Vsauce! Kevin here, with a homemade deck of 52 meme

cards to show you a game that should be perfectly fair… but actually allows you to win most

of the time. How? BECAUSE. There’s a hidden trick in a simple algorithm

that if you know it, makes you the overwhelming favorite even though it appears that both

players have a perfectly equal 50/50 chance to win. Well, that’s not very fair. What is fair? We can consider a coin to be “fair” because

it’s binary: it has just two outcomes when you flip it, heads or tails, and each of those

outcomes are equally probable. Although… it could land on its edge… in

1993, Daniel Murray and Scott Teale posited that an American nickel, which has a flat,

smooth outside ridge, could theoretically land on its edge about 1 in every 6,000 tosses. But for the most part, since the first electrum

coins were tossed in the Kingdom of Lydia in 7th century BC, they’ve been pretty fair. As are playing cards, like this deck of hand-crafted

meme legends. When you pull a card, you get a red or a black

card. Crying Carson. It’s perfectly binary, and there’s no

way for a card to like, land on its edge. It’s either red or it’s black. It’s 50% like a snap from Thanos. Given that, is it possible to crack the theoretical

coin-flipping code and take advantage of a secret non-transitive property within this

game? Yes. Welcome to the Humble-Nishiyama Randomness

Game. But before we get into that. Look at my shirt! I’m really excited to announce the launch

of my very own math designs. This is Woven Math. The launch of my very own store bridging recreational

mathematics and art. This is the Pizza Theorem. These are concepts that I’ve talked about

on Vsauce2 like this Pizza Theorem or also the Achilles and the Tortoise paradox. And my goal here is to take cool math concepts

actually seriously and create soft, comfortable shirts I actually want to wear. So there’s a link below to check them — this

is the first drop ever there will be more to come in the future — but I just really

like the idea of blending clean sophisticated designs with awesome math. And these shirts just look cool so that when

you wear them people ask, “What is that shirt?” and then you get to explain awesome math concepts

like Achilles and the Tortoise or The Pizza Theorem. So I think it’s great, I think that you

will too, check out the link below now let’s get back to our game. Walter Penney debuted a simple coin-flipping

game in the October 1969 issue of The Journal of Recreational Mathematics, and then Steve

Humble and Yutaka Nishiyama made it even simpler by using playing cards. The first player chooses a sequence of three

possible outcomes from our deck of cards, like red, black, red. And then the second player chooses their own

sequence of three outcomes. Like black, black, red. And then we just flip our red and black meme

cards and the winner is the one whose sequence comes up first. So in this example, thanks to Guy Fieri, player

one would’ve won this game because player one chose red, black, red. Here’s a little bit of a nitpick. Because we’re not replacing the red and

black cards after each draw, the probability won’t be exactly 50/50 on every draw — because

each time we remove one colored card, the odds of the opposite color coming next is

slightly higher — but it’ll never be far from perfectly fair, and as we play it will

continue to balance out. So given that each turn of the card has a

roughly equal chance of being red or black, and given that the likelihood of each sequence

of three is identical, the probability that both players have an equal chance of winning

with their red-and-black sequences has to be 50/50, too, right? Wrong — and to demonstrate why I’ve invited

my best friend in the whole wide world. Where are you best friend? Keanu Reeves. Ah, alright. Keanu, you’re a little tall. Hold on. How’s this? Okay, Keanu will be player 1. There are only 8 possible sequences that Keanu

can choose: RRR, RRB, RBR, RBB, BRR, BRB, BBR, and BBB. No matter what Keanu chooses, the probability

of that sequence hitting is equal to all the other options. For player 1, there really is no bad choice,

one choice is as good as the next. So let’s say Keanu chooses BRB. Great choice there, Keanu. Now that I know your sequence, I’m going

to choose BBR. Okay, now we’ll just draw some cards and see

which sequence appears first. Red, Tommy Wiseau. Some red Flex Seal action. So far nobody has an advantage. Black, where are you fingers? Uh oh. Sad, sad Keanu. You should be sad once you realize that now

there’s no way that I can lose. Because of having these two black cards in

a row, even if I pull five more black cards in a row, eventually I will get a red and

I will win. Ermergerd. Ah hah. There it is. Minecraft Steve had sealed the victory for

me. Sorry, my most excellent dude. But I win. Because regardless of what player one chooses,

what matters is the sequence that player 2 picks. As player 2, the method here is very easy

— I just put the opposite of the middle color at the front of the line, so when Keanu picked

BRB, I changed his middle R to a B, and then put that in the front of my sequence. So I just dropped the last letter and my sequence

becomes BBR. I’ll show you another example. If Keanu had chosen red, red, red. Then I would’ve just changed that middle R

to a B, put that at the beginning of my sequence, drop the last R, and my sequence would be

BRR. Just that little trick allows me to have an

advantage anywhere from about 2 to 1 up to 7.5 to 1. Which means in the worst possible scenario

for me, I win 2 out of 3 times. And in the best, it’s nearly 8 out of 9. Look, I’ll write out all the choice options

and their odds. As Player 2, when we apply the algorithm we’re

jumping into exactly the right place in a cycle of outcomes that Player 1 doesn’t

have any control over. The best Player 1 can do is choose an option

that’s the least bad. How is this possible? How can I take something so seemingly fair

to both players, so obviously 50/50, and turn it so strongly in my favor? The key is in recognizing that this game is

non-transitive. So there ya go.The end. Wait… What is transitive? Think of it this way: you’ve got A, B, and

C. A beats B, and B beats C. Therefore, A beats C. Because if A beats B and B beats

C then obviously A can beat C. That game sequence is transitive. So like if you and your Keanu had transitive

food preferences, you’d rather have Pizza than Tacos, and you’d rather have Tacos

than Dog Food. You’d also rather have Pizza than Dog Food. Simple. If you and Keanu somehow preferred Dog Food

to Pizza, then all of a sudden your food preferences become non-transitive. In a non-transitive game, there is no best

choice for the first player because there’s no super-powered A. Instead, there’s a loop

of winning choices… like rock, paper, scissors. In rock paper scissors, rock — which we’ll

call A — loses to paper, which we’ll call B. B is better than A. But A beats scissors,

which is C. So A is better than C. But B loses to C, so C is better than B, and

paper B beats rock A, so B is better than A. Scissors C loses to rock A and beats paper

B — and we’ve got a loop of possible outcomes that goes on forever, with no one choice being

stronger than the other. That’s non-transitive. Since we’re in the flow chart mood here’s

a flow chart that illustrates the player 2 winning moves in the Humble-Nishiyama Randomness

game. So if you follow the arrows you can see that

like RBB beats BBB and like BBR beats BRB. And so forth. With the odds added, you can clearly see how

some sequence scenarios go from bad to worse. In the Humble-Nishiyama Randomness variation

of Penney’s Game, we know what sequence of card colors player one has chosen first,

so we can jump in the most advantageous part of the non-transitive loop and make a choice

that gives us a significant advantage. By recognizing that the game is non-transitive,

we take seemingly-obvious fairness and find a paradoxical loophole that nearly guarantees

us success. To everyone who doesn’t recognize the intransitivity,

it just kinda looks like we’re extremely lucky. And why does all of this matter? Because bacteria play rock paper scissors

to multiply. Benjamin Kirkup and Margaret Riley found that

bacteria compete with one another in a non-transitive way. They found that in mice intestines, E. coli

bacteria formed a competitive cycle in which three strains basically played a game of rock

paper scissors to survive and find an equilibrium. Penney’s Game and its variations illustrate

how even a scenario that seems perfectly straightforward, like unmistakably simple, should never be

taken at face value. There’s always room to develop, strategize,

and improve our odds if we put in the effort and imagination required to understanding

the situation. And that truly is…breathtaking. And as always — thanks for watching.

I can't sell the meme cards but I hope you enjoy Woven Math! Wrap your body in sweet, sweet knowledge. https://represent.com/store/vsauce2

nice video

But you didn't tell why rearranging the pattern helps. Did those sequences just happen to defeat each other in a specific way ?

I love you for making Elon Musk and Pewds as Kings

What's the name of the ending song before the merch shirts song?

Kiano

5:43 i love how aware Vsauce 1, 2, and 3 are about the fact that they're memes XD

Haha I like crying Carson too

Meme cards! 😂❤️🇵🇭

Vsauce 1 and 3: come back in 2019

Vsauce 2: Still been here this entire time

P i z z a s h i r t

Damn, sans is getting added to everything these days.

Oh no, you're starting to morph ino Micheal, soon I won't be able to tell you apart

Playing a fair game deals ALOTTA DAMAGE!!!!!

I'm more interested on the playing cards, can I get those?

Subscribe to CallMeCarson on YouTube and Twitch

9:05 i knew he would say that.

“Great choice there, Keanu”

Thanks, Kevin😎

I’m really enjoying this Keanu Reeves popularity. It’s nice hearing my name😅

I love the outro song

I was expecting a Keanu pun at the end. A little disappointed the haha

why RRB beats RBR 3:1 but BBR beats BRB 2:1 ?

I work in a pizza place so if i were to wear that pizza theorem shirt everyone would love ot

I just watched the recent LQG episode on PBS spacetime, and now I want to know: Can we simulate spacetime through non-transitive gamelogic and maybe the amount of variables which stringtheorie suggests as dimensions?

I waited the whole video to hear that "breathtaking"…

How to win Rock, paper scissors every time ?

How is no one talking about how Vsauce2 got the internet's boyfriend on the show!?

Kevin: As Player 2 here, the method is very easy.

Sprint guy: Isn’t it nice when you keep things simple?

Me, not currently looking at the screen: Yes, it i- Hey you’re an ad!

11:39 That truly is breathtaking

I see what you did there 👹

as a furry i prefer dog food

Damn I Still have no idea what he's talking about

hOW DO YOU BRAKE rOCK pAPER sCISSORS ?

I guess you could make it so that each player has to write it down secretly at the same time… or do that, but then make it so you are deciding your opponents sequence, and vice versa

wat

haha funny

Can someone please explain the top entry (BBB vs RBB) in the table of odds in favour of P2?

By that I mean that the odds when P2 counter picks RBB vs P1's BBB are 7.5:1 when it should be 7:1, as the only way P1 will win is if 3 Black cards are dealt right at the beginning, as if a red card is drawn in any of the first 3 cards it would be a theoretical win for P2

This means player 1 has a 1/8 chance of winning so the odds should be 7:1 not 7.5:1.

Are these odds based on the fact that there are only 52 cards in the deck and there is a small chance that the game ends in a tie? And if so, would the odds be changed back to 7:1 if this game was played with rounds of coin tosses instead of cards?

Or am I missing something here in my calculations?

6:25

RIP Keanu Reeves… 😭😭😭😭😭😭😭

I thought your best friend was Yoda

You're breathtaking!

yo shirt is cool an all but where can a guy get the meme card deck?

How to make the game fair: just have both players choose at the same time like Rock Paper Scissors. By the way this game is garbage.

2:42 sadly my cladsmates give a * about math

time

Because Bacteria play rock paper scissors to multiply

This was very specific

What about 4 cards sequences ?

I like that PewDiePie is the king

If I knew about this in jail… I could've made so much ramen.

buys math shirtdoesn't watch corresponding video"Hey, what's your shirt of?"

"Oh yeah, it's….. uh….."

Vsauce 2 is just jesse reforming his life after breaking bad

hahaha crying Carson

The solution for P1 is to just propose to write down your chosen pattern on a paper first before starting the game. That way P2 has no chance of knowing what pattern P1 chose and therefore would also have to guess.

crying carson be like:

criesF

8:25

How dear you Kevin? you killing keanu reeves???????????????????????

Someone else remember that voice from the cartoon with Charlie Brown?

I would or really liked you to explain what was actually going on more than just saying the game is nontransitive. like why is it nontransitive and why is BBR a better choice than RBR to beat BRB/BRR

your opponent is breathtaking

Doesn’t anyone here think that Jake

looks

Like

Jessie pinkman from breaking bad?

I miss the old Vsauce2 video styles like "The Invention Of Blue" and "The Planet Behind Your Eyes" instead of these game/puzzle videos.

point at kevinYou're breath taking !When you lose in card game and realized that you are being cheated on seeming fair card game 👀👀👀

It would be fair if neither player knew what the other's sequence was until they started laying out the cards

On behalf of our Lord and Savior John Wick, please stop calling Keanu “Keano”

10:05 How can it be that BRR beats BRB with a 2:1 ratio, meanwhile RRB beats RBR with a 3:1 ratio? Shouldn't it be the same probability, since it's the same sequence just with flipped colours?

Does it become fair if both players reveal their choices at the same time?

Sounds a little like mumkey Jones / simian Jimmy. Same vocal cadence.

God I love when he yells “WRONG!” like that

I guess this is why we have a base 4 genome, and not base 2.

And why the start codon is made of 3 different bases (AUG). Had it been AGA for example, 2 point mutations prior to AGA can move the codon back and start translation prematurely.

Is beanos there

With a shaved head and no glasses you could totally pass as a Jesse Pinkman look-alike

Me is a cool video and the back of my brain where the heck and I get the card deck

The real trick is to know what player 1 did before it's your turn. The transitive / non-transitive thing does not matter at all. For rock-paper-scissors, if you know what the other player chooses beforehand, you can also always win.

Is it weird everything that I watch i would have done like 3 days before at most

(Unless we talking einstein mega super science)

So… all you have to do to make the game fair is to choose sequence at the same time, or just not reveal it until both has chosen? Since it's entirely based on player 2 knowing both the trick and player 1s sequence, seams like a easy workaround to make it perfectly fair then.

Still… having knowledge of how to turn a fair game so very tiled in ones favor might come in handy sometime….

@Vsauce2 I'm not happy with this video for the reason recently mentioned by @Vsauce in the video named Laws And Causes. You did explain that the behaviour we see is called Non-Transitivity but you failed to explain the cause of that in this specific case. Looking at your chart near the end, I still do not know

whythe odds are they way you drew them.Keanu, not Keano!

THE CARD NUMBERS ON THE TABLE ARE A SECRET MESSAGE!

Dude seriously though, that's a glorious deck of cards.

What if you added more players?

too many memes.

damn, anybody hoped that he was selling the meme cards as well?

So, is the game fair or not?

Kevin: Well yes, but actually, no

How can you know that a game is transitive or not ?

And how do you calculate the odds of "duels" of triplets of cards ?

Uganda Knuckles always wins

"I can't sell the meme cards"

DON'T YOU DARE OPPOSE ME MORTALI have a question: the advantage appears when the second player knows in advance the choice of the first player. What happens if player one and two have to blindly choose the sequence and then communicate it at the same time? Does the advantage still appear (as in tic tac toe, where I know for sure that I need to begin with a corner or the center)?

Even if your opponent wasn't picking to counter pick you, wouldn't three of the same color always have a disadvantage, making this game unfair from the start?

For why, if you take three of the same color, there are two points at which you can fail the streak, at zero streak, at one and at two. Basically you can completely reset to zero progress at any point in the streak. Unlike red black black, which can only go to zero progress from zero. Once a red card has been played, the furthest you can go back is to one red card. And even red black red (and black red black) should have an advantage over full one color, as the only possible full resets are at zero and two cards, as picking Red means you are always two cards away from winning, but picking two blacks in a row would reset you. Red red black and black black red can't completely reset after a streak of two, meaning winning is always one coin flip away after you get two correct. Basically every combination of cards has an advantage of some kind in terms of chain breaking points, except for pure one color which can break at any point.

If someone knows why my thinking is wrong, feel free to tell me. I just can't currently see a flaw in that thinking.

When Kevin has a 50/50 chance of properly pronouncing Keanu's name every time he says it. "Kee-Aw-New" vs "Kee-Aw-No"what are the odds that Kevin chose Keanu to be his celebrity friend just so he could make the reference at the end?

I study computer sciences at an university and nobody explained transitivity as simply as you did, Kevin. Never thought of "liking food" and rock, paper, scissors to be such great examples for transitivity and non-transitivity!

Where's your classic red shirt?

No Game No Life

in a nutshellI NEED THOSE MEMES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

i can win rock paper scissors everytime by choosing rock

rock beats scissors and scissors beats paper

so rock can beat paper and scissors

this video and that deck would be impossible if vscauce was in england

Gotta admit, that was interesting.

Ok then now find a strategy in Snakes and Ladders

Wait according to my calculations, the RBB to BBB and BRR to RRR win ratio should be 8.5:1.

I could be wrong so please correct me if I am.

That's why folks Sora and Shiro of No Game No Life wins the games that they play

I was expecting at some point to hear "the odds be ever in your favour"…