The Infinite Money Paradox
Рет қаралды 3,133,114
Күн бұрынNot a real offer. Deciding whether to play a game is usually very easy… you crunch the numbers and if they work in your favor, you play. If they don’t, you shouldn’t. Mathematical case closed.
But what happens when the math of a game tells you that you have access to infinite wealth and unlimited expected value and real life tells you not to play? Enter: The St. Petersburg Paradox.
The Bernoulli family first started corresponding about the paradox in the early 1700s with a series of letters examining the puzzling math behind the simple game. But it wasn’t until 1738 when Daniel Bernoulli realized that he could factor real life utility -- how much something actually means to you -- into the calculations.
The St. Petersburg Paradox opens up doors to how we think about what math really means to us, including modern research into Prospect Theory and everyday issues like whether we decide to buy life insurance. And in the end, one thing we know for sure: we’re all much, much more than numbers.
** SOURCES **
Original Bernoulli family correspondence: cerebro.xu.edu/math/Sources/NB...
Play the St. Petersburg Paradox game: www.mathematik.com/Petersburg/...
“Ending the Myth of the St. Petersburg Paradox,” by Vivian Robert William: mpra.ub.uni-muenchen.de/50515...
“St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described,” by Paul Samuelson: www.jstor.org/stable/pdf/2722...
** LINKS **
Vsauce2 Links
Twitter: / vsaucetwo
Facebook: / vsaucetwo
Hosted and Produced by Kevin Lieber
Instagram: / kevlieber
Twitter: / kevinlieber
Podcast: / thecreateunknown
Research And Writing by Matthew Tabor
/ tabortcu
Huge Thanks To Paula Lieber
www.etsy.com/shop/Craftality
Get Vsauce's favorite science and math toys delivered to your door!
www.curiositybox.com/
Select Music By Jake Chudnow: / jakechudnow
#education #vsauce2
@Lorenzo-tm2cr 4 жыл бұрын
Tried this a few times with my 2 euros coin. I gained 2, 2, 2, 8, 8, 16, 16, 128 and then lost my coin between the sofa cushions. So this game actually made me lose 2 euros without any reward.
@user-fv6nc7qi2x 2 жыл бұрын
i wonder why this comment hasnt "blown up"
@glowstonelovepad9294 2 жыл бұрын
mogus
@theman4884 2 жыл бұрын
I simulated it 10,000,000 times. The average win was 21.5 with the largest win being 2,097,152. So it looks to me that betting up to 20 would make sense.
@fos1451 2 жыл бұрын
@@theman4884 I feel like the outliner really does make a difference in the average, can you give us the median and the winning that shows up the most?
@ethanvon222 2 жыл бұрын
@@fos1451 well the most common would be 2, duh, and median would be like 4 or 2
@Keyboardkat3 4 жыл бұрын
If I had a nickel for every time that i had a nickel, i'd have a lot of nickels
@griffin7670 4 жыл бұрын
Infinite nikle
@its_lucky252 4 жыл бұрын
You’d have double the nickels
@okktok 4 жыл бұрын
Keyboardkat3 you will have 2 nickels
@thefountainpendesk 4 жыл бұрын
@@its_lucky252 then you get a nickel for each of them nickels
@fluxion2049 4 жыл бұрын
You do have a nickel every time you have a nickel, therefore you have 1 nickel.
@reedphillips3083 3 жыл бұрын
“This game can’t exist!” *MrBeast enters the room*
@Rekdon 2 жыл бұрын
Same
@ThePixelKid903 2 жыл бұрын
What does same mean for this sentence?
@mrcrispybacon578 2 жыл бұрын
It means he’s rich I guess
@barbmcelderry9164 2 жыл бұрын
*game shows enter the room*
@Rekdon 2 жыл бұрын
Hi
@Byran-op7sf 3 жыл бұрын
“if things go really well, things go really well” *every 60 seconds in africa, a minute passes*
@oswald0_ 2 жыл бұрын
*Spread the word*
@redcrewmate2101 2 жыл бұрын
ah yes the floor here is made out of floor
@Healthandwealth9422 2 жыл бұрын
Yes the wall is made out of wall
@Albert-yu1cg 2 жыл бұрын
every 60 seconds in orbit, slightly less than a minute passes
@drewidlifestyle7883 2 жыл бұрын
Reduplication* *as described in VSauce- Is Cereal Soup
@billmcneal2276 4 жыл бұрын
so this is where mr beast gets his money from
@yinyang1217 4 жыл бұрын
yh
@TheReplay324 4 жыл бұрын
@@yinyang1217 Mr Beast wants to know your location.
@wildtangent6890 4 жыл бұрын
666 likes ;)
@nakiado 4 жыл бұрын
He actually did a video similar to this, had random people pick between two cups with one holding like 50 bucks and then the player could go again for double the price until they wanted to cash in.
@TheEpicFace007 4 жыл бұрын
@@wildtangent6890 ya boi
@SergioEduP 4 жыл бұрын
Kevin: "what is a chance of infinite wealth worth for you?" Me: Idk, like 5$ maybe
@SergioEduP 4 жыл бұрын
Okay I just flipped a coin a couple of times and would have walked away with 8$ so I stand by my previous comment.
@darkslayer8607 4 жыл бұрын
@@SergioEduP cool
@yinyang1217 4 жыл бұрын
@@SergioEduP cool
@benjaminwilkin2960 4 жыл бұрын
Cool
@LiamNebe 4 жыл бұрын
Working backwards with Bernoulli's logarithmic equation then, looks like you've only got about $4.46 in the bank.
@GRLDT 3 жыл бұрын
"Who would empty their bank account to play a game whe-" **Mr. Beast wants to know your location**
@ActuallyDaghen 2 жыл бұрын
Its Michigan
@handsomehead1381 2 жыл бұрын
Its Washington
@RafaelMunizYT 2 жыл бұрын
earth
@mr.waffles5358 2 жыл бұрын
“1 piece of something is called an item, 64 items is called a stack”
@ishaankapoor933 2 жыл бұрын
MineCraft
@XentriaNova 2 жыл бұрын
Crafting and mining
@iranam1004 2 жыл бұрын
Haha funny cube game
@spocite 2 жыл бұрын
Haha funny cube game
@duchi882 4 жыл бұрын
*"This game can't even exist"* I want 10 minutes of my life back
@idontunderstandjokes8308 4 жыл бұрын
Duchi so what did you do with those other 2 minutes
@marcopasta6274 4 жыл бұрын
@@idontunderstandjokes8308 Dying
@pidgeon708 4 жыл бұрын
@@idontunderstandjokes8308 it was at 10 minutes when he said that.
@andrewjones9547 4 жыл бұрын
sooooo you dont enjoy him talking and educating you
@BboyKeny 4 жыл бұрын
Lets play the game, I start as the dealer then you be the dealer. The price is the difference in amount won. So we cant reach infinite if we both reach infinite cause that would be 0
@orealis8576 4 жыл бұрын
"...And a person with $2 should spend $3.35..." *stonks*
@DarthMauldinOfficial 4 жыл бұрын
*STONKS*
@bloroxcleach3439 4 жыл бұрын
*SKNOTS*
@maulwurf9414 4 жыл бұрын
*onskst*
@bloodlust_9890 4 жыл бұрын
SNOT
@amzwl1671 4 жыл бұрын
S
@chefizzy2238 3 жыл бұрын
Knowing my luck I’d be the only person to win $0
@oslonicl6251 3 жыл бұрын
The coin lands on its side, meaning it is not heads so the game ends but it is not tails so you do not get the profits
@livedandletdie 2 жыл бұрын
50% of people will lose on average whatever they'd bet on it, so no matter the prize, if 50% will always lose, then sure 50% will always win, let's say that the cost of playing is $2.1, then we get that in a game of 1000 players, all piling together $2100 500 of those would go home with $0, meanwhile 500 people would win a minimum of $2... Well we get that... for k players, the prize for playing has to be k/ln(12)^1.1 let's enter 1000 into that, and we get that each player needs to pay $367.5 to play and never let the prize pool reach zero. The price increases with the expected amount of players, by a lot for 2 players it's 73 cents per player. For 3 players it's $1.1 for 10 players it's $3.6... For a million players it's $367416.79...
@diamond_hcr2 2 жыл бұрын
@@livedandletdie just acknowledging your comment so you know it wasn't for nothing 🤣
@spazzwazzle 2 жыл бұрын
I get it.
@mr.cheese5697 2 жыл бұрын
The are no such thing as luck. You just Loking at examples where you lose, ignoring all of them. It's permitic point of view, you should be more realistic, If you're not are teen go to a psychologist.
@DavidPysnik 2 жыл бұрын
The issue here is that you literally need to play the game an infinite amount of times for the infinite expected value to be valid, and that isn't possible. The better way to think of it is that the expected value can become as large as you want as long as you are willing to play a sufficiently high number of times. The question of what is good to pay is then tied to how many times you will play. It's intuitive not to pay too much to play because you know you are probably not going to get a long string of "fact" flips unless you play a ridiculous amount of times, and you know you aren't going to play a ridiculous amount of times. There is really no paradox here, so I will go back to being a logarithmic function now.
@flatfingertuning727 2 жыл бұрын
The expected value is dependent upon how large a payout one would be able to collect if one were to win it. If winning ten times would result in the opponent defaulting the portion of on any prize value over $1,000, then no upside over $1000 should count toward the EV.
@abdulmasaiev9024 2 жыл бұрын
Well, not really. Imagine a modification of this game where after 100 rounds the game stops no matter what the toss result is and you just get an infinity dollars. You can now in fact realistically get to the infinite reward in about an hour and a half, assuming a very leisurely rate of 1 coin toss per minute. Are you now willing to pay any price to play this game, or is it still something you'd spend maybe like $20 tops on, if that? The actual explanation is what's in the video. There's pretty much no practical difference between having 1 quadrillion and 1 quintillion dollars, even though numerically they're extremely different. The expected numerical value of this game is infinite, but its expected utility is not and in fact it falls off pretty quickly.
@joanaguadomedina3060 2 жыл бұрын
yes
@Anonymous-df8it Жыл бұрын
Except that you need to play infinitely many times for *_any_* expected value to be valid. How is this any different?
@jaketerpening3284 Жыл бұрын
@@Anonymous-df8it That's not necessarily true. If we were to toss a coin 100 times, we could be fairly confident that we would probably get between 40 or 60 heads, pretty close to an expected value of 50 heads. Sure the chance of ending up with exactly our expected value is pretty small, but because our variance isn't that big, we can use an expected value for this type of game to judge on if it's a good bet or not. However in the infinite value game, our variance is also infinite so the expected value isn't useful for even large sample sizes like 1000 games played.
@jamesdickson4219 4 жыл бұрын
see yall in 6 years when this is in everyone's recommended
@lemonkes8618 4 жыл бұрын
Lmao
@iammrblue2774 4 жыл бұрын
Okay hope so
@tortistortis 4 жыл бұрын
How is your life future me? I will answer this when it’s in my recommended again
@bingovalue 4 жыл бұрын
Canadian Cookies Entertainment its in to nów tho
@angusb1434 4 жыл бұрын
Lol yeah
@SJrad 4 жыл бұрын
I’d pay $2, at worse I break even.
@Dragosmom. 3 жыл бұрын
Im gonna offer this game at school for 3 bucks. They have a 25% chance to win 2 bucks and a 50% to lose 1 i wont make losses and the 12.5% chance for them to get 5 bucks back ahould draw them in.
@Buphido 3 жыл бұрын
Mark Richard Hess Do it like this: tails ends the streak. Price for entry: 5$ 1 throw: 1$ 2 throws: 2$ 3 throws: 4$ 4 throws: 8$ 5 throws: 16$ 5 throws (5th is heads): 32$ The average winnings would be 3.5$, so you‘d make 1.5$ profit per player!
@Dragosmom. 3 жыл бұрын
@@Buphido thanks ima try bbn it
@BananaWasTaken 3 жыл бұрын
@@Dragosmom. how did it go
@artit91 3 жыл бұрын
@@BananaWasTaken never try to do it
@Jester_The_Jynxster 3 жыл бұрын
That music at the end of every video always gives me the feeling like I've just watched something of monumental importance. Even when I've just watched him run a toy monkey down a piece of string or something...I still come off thinking, "that was deep"....
@guillis9952 4 жыл бұрын
I’d pay one dollar, lose at the first round, and then play again with one of my 2 dollars. Bam, broke the system, I don’t need infinite luck
@datdamndog389 2 жыл бұрын
But you only get 1 try at the game tho
@akashp9471 2 жыл бұрын
I am perplexed by the ease of decision making you have shown. But the catch with math is, if it feels easy, it must be wrong.
@halc5975 2 жыл бұрын
Assuming you're allowed to play for only 1 dollar. Id charge $20
@adamtaurus7840 4 жыл бұрын
"If things go really well, things go really well" Ah yes, the floor here is made of floor
@kexek7975 4 жыл бұрын
😂😂😂
@negus9298 4 жыл бұрын
Hmm very interesting hypothesis
@slysamuel5902 4 жыл бұрын
Ah yes, O is the same letter as o.
@Alex_...34565 4 жыл бұрын
@@slysamuel5902 Omg I always thought it was y😱
@slysamuel5902 4 жыл бұрын
@Maria Koch Like, same dude.
@epic_gamerXD12345 4 жыл бұрын
but when u gonna talk about infinite water sources
@kraio-sfu 4 жыл бұрын
*Nestle wants to know your location*
@stopstaringandsubscribe5189 4 жыл бұрын
You only need 2 water buckets and 2 by 2 1 depth hole and you are gtg
@bmxscape 4 жыл бұрын
@@stopstaringandsubscribe5189 or a 3x1 hole, and gtg does not mean "good to go"
@stopstaringandsubscribe5189 4 жыл бұрын
@@bmxscape nice profile pic ... gtg means good to go / got to go ...
@bmxscape 4 жыл бұрын
@@stopstaringandsubscribe5189 thanks yours is pretty neat aswell. but i never heard anyone use gtg for good to go
@LilacShowers Жыл бұрын
"The St. Petersburg paradox reminds us that we're all more than math" he says, after showing that the initial math was simply not good enough and it just boiled down to different math
@Kazperian 3 жыл бұрын
Vsauce makes everything interesting... Vsauce2 makes everything mathematical
@SomeoneYouDontKnowOfficial 4 жыл бұрын
"You aren't a logarithmic function." Bold of you to assume that.
@frostcrackle2374 4 жыл бұрын
Name checks out.
@acro9779 4 жыл бұрын
Name checks out.
@somerandomashellperson7130 3 жыл бұрын
But if you aren't someone I know you are now someone I know but still not someone I know, so what are you?
@danthedanator2765 3 жыл бұрын
You remind me of someone I don't know
@yulianairaisortizlira8078 3 жыл бұрын
Bold of you to assume that he is assuming that
@caleborg5688 4 жыл бұрын
Kevin in a previous attempt at recording this: in the end, you are you. *flips coin* coin: *false* Kevin: oh shoot
@davidj5642 4 жыл бұрын
Caleborg *reshoots video until coins lands on fact*
@natekoyle9356 2 жыл бұрын
Always love your videos. I always finish them with a feeling that lays somewhere in the middle of smarter/more empowered and completely dumbfounded about everything I’ve known. Which is for some reason why I love your content! Thanks Vsauce!
@Airwolf-lm9cm 3 жыл бұрын
Tell me if I’m missing something but the problem is that the expected value of an potentially infinite game gives no useful information. There is no paradox here. You can still pretty easily calculate that the chance of winning something is very small. You chance to win more than 8$ is about 6%. If you are hoping for 128 that is already less than 1%.
@src175 2 жыл бұрын
The paradox isn't mathematical, IIRC, it's more economical. Like, "can you actually convince anyone to both host AND play this game", appears to be the paradox. A lot of the proposed solutions for it are economic theories.
@yellowpowr8455 Жыл бұрын
@@src175 I suppose in that sense this problem is veridical?
@NorthernRealmJackal 10 ай бұрын
@@src175So in other words, the "paradox" is that people don't like taking infinite risks..? I'm still not sure what's so baffling about getting a meaningless result when applying abstract math to a problem about non-abstract risks. Maybe I just don't get it.
@6byrontenorio 4 жыл бұрын
Editing this comment 'cause I sound edgy here lmao
@arzan28 4 жыл бұрын
Byron Tenorio wait for the coin to be worn out
@gabano1311 4 жыл бұрын
Well sheeeeeet
@Ernad1 4 жыл бұрын
Wow.
@renookami4651 4 жыл бұрын
Now that's a good conclusion to this experiment. Let's just cheat your way out, since you dont need cheats to win anyway.
@eternalreign2313 4 жыл бұрын
Can't you walk away when you want to or do you have to play until you get a flip wrong? You only need to get 20 in a row to win a million, and 30 to win a billion.
@colemyhre8332 4 жыл бұрын
Just wait until he finds out how much people spend on the lottery.
@thoryan3057 3 жыл бұрын
The expected value of lottery winnings is always less than what it costs to play. Even if a lottery cost $1 to play, the prize is $200 million, and the odds of winning is 1 in 100 million, the odds that there are multiple winners with that higher jackpot is higher and thus causes the overall expected value to still be less than $1. Every lottery has it's own apex (the highest expected value possible based on all possible jackpot amounts), but the apex is always less than the price to play. Casino games also have expected values less than the price to pay them, but these expected values are usually much closer to the price to play than the lottery. The way I see it, casinos and/or lotteries can be worth it to anyone, but those people need to have an economic demand for playing the game for the sake of it. So a person might spend $1 on a lottery with a $0.50 expected value, but have a $0.60 demand for the excitement of playing. In that case, their economic equilibrium is $1.10 and it actually would be worth them playing. However, if they were to buy two lottery tickets instead of one, their economic demand would be $1.60 even though it would cost them $2 to have two lottery tickets. Then, it would not be worth it to play.
@yeetyboix6595 3 жыл бұрын
@@thoryan3057 k
@ortherner 3 жыл бұрын
@@thoryan3057 k
@noobiamyes4853 3 жыл бұрын
@@thoryan3057 k
@polyminutes8788 3 жыл бұрын
@@thoryan3057 k
@bigbadt392 3 жыл бұрын
Now that title is easy for anyone to see this randomly at 3am for no reason at all. Specially when there are 69k likes on the video
@Grandflea02 3 жыл бұрын
3am? Naw, I'm watching at 6am *Sleep is for the weak* And for the mentally stable.
@RandomDucc-sj8pd Жыл бұрын
2:05 I tested this with a computer simpulation and for the first few million trials the expected value hovered at around 24.
@rahuldhali7681 4 жыл бұрын
How to make a Vsauce video : *put the word paradox in everything* .
@johntate6537 4 жыл бұрын
Everyparadoxthing
@Aerialyn 4 жыл бұрын
The P O T A T O paradox
@fredwood6107 4 жыл бұрын
Water Paradox
@alessiobenvenuto5159 4 жыл бұрын
This is a paradox
@RobertoDeMundo 4 жыл бұрын
The paradox paradox.
@Path-of-Islam- 4 жыл бұрын
My bank account has $12 dollars so yeah I’d empty it out for a chance to play
@vaszgul736 4 жыл бұрын
But what if you're allergic to peanut butter
@elp4196 4 жыл бұрын
@@vaszgul736 thats true 🤔
@hittinghardtm8587 4 жыл бұрын
Mine has 3.04€ so you're set lol
@kmnakbonnnum5958 4 жыл бұрын
I have 17$
@mydickisincrediblytinyandi7380 3 жыл бұрын
Mine has 1500£ in right now but I wouldn't blow my wage on this game lmao
@Oreos_HQ 2 жыл бұрын
No one wants to empty their bank account to play this game” Poor people: Maniacal laughter
@WelcomeFellow 2 жыл бұрын
Your videos like always are some high quality content, thank you!
@JayFroste 4 жыл бұрын
“No one is cool with potentially infinite loss.” You clearly haven’t met wallstreetbets.
@xkomachionozuka3010 4 жыл бұрын
The people in charge won't lose anything though 🐍
@personhuman2239 4 жыл бұрын
😎
@Fassle 4 жыл бұрын
You can only lose 100% of what you have bet but you can win way more than 100% of what you have bet.
@xkomachionozuka3010 4 жыл бұрын
@@Fassle that's a super simplified way to put it and usually doesn't describe reality, especially not in the finance sector. more so in sports betting or so, maybe
@JayFroste 4 жыл бұрын
de minimis Selling naked calls is potentially infinite loss for a finite maximum gain.
@BetweenTheLyons 4 жыл бұрын
Is this the same paradox that Beavis and Butt-head used when they payed eachother $1 back and forth for the whole box of candy bars for the school fundraiser?
@idontunderstandjokes8308 4 жыл бұрын
White Templar and they ended up with a half dollar
@poppy3879 4 жыл бұрын
An you please link the episode or tell me the name
@PaulMeranda 4 жыл бұрын
*i appreciated* your joke, Lyons. all bout that KingTurd Collection, cheggit out if you never heard of it.
@bmwolgas 4 жыл бұрын
That is one of my favorite episodes of the series. "Hey Butthead, you want a candy bar?" "Uhhhhh....ok."
@jordanadkins1828 2 жыл бұрын
This game has one fatal flaw, what if the coin never lands on tails? You'd never get paid.
@cloverpepsi 10 ай бұрын
0% chance for that though
@jordanadkins4362 10 ай бұрын
@@cloverpepsi The odds tend towards zero very quickly, but it’s not actually zero. The average human lifespan is around like 78? Can someone flip heads for 70+ years? Doubtful, but with infinite attempts I’m sure it would happen. Actually, that reminds me of the twilight zone episode where the guy always wins at the casino and never loses, then realizes he’s actually in Hell. Lol
@hehh7161 3 жыл бұрын
I'd pay my entire bank balance to play this. *laughs in £0.42*
@pendantperuke9440 2 жыл бұрын
*laughs in american* what the hell is that symbol
@pineapplesandwich3906 2 жыл бұрын
@@pendantperuke9440 euros I suppose
@CowsCanCook 2 жыл бұрын
@@pendantperuke9440 it’s British pounds
@yellowpowr8455 Жыл бұрын
@@pendantperuke9440 WELL AT LEAST
@Corrupted 4 жыл бұрын
Consecutively winning is a huge difference, why do so many people miss that lol
@thegamesuniverse308 3 жыл бұрын
Egg
@denisdelinger3265 3 жыл бұрын
@@thegamesuniverse308 eggn't
@felixtt1329 3 жыл бұрын
It shouldn't matter , the real factor for the bet is whether the output of what you pay is less the the most likely input , the last part of the video covers this.
@schindy6385 3 жыл бұрын
Du hier? :O
@j.s.7335 3 жыл бұрын
Right on! I'm a bit on the poor side, but I'd pay maybe $300 to play this because it doesn't take a whole lot of flips before the cumulative payouts are in the $100s.
@thelifeofapenguin2159 4 жыл бұрын
You've got Vsauce 2; "The infinite money paradox" and then you've got Vsauce; "Should you eat yourself?" well...
@isaiahcampbell1782 4 жыл бұрын
Lawful Good Vsauce 2 vs Chaotic Evil Vsauce
@-wingsofwasp- 4 жыл бұрын
You're already eating yourself every time you swallow
@nikolaysergeevUSA 4 жыл бұрын
@@-wingsofwasp- ummm... nevermind...
@ThomasTheThermonuclearBomb 4 жыл бұрын
Don’t forget: How many holes does a human have? from Vsauce
@its_jasonBSF 4 жыл бұрын
vsause3?
@leiftorbjorn5621 3 жыл бұрын
This is the first vsauce video where I knew this stuff from before and so I completely follow everything that’s going on, I feel so cool
@raghavbhatnagar2329 3 жыл бұрын
You are connecting me again to sequences and series -nice to see math people together
@Slayer-Knight 4 жыл бұрын
Dammit, Kevin. You are now the sole survivor of the three Vsauce channels... It's actually pretty sad...
@sylveon_gaming 4 жыл бұрын
?
@aspiringcloudexpert5127 4 жыл бұрын
???
@GauravSharma-dy8xv 4 жыл бұрын
????
@Jake28 4 жыл бұрын
?????
@rakeshsharma-ps7oo 4 жыл бұрын
??????
@nashvilletennessee4391 4 жыл бұрын
“If someone allergic to peanuts won them, they would be... kil-less thrilled”
@emilior934 4 жыл бұрын
Or he could start his sandwich business!
@mayoraldrinzon4847 3 жыл бұрын
Haha very nice pun there haha please kill me
@nashvilletennessee4391 3 жыл бұрын
invalid user 👌🔪
@greywolf7577 3 жыл бұрын
Just sell the sandwiches.
@realbignoob1886 3 жыл бұрын
@@greywolf7577 yeah
@mr.cheese5697 2 жыл бұрын
We all know that in reality after ∞ flips you go home with -1/12 coins
@WeloTwelve 3 жыл бұрын
1:22 why does he know that off the top of his head?
@Ziroidex 3 жыл бұрын
He’s reading a script.
@SkyRecruit18 4 жыл бұрын
Did you guys forget the original vsauce password???
@janklitzke2624 4 жыл бұрын
Maybe that‘s why they‘re sponsored by lastpass
@SkyRecruit18 4 жыл бұрын
@@janklitzke2624 This deserves a heart xD
@Glac0 4 жыл бұрын
he's the only one who still remembers his because he uses LastPass
@Jamato-sUn 4 жыл бұрын
There are Red episodes
@monhi64 4 жыл бұрын
Wow a super original comment definitely haven't seen this commented 20 times on every vsauce video for years
@verachoi9362 4 жыл бұрын
vsauce: YOU are MORE than an expected value me, tearing up: THANKS FOR VALIDATING ME KEVIN
@THElarry27 4 жыл бұрын
alternative universe: coin: *f a l s e*
@pufftv6099 4 жыл бұрын
chuuya is worth the most
@DhirC35 3 жыл бұрын
Meh suicide is still the answer
@TheOne_6 4 ай бұрын
party tiem
@mlafleurhua 2 жыл бұрын
Just saw this interesting video. It seems to me that the paradox stems from not factoring in the upfront cost to play into the expected value calculation. This then captures the fact that you need to obtain a sequence of a suitable length just to break even.
@trentoninnewjersey Жыл бұрын
I wasn’t exactly sure what this video would be as I didn’t read the title (as it autoplayed) but he asked “How much is a chance at infinite wealth worth”, and I thought “There is no way he’s asking this”
@happyfakeboulder644 4 жыл бұрын
"If things go really well ... then things could go _really well_ . [Wink]" -- Kevin, 2019
@mothlastname2413 4 жыл бұрын
Happy Fakeboulder I watched the same video you did no need to repeat it in the comments
@GDCilia 4 жыл бұрын
@@mothlastname2413 They were emphasizing the second really well to play to dirty minded people, you human equivalent of a rotting cabbage with spilled spoiled milk on top mixed with flat diet coke and 2-year-old mentos
@man-throwing-thing 4 жыл бұрын
Aurorain rare but innovative as well. Far more innovative than new iPhones...
@flegmatika5758 4 жыл бұрын
Infinite... yawn. Me: *YAWNS*
@exotrrc1636 4 жыл бұрын
@Orion D. Hunter the infinity yawn
@asterix_knut 4 жыл бұрын
Why did I yawn at this comment, wtf
@griffin7670 4 жыл бұрын
Great. Now we have another thing Kevin can mansplain Jk I love kevin
@thefountainpendesk 4 жыл бұрын
I yawned at this comment
@certifiedfurry 4 жыл бұрын
@@asterix_knut why did i yawn at your reply
@FistroMan 3 жыл бұрын
THANKS for spending your time so I can spend mine watching your videos!
@robemeister 3 жыл бұрын
I played this game 10 times and my winnings would have been $20. If I would've put in $5 a pop like I thought I would be losing by $30. So much for infinite gain.
@eris4734 4 жыл бұрын
You have a 100% chance of getting less than the expected value.
@ApiolJoe 4 жыл бұрын
Nice! I love that!
@orionlax626 3 жыл бұрын
TIL $2 < $1.
@AngeK47 3 жыл бұрын
@@orionlax626 are you dense?
@orionlax626 3 жыл бұрын
@@AngeK47 Nope. The expected value is always $1, right?
@hackerulroman 3 жыл бұрын
@@orionlax626 1$ per step, and there are infinite steps.
@Gold161803 4 жыл бұрын
"No one is cool with [potentially infinite loss]" Never been to a casino, Kevin?
@bluzingtin 4 жыл бұрын
Gold161803 except a casino can kick you out
@unliving_ball_of_gas 4 жыл бұрын
@@bluzingtin No. I think he means that the players are the ones who experiences infinite loss and not 'the house'/casino but people still play them.
@Pablo360able 2 жыл бұрын
r/wallstreetbets
@RafaelMunizYT 2 жыл бұрын
@@unliving_ball_of_gas both experience infinite losses but the house has the power
@codinghub3759 Жыл бұрын
@@RafaelMunizYT Except casinoes can be rigged. So, they have a lower probability of losing.
@mr.potato981 2 жыл бұрын
0:28 bro i yawned like a second before he said that😂
@bigshot1724 2 жыл бұрын
Thanks for the tutorial!
@ilyaholt8607 4 жыл бұрын
Hey Kevin, why did you stop the Mind Blow series? It was every interesting for me and I always got excited when a new episode came up. These videos are cool too, but it would be nice to see some variety. (still better than vsauce1 these days tho)
@Jayberisk3793 4 жыл бұрын
Vsauce these days? No such thing :'(
@chiggs5483 4 жыл бұрын
DING is basically a mini Vsauce 1 and is pretty cool
@hamesbone 4 жыл бұрын
looking glass was good too... i think thats what it was called any way
@DaBunne 4 жыл бұрын
interesting timing Ilya. I was just thinking of mentioning Mind Blow in the comments here too. I've missed that series for a long time, but why did I not have an impulse to say something about it til today?? Now that it's been a few years.. a bet a lot of cool things have surfaced that Kevin could review too. :)
@richardgibson8403 4 жыл бұрын
Ilya Holt H E Y V S A U C E M I C H E A L H E R E
@Buttermilk0 4 жыл бұрын
The question is: *WHAT IF I FORGET MY LASTPASS PASSWORD???????*
@tylerboothman4496 4 жыл бұрын
I wrote mine down on a paper, and text file on a flash drive, stored in a safe, which is locked by a password.
@muhammadadeelzia4432 4 жыл бұрын
@@tylerboothman4496 What if you forget the password of the safe?
@joops110 4 жыл бұрын
Use another app to remember it for you.
@tylerboothman4496 4 жыл бұрын
@@muhammadadeelzia4432 prybar
@zyaicob 4 жыл бұрын
Use Dashlane
@cookiecakeeater6340 3 жыл бұрын
The robot doesn’t take into account the diminishing utility of money the more you have
@elymanic3497 2 жыл бұрын
The odds of flipping FACT in a row decreases as you play. So.. I feel like the numbers are being manipulated
@HoSza1 4 жыл бұрын
Big problem is that infinite gain comes ONLY after you played infinitely many rounds of this game. Because you don't have that much time, you have to cut in a finite time. Then the expected payoff will be finite after finite length of throws and you can easily calculate the maximal price that results in a positive net income. Even, you can calculate the cost of your time and the opportunity costs also. No paradoxes lurking in the darkness when we remain in the realms of finiteness.
@KP-fy5bf 8 ай бұрын
exactly
@amobilway1032 6 ай бұрын
Nope, there's still a paradox. Lets say you have 10 hours to play this game at 1 flip every 10 seconds. That is 360 flips an hour and 3600 flips. At 1 dollar per, thats $3600, but no rational person would ever pay anything close to $3600 to play the game once. That's the point of the paradox, not the infinite expected value.
@HoSza1 6 ай бұрын
@@amobilway1032 Nobody said you can play it only once! You can play it as many times you want to, that's crucial.
@tslex6477 5 ай бұрын
@@amobilway1032 i don't understand your point, why nobody would pay 3600$ when the all time worst theoretically imaginable play is if they always flipped false getting 2 dollars every flip gaining 7200$ dollars. Why would anybody be against playing this game?
@BEN-ys6gu 4 ай бұрын
@@amobilway1032 And also, I don't think it's correct to think that you need to play a game of chance x amount of times for it to be worth it. Even if you're only allowed to play once in your lifetime, you should still think the same way, even if there is a high chance that you don't win anything.
@jacobc874 4 жыл бұрын
Kevin should just take over Vsauce because hes the only one of the three that still posts on the main vsauce channels
@AirNeat 4 жыл бұрын
D!NG
@jacobc874 4 жыл бұрын
@@AirNeat re-read my comment. The main Vsauce Channels, other than Kevin's, do not post anymore. As far as I know, DONG is micheals project
@AirNeat 4 жыл бұрын
@@jacobc874 What's DONG? I've only ever heard of the very advertiser friendly D!NG
@thekrieger2959 4 жыл бұрын
@@AirNeat I see, not a true fan DONG was changed to D!NG along ago
@jacobc874 4 жыл бұрын
@@thekrieger2959 r/woosh
@imthesleepyskeleton5462 3 жыл бұрын
"If things go really well..... Things go really well." Makes sense to me
@aaronkou1751 3 жыл бұрын
This problem is also in the AoPS Intro to counting and probability book
@virtualdxs 4 жыл бұрын
"...potentially infinite loss, and nobody's cool with that" Short sellers would like a word
@Tlactl 4 жыл бұрын
darn, we can't use this to stock up on infinite supplies for the area 51 raid
@idontunderstandjokes8308 4 жыл бұрын
Tlactl that is why we are going in the first place
@Hydra-zr7ks 4 жыл бұрын
Can someone explain to me what the whole deal with this Area 51 meme because I’ve even seen it in Minecraft vids so it must be serious or popular
@iamwrong2239 4 жыл бұрын
@@Hydra-zr7ks It started with a Facebook event post saying "Let's raid Area 51, they can't stop us all". It was a joke but like most things it gained traction across the internet and more people joined in. It has gotten to the point the American government had to issue a statement on it. That's my version of this story.
@LemuelDunleavy 2 жыл бұрын
I've watched this video before, but I'm back for more!
@psychopompous489 2 жыл бұрын
Logarithmic functions are also a part of math. All this says is to factor in variance when you play a game with a high expected value.
@drewmur 4 жыл бұрын
You have less than 1% chance of winning the 7th round, which rewards you with $128.
@drewmur 4 жыл бұрын
@FishSticks True, I should have said you have a less than one percent chance of winning seven rounds consecutively. Although you can't get to round 7 without winning rounds 1-6
@eternalreign2313 4 жыл бұрын
What's the odds of winning the 20th or 30th round? 20 is worth $1,000,000, and 30 $1B.
@Drummin003 4 жыл бұрын
@@eternalreign2313 The possibility of winning any number of times in a row = [(1/2^n) or (1/2)^n], where 1 = the number of possible winning positions on the coin during each round, 2 = the total number of positions on the coin (1 winning position & 1 losing position), n = the number of times you play. Or you can think of the "odds" as 1-in-2^n, where 2^n is equal to whatever the payoff is for that round. The odds for 20 wins in a row is 1-in-1,048,576 and 30 wins in a row is 1-in-1,073,741,824. The "Expected Payoff" is always equal to $1, because you are multiplying the payoff for that round (2^n), by the odds [(1/2^n) or (1/2)^n] of winning that particular round and every round before. The possibility of winning 100 times in a row is 1-in-1,267,650,600,228,230,000,000,000,000,000. If you made $10,000.00 every day (assuming 365 days in a year) it would take you 4,016,947,991,725,950,000 years (4.01694799172595 x 1 Quintillion) to collect that amount.
@KalOrtPor 4 жыл бұрын
1 in 1,073,741,824 to win $1,073,741,824.....Mega Millions has gotten higher than that, and with odds of just 1 in 302,575,350. And it's $2 without any kind of extortion racket negotiation.
@ykhenessey3924 4 жыл бұрын
False. You donth have 50% chance of winning the 7th because if you lose before that you wont have a 7th round. Maybe a 7th first round of a new game but not a 7th round. So that guy was right and you were actually wrong
@youreallinsane 4 жыл бұрын
These videos in a nutshell: Here's an illogical mathematical algorithm and here's logical psychology. IT'S A PARADOX.
@Granateseeds 4 жыл бұрын
I think that's just the nature of paradoxes based on mathematical principals, since this is a legitimate paradox in academia.
@jetjazz05 4 жыл бұрын
I'd like to think of it as this is just a piece of the puzzle and our mind is computing much more. It's like if you throw a wad of paper, your brain will take into account more than just gravity because it's so light, and while gravity might be a big part of deciding how hard to throw the paper your brain knows there's more to the real world than just that principle.
@lilbuggers3 3 жыл бұрын
I like how he complicates and tries to explain a simple idea so you have to stop watching half way through. He is 100% for me on his videos
@syweb2 2 жыл бұрын
What do you mean "have to stop watching half way through"? Also, did you even see the end? He explains the point of the video pretty succinctly there.
@moriskehl5991 17 күн бұрын
In our finite world you cant give an invinite reward of any sort
@TheHippieRat 4 жыл бұрын
See I wouldn’t play because I know that a Schrute Buck is only worth 1/100th of a cent.
@dvlce_music 4 жыл бұрын
How many Stanley nickels is that
@vasaskyle 4 жыл бұрын
@@dvlce_music just use the unicorns to leprichans ratio
@JorgetePanete 4 жыл бұрын
@@dvlce_music You forgot the question mark.
@dvlce_music 4 жыл бұрын
@@JorgetePanete I bet you're fun at parties, huh?
@accordintojordan4250 4 жыл бұрын
Love that classic opening: “Vsause! Kevin here” *w a i t*
@Thomfamily5 4 жыл бұрын
Uhh I'm sorry I will not make you bored of people commenting spelling corrections
@accordintojordan4250 4 жыл бұрын
What?
@jacobstockbridge6413 4 жыл бұрын
@@accordintojordan4250 u spelled vsauce wrong
@harrisonkey698 4 жыл бұрын
sauce*
@trunestor 4 жыл бұрын
sous
@teatowel11 3 жыл бұрын
The buy in needs to be low enough that you can play multiple times so that the likely hood of the average outcome being close to the theoretical outcome is improved.
@tractorcannon8487 2 жыл бұрын
I just learned this in my sophomore math class why are you guys teaching people this stuff like it’s difficult.
@OrionFyre 4 жыл бұрын
"would have to be ok with infinite loss, and no one is ok with that..." Nihilist: hold my Nietzsche
@ChatGPTpowered 4 жыл бұрын
Orion Fyre Nietzsche argued that nihilism would be the death of western society.
@hedgeearthridge6807 4 жыл бұрын
I love how deciding whether to play a game or not is a game in itself. Including trying to decide whether to buy the expensive Steam game now, or wait a few months for the sale...
@someweirdstuff1256 10 ай бұрын
1:33 *”if things go really well, then things go really well.”* -vsauce2 best quote ever
@jimmjamme3067 2 жыл бұрын
"No one is cool with infinite loss" The fed has entered the chat
@Mobay18 4 жыл бұрын
How to talk about 50/50 chance of winning for 12 minutes.
@OvertonWindex 4 жыл бұрын
The add was the important bit. The rest is filler.
@NickRoman 4 жыл бұрын
I think the point is for people who think about this stuff: caution: reality is not that simple.
@99xara99 4 жыл бұрын
It's not 50/50 at all tho. It's 100% to get $2 50/50 to get $4, everything above should be 0,5^n I think.
@Mobay18 4 жыл бұрын
@@99xara99 No! There are two sides of the coin. With each throw it is always Win/lose. This guy is just overthinking reality.
@silkwesir1444 4 жыл бұрын
@@OvertonWindex oh I had already forgotten there even was an ad. i skipped it with the right arrow key multiple times. since I discovered that trick, KZfaq has gotten a lot easier! My previous method of trying to gauge by the tiny preview picture where the ad is going to end and then clicking to jump to there was much more hassle.
@sabrinagilberttt 4 жыл бұрын
When he said "middle of the night if you can't sleep" I felt that It's 2:17am
@patroohb 4 жыл бұрын
I red this at exactly 2.17 am
@jonasbolden 4 жыл бұрын
It’s 2:09am for me right now
@airplayrule 4 жыл бұрын
@@jonasbolden 2:53am here
@hristijanzdravkovski5970 4 жыл бұрын
3:31 when I write this
@mkaali 4 жыл бұрын
Rookies
@dom9710 2 жыл бұрын
This is pretty much the most common roulette strategy. Bet X amount on black or red. If you lose, you double your bet and do the same again until your color hits. If you win, you start at your first bet again.
@brianbarber5401 Жыл бұрын
Except, expected value isn’t how you determine you’d play a game. It’s the expected amount you’d win, an average, if you played it. When the rewards get big, you are now wagering on how likely you are to get lucky.
@Reddles37 4 жыл бұрын
But if you get rid of the infinite payout and cap the game at a maximum winning of 2^n, then the expected value is only n. So even if the casino had a trillion dollars to give out, the expected value would only be $40...
@brianvernaglia9449 4 жыл бұрын
This is huge. I hadnt thought about it this way!
@hellkaiserzane 4 жыл бұрын
That sounds right I was also thinking the infinite payout is also infinitely unlikely to happen so the two infinites cancel each other out and your left with 2^n or have I gone horribly wrong here?
@callie4579 4 жыл бұрын
I am confused!
@rednecktash 4 жыл бұрын
@@hellkaiserzane kevin didnt do the math right. in order to get infinite reward from it...you would have to devote infinite time to playing. the maximum reward would be, let's say, 50 years x 365 days x 18 hours per day x 60 minutes per hour x 60 seconds per minute x 1 coin flip per second (this can be done if you have two coins to play with.) this means you could achieve a maximum of about 10 billion coin flips, or a payoff of somewhere around 1*10^3,000,000. unfortunately, there's a 1/1*10^3,000,000 chance of that happening. unless you have the ability to rewind time to a precision within the space between two coin flips, the game isn't worth playing.
@Epikk 4 жыл бұрын
"If things go well, then... *things go well* -Kevin
@mahir_labib 2 жыл бұрын
The last 30 seconds: Us having goopsebumps for no reason
@alexanderwizardjar9540 2 жыл бұрын
amazing as always
@Zorro9129 4 жыл бұрын
It's the economic principle of risk versus reward. What Bernoulli got wrong is assuming that an amount of money MUST be worth more to a poor man than to a rich man. It's easy to make this assumption but compare a poor ascetic who doesn't care about money to a rich miser. EVERYTHING, even money, has subjective value and cannot be measured with "utils" because utility is only ORDINAL. I'm glad that Kevin mentioned subjectivity but he needs to read some Mises. This video is great proof of the subjective theory of value.
@therealgamer8150 4 жыл бұрын
I’ve got an easier explanation. The probability of having a net loss approaches 1 the more you are prepared to pay. Which will put you off paying
@ggdk2865 4 жыл бұрын
Yes. The chance of winning that infinite amount is infinitely small and therefore 0...
@RafaelMunizYT 2 жыл бұрын
@@ggdk2865 at some point the probability of you winning a coin flip will be lower than the probability of humans evolving to chickens
@Anonymous-df8it Жыл бұрын
Exactly!
@Space_Reptile 3 жыл бұрын
me after watching the intro: ah so double or nothing me after watching the whole video: ah so double or nothing
@HeadsUpTV 3 жыл бұрын
7:49 'You probably can't' Jeff Bezos watching this video: You bet..
@eladfeldman1152 4 жыл бұрын
the problem with the game IS NOT the moral expectation.but that fact that in real life you can't really play infinite amounts of times. If you pay 10$ to play a single game, you will need to play 5 games to get 16$(on average), means you will need to pay 50$ for the chance to get 16$.
@prim16 4 жыл бұрын
Exactly!! Thank you
@johnathanwhite4878 4 жыл бұрын
Nothing is Infinite Kevin.. we discussed this
@michuumichowski 4 жыл бұрын
Cobblestone and water are.
@SergioEduP 4 жыл бұрын
@@michuumichowski once we get to area 51 and unlock creative mode everything will become infinite
@michuumichowski 4 жыл бұрын
@@SergioEduP Remember to place beds so we can respawn closer.
@yinyang1217 4 жыл бұрын
@@michuumichowski yeah and get enderpearls
@PaulMeranda 4 жыл бұрын
Death Metal is *forever* 🙂
@Michael-fd1gx 7 ай бұрын
Try using a pie chart for the probability of the outputs, until the probability of an output is less than 1%.
@neilgooge 3 жыл бұрын
And I point you to my excessively long comment on a previous video about the way I used to play roulette... ;)
@yinghungman4471 4 жыл бұрын
Me: *uses LastPass Also me: *forgets the password to LastPass *_Wait. That's illegal._*
@verdantbf 4 жыл бұрын
That's really funny 😂 you've just earned a new subscriber_
@k-dog7442 3 жыл бұрын
Get last pass for last pass
@ryanxin1848 3 жыл бұрын
Marco Vissuet what if you forget the password to that
@roccotarli762 4 жыл бұрын
“... one plus one, plus one, plus one, plus one, pus whon, wus plun, ous hon, uhs one, uh heh, pleh, huh huh.” - Vsause Kevin 2019
@_caith 3 жыл бұрын
Just a big yes for LastPass. Worked in IT for many years. Can only recommend it to everyone
@OliverPruitt 3 жыл бұрын
0:31 thanks for clarifying that this was indeed a YAWN