will always have an advantage. I don’t see why you’d go into the game with the assumption that there would be a best dice.
Exactly. Now, Charizard DOES have Thunder Punch, akin to how the dice have small chances to win anyway. Though, Blastoise could survive and still win.
Yeah, while my mind didn't go to pokemon(I am a fan of pokemon, maybe subconsciously I thought about it or something), but I just imagined it as a circle, a>b>c>d>a... it's very simple to grasp this concept
I feel like this is really easy to grasp. It’s like Pokémon starter types and how they have an advantage against each other. Fire is super effective on grass, grass on water, and water on fire.
Almost immediately before Kevin went into any of the transitive stuff I said "this is just gerrymandering with fewer steps." It's not totally the same but it's the same part of my brain that made it make sense. And I think seeing this would improve comprehension in people who struggle to understand gerrymandering. Annoyingly though I can't put my finger on their exact mathematical connection, and I'm too old to furiously work it out like I'm back in calculus haha