You and a fellow castaway

are stranded on a desert island playing dice for the last banana. You’ve agreed on these rules: You’ll roll two dice, and if the biggest number

is one, two, three or four, player one wins. If the biggest number is five or six,

player two wins. Let’s try twice more. Here, player one wins, and here it’s player two. So who do you want to be? At first glance, it may seem

like player one has the advantage since she’ll win if any one

of four numbers is the highest, but actually, player two has an approximately

56% chance of winning each match. One way to see that is to list all

the possible combinations you could get by rolling two dice, and then count up

the ones that each player wins. These are the possibilities

for the yellow die. These are the possibilities

for the blue die. Each cell in the chart shows a possible

combination when you roll both dice. If you roll a four and then a five, we’ll mark a player two

victory in this cell. A three and a one gives

player one a victory here. There are 36 possible combinations, each with exactly the same

chance of happening. Mathematicians call these

equiprobable events. Now we can see why

the first glance was wrong. Even though player one

has four winning numbers, and player two only has two, the chance of each number

being the greatest is not the same. There is only a one in 36 chance

that one will be the highest number. But there’s an 11 in 36 chance

that six will be the highest. So if any of these

combinations are rolled, player one will win. And if any of these

combinations are rolled, player two will win. Out of the 36 possible combinations, 16 give the victory to player one,

and 20 give player two the win. You could think about it this way, too. The only way player one can win is if both dice show

a one, two, three or four. A five or six would mean

a win for player two. The chance of one die showing one, two,

three or four is four out of six. The result of each die roll

is independent from the other. And you can calculate the joint

probability of independent events by multiplying their probabilities. So the chance of getting a one, two,

three or four on both dice is 4/6 times 4/6, or 16/36. Because someone has to win, the chance of player two winning

is 36/36 minus 16/36, or 20/36. Those are the exact same probabilities

we got by making our table. But this doesn’t mean

that player two will win, or even that if you played 36 games

as player two, you’d win 20 of them. That’s why events like dice rolling

are called random. Even though you can calculate

the theoretical probability of each outcome, you might not get the expected results

if you examine just a few events. But if you repeat those random events

many, many, many times, the frequency of a specific outcome,

like a player two win, will approach its theoretical probability, that value we got by writing down

all the possibilities and counting up the ones for each outcome. So, if you sat on that desert island

playing dice forever, player two would eventually

win 56% of the games, and player one would win 44%. But by then, of course, the banana

would be long gone.

Why is p2 a furry?

The chance for player 2 to win = the chance one dice is 5 or 6 (1/3) + 1/3 of the remaining 2/3 for the other dice being 5 or 6 = 5/9

That's how I did it, it's just more confusing to explain.

It's the saddest thing I've ever seen its just a ba and a na

Wouldn’t this work no matter what 2 numbers the second person picked.

If you make it so player 1 wins if the highest number is 1, 2, 3, or 5 and player to wins if it's 4 or 6, they'll each have a 50% chance of winning.

Also, if you use dice with sides that are divisible by 4, you can give the lower 4th and the upper 4th to one player and the middle half to the other and they'll both have a 50% chance of winning.

Just eat the darn cat. Asians do it

Cat don't eat bananas

,🍌🍌🍌🍌🍌🍌🍌

just cut the banana

‘1-in-36 chance that ‘1’ will be the highest number’.

But, you’re rolling two dice, so the minimum amount you could get would have to be 2, right?

That make no scene. They still die together =((

I don’t like bananas, the other guy can have it

But how could they play game while they are hungry,they have no power so theoretically they both will die.it is great to fight for a minute and there is 75% chances for the winning of cat practically.

Can any1 explain th interest paradox ?

first

🍌

Nothing is truly random

Why not just split the banana

Yuck! I hate bananas! >:(

Boohoo! The banana!

At first i didnt understand But then an idea popped into my mind So … think of it this way if 1,2,3,4 pop only one time player 2 Wins So that means 1,2,3,4 neted to pop 2 Times to give player 1 a victory.if 5 or 6 pops one time player 2 wins

I can see this is educational, but I'd just split the banana with the other…. I'm smart

I wanna be player 3

roll bananas for the last dice

I am so confused. Not by the video, but by the comments. Some say "one person eats the other and banana". Others are saying "the cat doesn't eat bananas". And 50% of the comments are arguing to split the banana. Still, others are stuck how they got the dice in the first place, or why there's only 1 banana. Or why they can't go fishing. (If this comment seemed rude, then no offense to anyone.)

The solution? Make a fishing rod.

Either way, we're both gonna use the banana for the same thing, if you know what I mean…

Seems like all these probabilities go out the window when I'm playing DnD

i would give give the banana to the other person because i I HATE EM

But but……the chance of getting 5 or 6 is 2/6. 2/6 multiply by 2/6 is 4/36. So the chance of player 2 to win is 4/36 or 1/9 which is higher than player 1(16/36). Am i correct? Or is it? I need to know where is my mistake…

Won't 6 tie? It says higher. 5 and 5 will tie

This is beautiful. I especially like the visual showing the probability as a two dimensional square. If we had three dice you could show it as a cube.

So what is the probability of four dice? That would be the probability of a fourth dimensional object, no?

https://www.youtube.com/watch?v=bgEvLW15-VY

I thought the probability for player 2 winning the banana was 2/3

Reason:

Player two needs a roll of 5 or 6 to win, meaning he has a 1/3 chance to win

But since two dice are rolled, the chance for player 2 to win is 1/3 + 1/3 = 2/3

Why pie is used to measure about circle

im almost sure this is wrong

To all these smartass people saying that they would split the banana- You are not funny

Its just a thought experiment, not a real life scenario

I am not surprised. Cats don't like bananas. They just want others to be miserable

If there aren't any bananas left, then cut down the tree and make a boat

Hope you boys learned some hustling tricks here this is gold!

The longer you play, the closer to theoretical probability the actual frequencies are…says who?

Smack with this video every BDO player that says stuff like: "Fs are memes, I once got tet with 10 and failed DUO with 70"

Just use loaded dice.

C A TMy suggestion is

F*ck I'd never go onto a ship

I cant understand anything.

Eat a cat

This is such a great idea in teaching theoretical and experimental probability! Thanks!

just murder the cat and eat it, let it have the banana as a sign of your magnanimity

The 6 in a dice actually weighs the most so de cat

I wont become both

They gonna die soon

Comment Section Filled with Sarcastic Smartass Creatures

wait cats eat banana > aren't they carnivorous ? never mind that sharing banana is lot fair and better

Never seen a cat playing dice on a deserted island!

Being player two is pointless because even if you won, cats can't properly eat bananas.🐱🍌

I thing, Hint: Luck

Why waste time rolling dice if you are so hungry? Just split the banana.

A different Thought Experiment helping you to understand the greatest enigma of all times. Who or what opened the Space-Time Inversion and set off the "Big Bang". Listen to my Podcast: https://youtu.be/2nTtoiNIkDk

Just share the goddamn banana

The Last BananaConning to a theater near you

I figured out easier by checking the cons of Player 1 and pros of Player 2:

* Player 1 wins ONLY if both dices don't roll 5 or 6.

* Player 2 wins if either dice rolls 5 or 6.

So:

* Player 1 needs both dices' results.

* Player 2 doesn't.

So:

* Player 2 has "two tries" to win and Player 1 "one try".

Cat have 9 lives girl just 1

Player 1 should receive 44 percent of the banana,and player 2 should receive 56 percent of the banana.

I was really confused about why the order mattered. I obviously didn't pay attention to the beginning of the video.

Player 1 looks like she's from animal crossing

Cat's don't even eat bananas

Why didn't they just cut the banana into 50% 50% 🤦🏽♀️😂

Solution: girl eats banana, cat hunts for fish.

Excelente ideia!

You made a video but still didn’t use a real banana

Why don't they just share?

Cats eat banana???

That moment when you study statistical physics and forget that normal people don't actually know this stuff.

I misread the title as "The singing banana: A thought experiment in probability". I was hugely disappointed in the lack of James Grime in the video.

this is like the Monty hall problem

Ted ed for the million time you are my best YouTube channel

yeets the banana into the ocean before consuming both of the diceeat the turtle.

Do cats even eat bananas?

first why didn't the y make a fishing net

and second cats can't eat bananas

third is this artist a furry?

I just wanted to be a cat

Give the other castaway the banana, when their guard is down while eating, hit them with a big rock and feast on their corpse

That's called survival

Supposing the chance change if one player were to learn how to intuitively spin a die to get their desired outcome

Fatalistic outcome obervance, all else is character

This is trivial

really good video, like the cartoons and makes sense.

Just give the banana to other person

The comments section here signifies the end of progress of humans

one is the lowest number bub

Furries liked because they chose the cat and won.

banan

I'm here from a sandbox breakout

My first attempt was player 2 and then I knew it had a 56% chance of winning

how bout the stock market?

Cool

but theres a 2/6 chance of it being 5 or 6, so timesing that gets 4/36. im confused

The banana. . . . . finally!!!!

why don't They Just cut it in half

Soo satisfying to watch these videos after you learn it's topic. Just had some lessons in college about probability and that's really accurate!

i just wanna know how they got the dice in the first place

But I've always thought that the number 1 side is slightly heavier because they indent holes into the surface for the number of spots, if this is the case number 6 (the opposite side) would come up more frequently than its 'probability' would claim?

God forbid I be stuck on a deserted island with a cat rolling dice over the last banana.