Ok, so you remember the setup: 100 people

have had marked dollar bills put randomly into 100 boxes, and every person, one at a

time, gets to look in fifty of the boxes, and you all collectively win only if every

single person finds their own bill. $100 dollar payout to each of you if you win, nothing

if you lose. In the last video I asked whether or not you should take the bet. Did you make the right choice? I mean, clearly, if all 100 of you gamblers

just choose 50 boxes at random when you go into the room, the likelihood of each of you

finding your bill is one half, so the probability of ALL of you finding your bills and winning

the whole game is one half times one half times one half… a hundred times. And one

half to the power of 100 is about 0.0000000000000000000000000000008. Basically zero. You’re more likely to roll

9 one-roll yahtzees in a row – and then pick the king of hearts at random out of a deck

of cards. You could do a little better by trying to

correlate which boxes you pick – like, if there were only two people and two boxes,

they should each pick different boxes, because if they pick the same box only one of them

can possibly find their own bill, and they’ll automatically lose. But this kind of strategy

only improves your odds a tiny little bit, and it has less benefit the more people there

are. However, despite all this, it turns out that

there’s a strategy that results in you gamblers winning over 30% of the time! This strategy

is SO GOOD that you’re more likely to win using it than if just TWO people out of a

hundred picked randomly, since one half times one half is twenty-five percent. What we’ve forgotten is that you can obtain

information FROM the boxes themselves, because the room is exactly the same each time. The

first box will always have the same-numbered dollar in it, and so will the second box,

the third, the fifty-seventh, etc. All you have to do is use the dollar in one

box to tell you which box to go to next. This might not seem like a great advantage, but

it’s HUGE. The trick is to start with the box that corresponds

to your number. Your dollar probably isn’t IN that box, but the bills inside will take

you on a random path through the boxes, a scavenger hunt where each box tells you where

to go next. You can think of this as linking up boxes

in chains, connecting them based on the bills inside. Any random arrangement of the boxes results

in a different set of chains, some long, some small. Short chains are ones like “box 30

says go to box 82, box 82 says go to box 5, 5 says go to 30.” That’s a chain of link 3.

Long chains link up more boxes before circling back – and the LONGEST possible chain links

up all 100 boxes. But each chain ALWAYS circles back, since there are finite boxes. And of course, if you end up back where you

started within 50 boxes, you’ve won, because that means the previous box had a dollar bill

that told you to go your starting point, and you started on your number, so the previous

box’s dollar bill was YOURS! And that’s why this strategy is so good – because

when the boxes are randomly arranged, about 30% of the time there will be NO chains connecting

more than 50 boxes, so not only will you win, but so will everyone else – as long as they’re

following the same strategy! The magic of this solution isn’t that it’s

better odds for any single individual to find their dollar (it isn’t) – it’s that all of

the successes and failures are forced to happen together – everyone wins together, everyone

loses together – your fates are linked by using the numbers inside the boxes to guide

you along invisible chains… towards victory.

If you take yours out that breaks a chain

"so you remember…" then explains everything again…

Beep Beep Lettuce

#MemeAwards #FeatureMe

Doesnt this all go to shit as soon as someone takes the first doller and breaks a chain?

Nope, I know how to win just not why it works

the same matrix is used to decode passwords of whatever kind. just replace the boxes with letters and numbers. also it is used in logistics. where to go first and next and so on and even with conditions to comply.

Except that the boxes are not numbered, and therefore must be able to agree on a numbering during the draw. But indeed, no contrary mention, so implicitly, it's possible. And maybe it is what is interesting, you have to interpolate to do math.

Vsauce just recreated this video and you were in it 😂

I don't understand how this "strategy" is useful. Each individual still pulls a chain of 50. If they hit a cycle, it doesn't help them. What am I missing?

This video is better than Vsauce2's

This is the first video that explained this in a way I get. Thankyou.

Why the hell do u run so much fast while telling

Is there any other strategy with a higher chance to win? Or equivalently, is 31% the highest possible probability for any n>1?

wouldn't it be 0.31 to the power of 100 tho ?

"burp" yawn

I know this from ted-ed

You videos are like 1.2x speed.

Traveling Time? 🤔

I've seen this riddle tons of times before, but this is the first video that really explained how it worked well enough.

MATH!!!

Who the fuck got this right?

if you are allowed to speak to each other before each of you picks a box you have a chance of 50%. the first guy does that chain thingy and then he tells the second one if he saw his number. if yes then number two knows where 2 is and he then looks up all left over boxes nobody looked in. then one of number one and number two tells number 3 where the 3 is and so on. only if the first guy didnt get his number(wich has a chance of 50%) they lose, otherwise they win.

Can you just slow down a bit please? Like about to 60% to your current speed?

But if you find out a Empty box and if you cant contact or see with other. Or simple if number in cash but not in box.

Communists approve

It all comes down to how you arbitrarily choose to number the boxes in the beginning. If the players are not allowed to communicate with each other once the game begins (so you can't just open a box with one of your 50 guesses, announce "this box has 4 in it" and then the person who needs 4 comes forward and picks that box), then how could you all agree on a numbering system, how could you all agree on which box is box #4 and which is box #7? This strategy won't work because individually each and every one of them will be individually just picking 50 at random if the boxes are unlabeled and it is up to the players to arbitrarily decide on a numbering of them. Though the odds are not .5^100, it's actually 50^100*50!/100! or 50/100 times 50/99 times 50/98 times 50/97…. times 50/51 if on finding the right box, a player can take it out of circulation for the others.

Bro this is some 600 iq shit right here

Seems similar to a hash table in programming.

0:55 anyone notice that the king is shtabin himself in the head

Saw this on Vsauce2

I never would have thought of that but that is very smart!

V sause 2?

I would probably sign up for this just for the fun of it. It sounds awesome.

This is really useful information for the next time time I'm stuck with a 100 people searching boxes for money as a bet. #relatable

I dont understand the bet so the solution makes no sense to me. And if you can look inside the boxes why not just look for your own marked bill and take it? What am I missing here?

This looks similar to the solution for one ted Ed riddle

what

a 69% of a chain >50? ( ͡° ͜ʖ ͡°)

Probability of 31.18%, NOT odds!

Basically, he used the concept of linked list

The odds tend to 1-ln(2)

This sounds like communism propaganda.

Wat

I love this channel because I love being the only person I know to know how to solve and win at theoretical gambling scenarios, riddles, and puzzles, that I will literally never be asked to be a part of. 😀

Illusion 100vsauce2 already covered that..

i have a better strat 50 % win guaranted -_-".

Since the box are the same for everyone the first seek the number 1 and 2 and open the 50 first box.

If he don't find his number = lose.

If he find his number he then tell the second participant if he found his number is the first 50 box. If not the second go to the 50 last box.

The second go grab his number and seek the number 3 …

Who need 31% when you can have 50% ?

3:31 who else was using captions and was waiting for him to say “or loss”

But what if there is one chain of boxes with 49 boxes so they all win but also one chain with 51 boxes. You said "you either win all together or lose all together" but that's simply not true?

Are u able to speak a bit slower? It's not understandable for non-americans.. thx

Ok, I think I got it… but tell me that whole thing again, I want listening.

Oh darn I thought this was on Pascal’s Wager.

0:38 Male siri

It would be 0.3118% you forgot that the first person has to choose randomely from 100 boxes. If they choose correctly, then it is a 31.18% chance.

Can't you just… tell the other guys where their money is?

HEEEY I SAW THIS ON TED RIDDLES

Vsauce did a video on this too ☺️

Why would anyone even consider taking that non-sensical bet, jobs cover it 100-fold already.

I didn't understand a word of this and now I'm out of money and my butt hurts

Could you maybe explain that 1000 more times

Seems like Ted ed stole stole your idea and got almost twice the number of views😐☹️

This still doesn’t explain how you would get $10,000 out of $100.

But if you open a box and its not your bill then everyone losses. How are you going to know what is inside the box so you can follow the number and go to the other boxes ?

There's gonna be that one guy who lose on purpose.

Thas alotta bills man, 100 uniquely marked notes each time a person goes so i can keep track? They sure are generous… What do you mean i have to put them back in the exact order they came in?

if too random, add rules

its a bonkers concept at first sight, but it can be thought of as adding your own neat and tidy scaffolding to a problem, if the problem is too messy by itself to navigate around. it will be orderly, based on your rules, even when you're generating something from random junk numbers

But doesn't 31% mean that all 100 of us can't get it right so what's the point

30 percent still nothing man rip my dollar

Me: laugh in ted ed

What if you find an empty box?

Already saw it on vsause 2

WHat the hell……im so confused

TedEd made a video about this same thing

This is cool but there's a TEDTalk riddle that explains it better

You still should not play, as odds are lower than 50%

Or you could leave the lid open after you find a dollar in it.

You get all 100 people to take turns looking at 1 unique box, then one at a time call out the number on the bill and give the box to the person that owned it. Works 100% of the time and they don't have to look at the rest of the 49 boxes.

You see, the problem with your description is you didn't mention that they had to find the bill on their turn through the method of looking in the box themselves on one of their 50 tries.

But its not a 100% chance to win

This vid is also available on ted ed

2:58 Nice

Isn't there a problem though? As soon as a bill is taken out of a box, the chain is broken, and how can the next person (since it's just one at a time) know how to follow the chain?

Ok but my brain?

My question is whether they take the bill after finding it in a box, it may change the odds of the game.

Ted-Ed had a riddle like this.

Now let's calculate the odds we will successfully convince 100 people to follow the same strategy.

Wouldnt it be 30% of 30% of 30% …. 100 times ?? Which is equal to( 3/10)^100 < (1/2) ^100??

This method makes the chance for one person as 30%, for everyone to win it should be (3/10) ^100 ? I may be wrong xd

So you take the note away because you need to, then theres nothing in the box. How is another person gonna contimue the chain if theres no note there

Well it isn't very impossible now?

What are the odds of me getting the last 3:58 minutes of my life back???

please turn off auto translate for the video title

i kno big tric just gvie nigerian price ur pin and ur credit card no so he can send u back x10….l simepl

I accidentally thought of the solution

I'm literally not even joking, like wtf

What if you're in the wrong chain?

Dude! Slow down

Wasn’t this on vsause2?

Initially you said boxes are identical and now you have numbered them 🤔

magic trick:

1/51+1/52+1/53+…+1/98+1/99+1/100≈0.69

Is time travel possible

wait what if a person in a hundred was named Schrödinger?

1:59 So basically that thing people drew in science textbooks where someone writes go to page 272, then that says go to page 69 and then then you end up on page number 573 and it’s just like a penis

3:24 your Personal odds with the chain method is 31%only and 50% with random