# The Card Game You Can Almost Always Win

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

VS2: Sissors

Me: SKISSORS

I always watch Kevin explain because it’s very interesting! Keep it up!

Hold on, I'll

brbbet this guy gets all the girls and then gets bored with them…

Does this work with only 32 cards?

Dammit I just lost the game

How to make the game fair. Both players must show their choice at the same time

in a horribly sad nightmare dimension, Vsauce2 videos never get seen by anyone, and he's just talking to himself and explaining things and talking to props…because there is nothing and no one else. Its just him, alone with whatever he can find to personify or amuse himself with. That thought just occurred to me… I'm glad I'm in this dimension. I'm glad he is too.

"I have a deck of meme cards."

Wer kommt von Pietsmiet?^^

Would loved the explaination for the odds but thats a pretty cool trick

He could've explained why this sequence ist more probable than the other…

but WHY is RBB that much better than BBB? if you have a red on the table there is a 25% chance to get BB, and if its black the chances are also 25%.i just dont get that.

10:08 Why RRB beats RBR 3:1, but the exactly opposite BBR beats BRB only 2:1?

Jemand von Pietsmiet hier ? 😂😂

Wer ist auch wegen Brammen hier xD

I saw crying Carson

Why is Thanos queen lol

You, sir

i like your card deckactually with the cars they can neither land face up so it's red or black or face down so you don't know what color it is so there's more than just a 50-50 chance

So…the player 2 advantage comes from the additional information they have.

If both players were unaware of each other's choice, the game would be fair.

is he saying keano lol?

K E A N O

it's like a game of rock paper scissors where the players pick their move in sequence rather than simultaneously.

How'd you get Keanu Reeves to agree to join?

Where's the math?

Thanks for showing us the trick, but why does it work?

hihihi, crying Carson :>

10:06 if you want to see the flow chart.

Hi,

this is a nice card-game. But i think there's something wrong with the 7,5 : 1 combinations. Checked it empirical with a simple c++ code and ist should be 7 : 1. I didn't calculate it yet…

i dont want the woven match i want the fukin meme cards

I have just one question…where can I buy that card deck? XD

It was funny when he pulled a vsauce meme

Bacteria plays Rock Paper Scissors to multiply.I never thought I would hear bacteria in such a random sentence lol

SSSSAAAANNNNEEEEEESSSSSSS

Me: The perfect card deck doesn't exis-

This video: Hehe Meme cards

So, at a bar, you play with someone ten times, each taking turns choosing first. When your opponent chooses first, the odds will be stacked in your favor. When you chose first, they should be even, more or less, assuming he doesn't accidentally pick the secret method.

In ten sequences, you should have time to make a profit.

If I'm player 1, how do I improve my chances of winning?

Yep John wick is coming to get you after you made him lose

what if when the players choose their configuration they don't know which the other has and it's revealed when the cards are being revealed?

Pokemon is non-transitive.

NNNOOOOOOOOOOOOO!!! I don't care how "MATHY" or "THEOREMY" It is, a pizza should NEVER – i repeat, NEVER be cut like that!!!

Yas. Thanos is a queen

Why does he look like a Mexican drug dealer.

5:46 VSauce xD

Where can I get those meme cards?

Ok boomer

Where can I get a deck like this for memory training?

1:23 Heh, crying CARDson

MEME CARDSWho else wants the cards?

But Vsauce2, I ask of you the most troubling question…

If you cannot sell meme cards, would it be possible if you could make a template for them, so people can produce their own?

The super need in me enjoys Thanos being the Queen of Spades

The Kakegurui twin game

did i see. . . SANS UNDERTALE!??!

Me:i like red

My black friend: 50/50 thats equal

Can you guys make an actual meme deck

3:21 MEGALOVANIA INTENSIFIES

Hey btw your chart of cards said RRB beats RBR 3:1 times but that is impossible because BBR beats BRB 2:1 times.

Finally a

perfectly balanceddrinking gameIsn't their a way to run out of cards in this game?

He actually included the VSauce meme 😂

I can’t believe Carson is black

What if you play with 2 or 4 cards?

Kevin! More Mind Blown in 2020 pls! 🙂

Also love all your videos man keep up the good work.

Best wishes for 2020!

And why exactly does the second player needs to wait for the first player to choose? They can make their choices simultaneously!

So it's like tic tac toe

Taking this game, adding alcohol, when you loose you drink for each card flipped so far

He turned over a meme card and it was vsauce don’t think that is wright

Keano

Okay

BUT I WANT THOSE CARDSSS

0:13 when u ask your mom why anything

Pokemon starts with an example of a non transitive game

But I need the meme cards.

Card games you say, seems fair but isn't you say,

Casinos: I'll keep this one in mindCarson!!

is one of the juniors is baby yoda?

You didn't even explain how it works….

Man discovers what memes are and proceeds to make video to showcase them (2019, Colorized)

Who doesn’t want Kevin as their high school math teacher

9:04 I'm kinda proud that I saw that coming

I know a way to beat my friends in Rock Paper Scissors tell them to pick Rock they think u will get paper so they take scissors you pice rock if u know their smart then pick Scissors

Which is better in your opinion?

Vsause2 = like

Vsause1 = comment

Thank you for this scam

Instructions unclear, threw cards at people on street. I'm being detained. Help.

So, if I understand, to make it fair you’d just have both players choose sequences without seeing the other players?

Keanu: "Be right back"

Time to win bets against old people that don't know what a Vsauce is and if it tastes anything like barbeque sauce

Kevin: Black Black Black

KKK: That's illegal!

4:58 would be funny if you insert the "we'll be right back" meme

С моим уровнем английского я понял ток что надо поменять цвет средней карты и переместить её на начало, тогда вин))

Hello unless

I N S E R T V S A U S E M U S I CNice coin

where did you buy these cards?

Why Thanos is Queen and not King?

My grandpa: I dont want red red red or black black black

Me: why not?

My grandpa: you wouldnt get it

I don't know why every time I see a card-related video from Vsauce I think if the anime Kakegurui

He turned Keanu into pewdiepie

But why is the game like that tho

Right?WRONG