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

why the end though

KEANO. KEANOUGH. KEANEU. KEANU.

That pizza theorem shirt is amazing.

0:30 Fair is when you jump to an inhuman height and thrust your leg forward with such force that your knee holds a deadly electric charge for a split second.

</showmeyourmemes>

Your best friend is breathtaking.

"The game that's totally fair but unfair" you mean capitalism?

That a Nerd city collab?

What if the players chose anonymously and revealed only after both were locked in? (Repick if match.)

I’m sorry, but I have to go check out those hot shirts before I finish watching this video. I brb

Those shirts are sick I love the look, now if only i didnt exclusively buy shirts at discount stores for 5$ max…

Key ano reeves

Rule change: you have to choose your sequence by pulling cards at random.

I mean it's still non transitive but you can't rig it for yourself.

Numberphile had a sequence video a few months ago with a similar concept.

We had lecture in maths class that touched on transitivity. Great to stay relevant to me.

Earned a sub Kevin!

Anyone watched this on Numberphile? https://youtu.be/Sa9jLWKrX0c

Should’ve made Stephan Karl Stephenson an ace for #1

Ok but where can I get the cards?

6:25

Keanu: Aight imma head out

Please more posters

That's called…. Strategy

CARSON IS BACK!!! WOWOWOWOOWOWOWOOWOOOOOOO OWO.

Even if Kevin can't sell the Meme Cards, I STILL WANT THEM!

What's basically being done is that you pick the first two colors of the opponent as your last 2. And by the time the opponent even has a chance to win, you could have already won if the 3rd last card was your first color.

c r y i n g c a r s o nWhy are you calling Cr1tical Keanu Reeves?

Do it with heads+tails or people will assume you're stacking the deck. 9/11 did no steel beams.

Ok, non-transitivity and stuff, but I don't feel like you explained WHY certain sequences beat others at all

I WANT THOSE CARDS😍😍😍

5:01 how Ariana grande like her men

These designs are pretty nice good job Kevin 👍

YouTube: i suppose you’re all wondering why I gathered you here today

when vsauce99 is going to appear?

Very disappointed that you didn't explain why the sequences can be better/more likely, ultimately making this video completely pointless.

I enjoyed this a lot more than the pasta chair. (I half expected Dr James Grime to turn up, as a non-transitive expert.)

Vsause 3 is the only real vsause anymore

What if players choose their sequences in secret?

Why does he keep pronouncing Keanu as “Keano”

imagine flipping a coin to make a difficult choice and its just about as unsure as you are

So I need clarification because one thing he didn’t describe was how/why a certain combination “beats” another combination. Now, it seems to me that it has to deal with the fact that the cards

aren’tbeing replaced, which is why the RRR and BBB combinations are the worst. But this fact seems like it was downplayed when he first introduced and almost seemed to not impact it at all instead of being the critical factor into why this game works. If I did this with a random number generator, I would expect any combination to be just as likely, regardless of who picked first.There was a numberphile video on this some months ago 🙂

Wanna play 52 pickup?

Yes, love the ending!

The Paul brothers play this game

Omg a Dwight coin

the meme cards are another method to save memes for later generations if they ever were to create article 14 or something that's supposed to specifically target memes… not giving the fbi and probably the 2000+ viruses that I may or may not have installed an idea, just stating the possibility.

“What is Fair?”

It’s a shorter way of saying

FORWARD AERIALPlease Please Kevin, you're driving me crazy. it's Key-ah-noo not Key-ah-noh

Damn its complicated af

Are we rick rolled at 4:52? For RBR?

Are we going to ignore that Walter Penney made a coin-flipping game?

Essentially, Player 2 will only "lose" if Player 1's pattern is drawn at the start of the game. Otherwise Player 2 will win or it will result in a draw. It's easier to explain this by saying the point of winning is to get a pattern. So Player 1 wants ABA, so when there is 2 Bs their pattern restarts, so Player 2 playing BAB means they will get Player 1's pattern prior to finishing the set if the first 3 cards are not Player 1's set.

Meme cards

You mean Uno

The most unfair game

Vsauce

Phil swift

some guy that looks like Keanu reeves

The best meme musketeers

"The Fair Game That's Totally Unfair"

visible confusionYou are breathtaking!

I know of a similar game that can be won like this. The idea is to lay out dozens of tokens that two players take turns removing 1, 2 or 3 of at a time. Whoever takes the last one loses. However, I've found that whoever leaves 5 tokens will win. So in play you want to want to make sure you have 2+(3×n) tokens at the end of your turn. Could make for a similarly fun vid?

E. Coli:

watches this videoE. Coli: welp, guess I'm immortal now

There are lizards who live in a non-transitive way.. they come in three colors. Red, blue, and (some other color I don’t remember… might have been yellow)

I prefer playing rock paper scissors. The odds of winning when I get to pick second are much better than in this card game.

I miss the old clips at the end of the video, about how people in the past thought the future would be.

This is why when someone says BRB you

haveto reply BBRHOW?

BECAUSE

me: Oh ok cool

clicks off videoI want the meme cards pleaseAt first i was thinking meme cards? really? but then as the video progressed i realized how amazing they are.

Impossible.

Matt parker already did this

I want these cards soo much

7:31 you wrote R in black

I absolutely need this deck of cards

Now that's gamer science video

I miss your long form videos

Like the jump game that you don’t jump

Don't get me wrong the meme cards are cool and all but I NEED a link to the Fact/False coin.

I no see MØTH meme me sad

This game is very clearly only unfair because of the rule that player 2 can see what player 1 picks before they pick their own combination. It's like playing rock paper scissors but one person gets to see the other person's choice before making theirs. If neither player could see each others' hand before picking their own, then the game would be perfectly fair.

Wanting anything over tacos should be a crime punishable by death.

Shouldn't BRR beat RRR 7 to 1? The only way RRR shows up before BRR is if the 3 first cards are red, which amounts to 1/8 chance.

Edge???? NO GAME NO LIFE???

i want the Carson card

I was hoping you'd go into the statistics of why some patterns defeat others

I just watched a 12 minute video explaining if the second player gets to pick after the first in rock-paper-scissors, the game is unfair.

If only all math classes presented the lessons like this

10:05 i belive upper left is wrong, it should be 2:1

And why changing the second card and putting in the beginning, makes it better?

The most important he doesn't explain

I want to buy the meme cards

Vibe check

Getting some strong boomer vibes from those meme cards Mr. Sauce

Could you please, send this meme deck to me?

You could always win R/P/S too if you get to see what P1 chooses prior to making your choice.

If BOTH players choose their sequence prior to playing then the information required to gain an early advantage remains concealed.

No one:

Absolutely no one:

Kevin: Right? WRONG!

Normal video about a fun little phenonemon.

Suddenly:

Bacteria play rock paper scissors to multiply!

PDF templates of the meme cards ARE NOT illegal, as long as you're not selling them.

EDIT: If at all possible, can we get a link to the meme card pdf

Your red light looks too bright.

@Vsauce2 Thank you so much for this video. The concepts presented in this video have real world implications outside of the bacteria you mentioned that I plan to apply in my work life.

As the lead ITSM developer at my company, it's my job to understand approval processes from end to end. One of the biggest impacts to that process that I've seen is when people start noticing the "power level" of the other approvers compared to them. For example, even though an emergency IT change request requires 3 manager approvals (all of whom are equal voters according to the approval engine watching the whole thing), if the VP of IT approves first, all of the other managers would see that and automatically assume that their vote no longer matters and that the VP of IT will always beat out any other approvers (transitive property).

By shifting certain approval processes to a non-transitive method (where it makes sense), I'm actually able to obscure the true "power level" of each of the individual approvers. This allows me to create a seemingly more fair approval process up front. THIS IS POWERFUL STUFF FOR ANYONE WHO DEALS WITH ITIL ON A DAILY BASIS.

8:14 JoJo's powerscaling video?

This game is not fair at all because P2 can choose sequence AFTER knowing that P1 chose, and NOT vice versa. P2 has more information than P1, so it's natural for P2 to win more.

BBC meets BBW

( ͡° ͜ʖ ͡°)

MATH make America think harder

I may be just a simple man, but the gamer in me says its just smart to make your select manifest before the opponents.

If they Pick BRB then i want XBR with X being either B or R. its only later do I realize the advantage of going BBR in this particular example. Simular how how the price is right people will say a single cent or dollar over or under the previous guy to cut them off.

Clearly, Keanu Reeves' cardboard likeness does not want to be part of your video…