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.
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.
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.
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
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.
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!
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.
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.
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...
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.
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.
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.
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?
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!
@@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
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.
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.
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.
@@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.
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)
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. :)
"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
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.
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 $3600 to play the game once. That's the point of the paradox, not the infinite expected value.
@@amobilway1032 i don't understand your point, why nobody would pay 3600$ 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?
@@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.
@@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, TH-cam 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.
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%.
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.
@@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.
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.
@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 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.
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.
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
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"....
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...
@@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.
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...
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?
@@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.
This is also known as a Martingale strategy and was originally conceived of as a way to beat Roulette. The problem is that each individual spin or a roulette wheen like each flip of a coin is not determined based on the previous flip (just because the last flip came up heads does not mean the next is any more or less likely to come up tails.) So as the odds do not change the utility of the return decreases after each subsequent flip. The only time I have seen this actually work in any meaningful way is in trading as the next movement of a market has a direct relation to the previous movement and so the odds of up or down for example increase with every subsequent movement.
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.
@@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
Did anyone get confused when he explained the answer and realized that for his answer you were having to pay an additional dollar when you lost the flip to go for double prize. The payout odds for the game he originally proposed with the single pay at the front for a potential infinite number of flips should have different outcome
Well the expected value technically approaches $1/4, for the sum of all 1’s approaches 1/4. It’s according to the series 1-2+3-4+5… which can be simplified to 1+2+3+4… Using Ramanujan summation, the first series becomes 1/4 meaning that the second series also must become 1/4. So any price under $1/4 is worth investing.
The expected value would be more important if not for the fact that the variance is also infinite in this game, which means something like "infinite risk". If one would be allowed to play the game several times in a row, say 100 times for 1 million dollars in total, then this would definitely be a good choice!
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.
Another excellent video! And when I heard the line, "How much is a chance at infinite wealth worth to you?," my first thought was, "Oh no, Kevin's trying to sell me a multilevel marketing scheme." :-D
That's just misinterpretation of expected value. It determins whether a game is profitable if the game is repeatable. It's necessarily relevant only when you've had several shots. This isnt math failing to describe something we perceive, we simply need to use something to quantify how fast the average gain converges towards the expected value.
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”
If the game has one million players, the expected break even price for "The House" is $20.19, the best player in the million wins 19 times in a row before losing, bagging $1,048,576 dollars
The chart you drew is inaccurate. The first time I've EVER noticed an inaccuracy in your video. The $2 prize doesn't come from a 50% chance. It comes from a loss. The $4 prize comes from a 50% chance. So the expected value should be $2 down the whole column.
Am I missing something here? It's not pay per turn, you elect how much you want to pay once for potentially "infinite turns". So pay 1c and watch your investment blossom.
This game would be a racket in practice for anything more than pocketchange since most people would already be out of the game by $4. Betting $2 on a roulette wheel and going all-in on your number coming up twice in a row would have better odds for a better payout.
@@StRanGerManY Nowhere in the first 5 minutes (i didn't bother to check the rest) does the video say you need to pay $10 per turn (or at anytime any value other than your initial wager). It implicitly asks how much would you pay for the privilege to play. Because I know the "trick" to this trick, I'd pay 1c. Even if I lose on the first round I'm guaranteed $2. If this is not the expected behaviour of the game, then Vsauce2 failed to explain the trick properly.
the problem with the game IS NOT the moral expectation.but that fact that in real life you can't really play infinite amounts of times. If you pay 10$ 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$.
I love Vsauce2 and 3 but micheal explains things in a way that makes me immediately get them where I feel here I’m hearing an explanation that’s 20 steps ahead of where I am watching it for the first time, don’t get me wrong I love it but what can I say micheals the best
Damn, Kevin is carrying the Vsauce brand on his back right now. With Jake not uploading in months and the chance of Michael returning to make videos anytime soon being super low cause of Mind Field, Kevin's all we've got!
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.
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.
i wonder why this comment hasnt "blown up"
mogus
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.
@@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?
@@fos1451 well the most common would be 2, duh, and median would be like 4 or 2
If I had a nickel for every time that i had a nickel, i'd have a lot of nickels
Infinite nikle
You’d have double the nickels
Keyboardkat3 you will have 2 nickels
@@its_lucky2526 then you get a nickel for each of them nickels
You do have a nickel every time you have a nickel, therefore you have 1 nickel.
so this is where mr beast gets his money from
yh
@@yinyang1217 Mr Beast wants to know your location.
666 likes ;)
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.
@@wildtangent6890 ya boi
“This game can’t exist!”
*MrBeast enters the room*
Same
What does same mean for this sentence?
It means he’s rich I guess
*game shows enter the room*
Hi
Kevin: "what is a chance of infinite wealth worth for you?"
Me: Idk, like 5$ maybe
Okay I just flipped a coin a couple of times and would have walked away with 8$ so I stand by my previous comment.
@@SergioEduP cool
@@SergioEduP cool
Cool
Working backwards with Bernoulli's logarithmic equation then, looks like you've only got about $4.46 in the bank.
"...And a person with $2 should spend $3.35..."
*stonks*
*STONKS*
*SKNOTS*
*onskst*
SNOT
S
"If things go really well, things go really well"
Ah yes, the floor here is made of floor
😂😂😂
Hmm very interesting hypothesis
Ah yes, O is the same letter as o.
@@slysamuel5902 Omg I always thought it was y😱
@Maria Koch
Like,
same dude.
“if things go really well, things go really well”
*every 60 seconds in africa, a minute passes*
*Spread the word*
ah yes the floor here is made out of floor
Yes the wall is made out of wall
every 60 seconds in orbit, slightly less than a minute passes
Reduplication* *as described in VSauce- Is Cereal Soup
*"This game can't even exist"*
I want 10 minutes of my life back
Duchi so what did you do with those other 2 minutes
@@idontunderstandjokes8308
Dying
@@idontunderstandjokes8308 it was at 10 minutes when he said that.
sooooo you dont enjoy him talking and educating you
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
see yall in 6 years when this is in everyone's recommended
Lmao
Okay hope so
How is your life future me?
I will answer this when it’s in my recommended again
Canadian Cookies Entertainment its in to nów tho
Lol yeah
I’d pay $2, at worse I break even.
Im gonna offer this game at school for 3 bucks. They have a 25% chance to win 2 bucks and a 50% to lose 1 i wont make losses and the 12.5% chance for them to get 5 bucks back ahould draw them in.
Mark Richard Hess Do it like this:
tails ends the streak.
Price for entry: 5$
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!
@@Buphido thanks ima try bbn it
@@Dragosmom. how did it go
@@BananaWasTaken never try to do it
“1 piece of something is called an item, 64 items is called a stack”
MineCraft
Crafting and mining
Haha funny cube game
Haha funny cube game
"You aren't a logarithmic function."
Bold of you to assume that.
Name checks out.
Name checks out.
But if you aren't someone I know you are now someone I know but still not someone I know, so what are you?
You remind me of someone I don't know
Bold of you to assume that he is assuming that
but when u gonna talk about infinite water sources
*Nestle wants to know your location*
You only need 2 water buckets and 2 by 2 1 depth hole and you are gtg
@@stopstaringandsubscribe5189
or a 3x1 hole, and gtg does not mean "good to go"
@@bmxscape nice profile pic ... gtg means good to go / got to go ...
@@stopstaringandsubscribe5189 thanks yours is pretty neat aswell. but i never heard anyone use gtg for good to go
Kevin in a previous attempt at recording this: in the end, you are you. *flips coin*
coin: *false*
Kevin: oh shoot
Caleborg
*reshoots video until coins lands on fact*
"Who would empty their bank account to play a game whe-"
**Mr. Beast wants to know your location**
Its Michigan
Its Washington
earth
*No Further Specification Available*, Java Island, Indonesia, Asia, Earth, Solar Solar System, Milky Way, Universe
The percentage i am correct is:
56.36%
Just wait until he finds out how much people spend on the lottery.
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.
@@thoryan3057 k
@@thoryan3057 k
@@thoryan3057 k
@@thoryan3057 k
How to make a Vsauce video :
*put the word paradox in everything* .
Everyparadoxthing
The P O T A T O paradox
Water Paradox
This is a paradox
The paradox paradox.
Editing this comment 'cause I sound edgy here lmao
Well sheeeeeet
Wow.
Now that's a good conclusion to this experiment. Let's just cheat your way out, since you dont need cheats to win anyway.
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.
I was the 222 like !!!! Im proud
Knowing my luck I’d be the only person to win $0
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
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...
@@livedandletdie just acknowledging your comment so you know it wasn't for nothing 🤣
I get it.
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.
Consecutively winning is a huge difference, why do so many people miss that lol
Egg
@@thegamesuniverse308 eggn't
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.
Du hier? :O
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.
Infinite... yawn.
Me: *YAWNS*
@Orion D. Hunter the infinity yawn
Why did I yawn at this comment, wtf
Great. Now we have another thing Kevin can mansplain
Jk I love kevin
I yawned at this comment
@@asterix_knut why did i yawn at your reply
You've got Vsauce 2; "The infinite money paradox"
and then you've got Vsauce; "Should you eat yourself?"
well...
Lawful Good Vsauce 2 vs Chaotic Evil Vsauce
You're already eating yourself every time you swallow
@@-wingsofwasp- ummm... nevermind...
Don’t forget: How many holes does a human have? from Vsauce
vsause3?
Vsauce makes everything interesting...
Vsauce2 makes everything mathematical
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?
White Templar and they ended up with a half dollar
An you please link the episode or tell me the name
*i appreciated* your joke, Lyons.
all bout that KingTurd Collection, cheggit out if you never heard of it.
That is one of my favorite episodes of the series. "Hey Butthead, you want a candy bar?" "Uhhhhh....ok."
My bank account has $12 dollars so yeah I’d empty it out for a chance to play
But what if you're allergic to peanut butter
@@vaszgul736 thats true 🤔
Mine has 3.04€ so you're set lol
I have 17$
Mine has 1500£ in right now but I wouldn't blow my wage on this game lmao
vsauce: YOU are MORE than an expected value
me, tearing up: THANKS FOR VALIDATING ME KEVIN
alternative universe: coin: *f a l s e*
chuuya is worth the most
Meh suicide is still the answer
party tiem
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!
"If things go really well ... then things could go _really well_ . [Wink]" -- Kevin, 2019
Happy Fakeboulder I watched the same video you did no need to repeat it in the comments
@@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
Aurorain rare but innovative as well. Far more innovative than new iPhones...
Did you guys forget the original vsauce password???
Maybe that‘s why they‘re sponsored by lastpass
@@janklitzke2624 This deserves a heart xD
he's the only one who still remembers his because he uses LastPass
There are Red episodes
Wow a super original comment definitely haven't seen this commented 20 times on every vsauce video for years
Dammit, Kevin.
You are now the sole survivor of the three Vsauce channels... It's actually pretty sad...
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?????
??????
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.
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.
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.
yes
Except that you need to play infinitely many times for *_any_* expected value to be valid. How is this any different?
@@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.
“If someone allergic to peanuts won them, they would be... kil-less thrilled”
Or he could start his sandwich business!
Haha very nice pun there haha please kill me
invalid user 👌🔪
Just sell the sandwiches.
@@greywolf7577 yeah
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)
Vsauce these days?
No such thing
:'(
DING is basically a mini Vsauce 1 and is pretty cool
looking glass was good too... i think thats what it was called any way
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. :)
Ilya Holt
H E Y V S A U C E M I C H E A L H E R E
You have a 100% chance of getting less than the expected value.
Nice! I love that!
TIL $2 < $1.
@@orionlax626 are you dense?
@@AngeK47
Nope. The expected value is always $1, right?
@@orionlax626 1$ per step, and there are infinite steps.
"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
"No one is cool with [potentially infinite loss]"
Never been to a casino, Kevin?
Gold161803 except a casino can kick you out
@@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.
r/wallstreetbets
@@unliving_ball_of_gas both experience infinite losses but the house has the power
@@RafaelMunizYT Except casinoes can be rigged. So, they have a lower probability of losing.
Kevin should just take over Vsauce because hes the only one of the three that still posts on the main vsauce channels
D!NG
@@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
@@jacobc874 What's DONG? I've only ever heard of the very advertiser friendly D!NG
@@AirNeat I see, not a true fan DONG was changed to D!NG along ago
@@thekrieger2959 r/woosh
"...potentially infinite loss, and nobody's cool with that"
Short sellers would like a word
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
3am?
Naw, I'm watching at 6am
*Sleep is for the weak*
And for the mentally stable.
The question is: *WHAT IF I FORGET MY LASTPASS PASSWORD???????*
I wrote mine down on a paper, and text file on a flash drive, stored in a safe, which is locked by a password.
@@tylerboothman4496 What if you forget the password of the safe?
Use another app to remember it for you.
@@muhammadadeelzia4432 prybar
Use Dashlane
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.
exactly
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 $3600 to play the game once. That's the point of the paradox, not the infinite expected value.
@@amobilway1032 Nobody said you can play it only once! You can play it as many times you want to, that's crucial.
@@amobilway1032 i don't understand your point, why nobody would pay 3600$ 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?
@@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.
How to talk about 50/50 chance of winning for 12 minutes.
The add was the important bit. The rest is filler.
I think the point is for people who think about this stuff: caution: reality is not that simple.
It's not 50/50 at all tho. It's 100% to get $2 50/50 to get $4, everything above should be 0,5^n I think.
@@99xara99 No! There are two sides of the coin. With each throw it is always Win/lose. This guy is just overthinking reality.
@@OvertonWindex oh I had already forgotten there even was an ad. i skipped it with the right arrow key multiple times.
since I discovered that trick, TH-cam has gotten a lot easier! My previous method of trying to gauge by the tiny preview picture where the ad is going to end and then clicking to jump to there was much more hassle.
Tell me if I’m missing something but the problem is that the expected value of an potentially infinite game gives no useful information. There is no paradox here. You can still pretty easily calculate that the chance of winning something is very small.
You chance to win more than 8$ is about 6%. If you are hoping for 128 that is already less than 1%.
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.
@@src175 I suppose in that sense this problem is veridical?
@@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.
These videos in a nutshell: Here's an illogical mathematical algorithm and here's logical psychology. IT'S A PARADOX.
I think that's just the nature of paradoxes based on mathematical principals, since this is a legitimate paradox in academia.
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.
Love that classic opening:
“Vsause! Kevin here”
*w a i t*
Uhh I'm sorry I will not make you bored of people commenting spelling corrections
What?
@@accordintojordan4250 u spelled vsauce wrong
sauce*
sous
You have less than 1% chance of winning the 7th round, which rewards you with $128.
@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
What's the odds of winning the 20th or 30th round? 20 is worth $1,000,000, and 30 $1B.
@@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.
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.
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
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"....
See I wouldn’t play because I know that a Schrute Buck is only worth 1/100th of a cent.
How many Stanley nickels is that
@@dvlce_music just use the unicorns to leprichans ratio
@@dvlce_music You forgot the question mark.
@@JorgetePanete I bet you're fun at parties, huh?
"would have to be ok with infinite loss, and no one is ok with that..."
Nihilist: hold my Nietzsche
Orion Fyre Nietzsche argued that nihilism would be the death of western society.
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
But you only get 1 try at the game tho
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.
Assuming you're allowed to play for only 1 dollar. Id charge $20
No one wants to empty their bank account to play this game”
Poor people: Maniacal laughter
Video summary: "Value is subjective + math + real world examples + {infinite gain (always) = infinite loss}"...Good video!
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...
When he said "middle of the night if you can't sleep"
I felt that
It's 2:17am
I red this at exactly 2.17 am
It’s 2:09am for me right now
@@jonasbolden 2:53am here
3:31 when I write this
Rookies
2:05 I tested this with a computer simpulation and for the first few million trials the expected value hovered at around 24.
darn, we can't use this to stock up on infinite supplies for the area 51 raid
Tlactl that is why we are going in the first place
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
@@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.
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...
This is huge. I hadnt thought about it this way!
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?
I am confused!
@@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.
This is also known as a Martingale strategy and was originally conceived of as a way to beat Roulette. The problem is that each individual spin or a roulette wheen like each flip of a coin is not determined based on the previous flip (just because the last flip came up heads does not mean the next is any more or less likely to come up tails.)
So as the odds do not change the utility of the return decreases after each subsequent flip.
The only time I have seen this actually work in any meaningful way is in trading as the next movement of a market has a direct relation to the previous movement and so the odds of up or down for example increase with every subsequent movement.
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
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.
"If things go well, then...
*things go well*
-Kevin
everybody gangsta til kevin figures out the duplication glitch
This game has one fatal flaw, what if the coin never lands on tails? You'd never get paid.
0% chance for that though
@@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
“... 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
when you pay $2999999 for a lottery ticket with a jackpot of $3000000
STONKS
You'll never know, How I got 422 likes 😉😊
This is a paradox
Ths Isnw yoooo this just blew my blown mind
Welcome to limits.
Time is not infinite paradox solved!
challenge to watch vsauce explain paradoxs before bed
Your videos like always are some high quality content, thank you!
Did anyone get confused when he explained the answer and realized that for his answer you were having to pay an additional dollar when you lost the flip to go for double prize. The payout odds for the game he originally proposed with the single pay at the front for a potential infinite number of flips should have different outcome
Yeah, I'd be happy to pay $1 an infinite number of times to play an infinite number of games, but I'm still only gonna pay one dollar to play one game
You forgot the question mark.
Kevin: No ones cool with infinite loss
Mr. Beast: I'm about to end this man's whole career
Nothing is Infinite Kevin.. we discussed this
Cobblestone and water are.
@@michuumichowski
once we get to area 51 and unlock creative mode everything will become infinite
@@SergioEduP Remember to place beds so we can respawn closer.
@@michuumichowski yeah and get enderpearls
Death Metal is *forever* 🙂
Well the expected value technically approaches $1/4, for the sum of all 1’s approaches 1/4. It’s according to the series 1-2+3-4+5… which can be simplified to 1+2+3+4… Using Ramanujan summation, the first series becomes 1/4 meaning that the second series also must become 1/4. So any price under $1/4 is worth investing.
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
Yes. The chance of winning that infinite amount is infinitely small and therefore 0...
@@gargaduk at some point the probability of you winning a coin flip will be lower than the probability of humans evolving to chickens
Exactly!
Me: *uses LastPass
Also me: *forgets the password to LastPass
*_Wait. That's illegal._*
That's really funny 😂 you've just earned a new subscriber_
Get last pass for last pass
Marco Vissuet what if you forget the password to that
The expected value would be more important if not for the fact that the variance is also infinite in this game, which means something like "infinite risk". If one would be allowed to play the game several times in a row, say 100 times for 1 million dollars in total, then this would definitely be a good choice!
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.
Another excellent video! And when I heard the line, "How much is a chance at infinite wealth worth to you?," my first thought was, "Oh no, Kevin's trying to sell me a multilevel marketing scheme." :-D
10:07 "infinite loss and no one is cool with that"
Mrbeast: I don't think so
Eat your cereal
Eat your cereal
Eat your cereal
Eat your cereal
drink your water
Thank you, Kevin, for being my Math Teacher.
THANKS for spending your time so I can spend mine watching your videos!
Mrbeast should get people to play this game, but cap them off at 10 million dollars or something!
$8,388,608
Do you have a concept of how much exactly 10 million dollars is?
@@Darkshadow-oq7rs is it 9999999 dollars and 99cents?
And how likely do you think getting 10 million dollars in this game is?
damn you missed opportunity to say the allergic to peanut butter person would be killed and rhyme it
I reckon that was intentional on his part
he knows the world isn't ready for him to stop dropping bars 😔
I WANT TO LOVE THIS COMMENT RIGHT NOW!!!!!!!!!!!
That's just misinterpretation of expected value. It determins whether a game is profitable if the game is repeatable. It's necessarily relevant only when you've had several shots.
This isnt math failing to describe something we perceive, we simply need to use something to quantify how fast the average gain converges towards the expected value.
Prénom Nom now this is big word time
@@getrekt2526 lol
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”
gonna answer to this in about 5 years when i get this in my reccomended
8 months close enough.
1 year is better than nothing, 2020 has been pretty bad recently. May not make it...
@@lusamine7925 just what the heck man?!
zamn
If the game has one million players, the expected break even price for "The House" is $20.19, the best player in the million wins 19 times in a row before losing, bagging $1,048,576 dollars
But it could be a lot higher so the house could end up losing billions. I wonder if they had this game at the Trump casinos.
@@nssimpson Did you watch the whole video?
@@aayushgupta8129 yes
Me: only wins two dollars and gave away my bank account
Jokes on you I was broke anyways
Hi this is cool to see this again. :)
The chart you drew is inaccurate. The first time I've EVER noticed an inaccuracy in your video.
The $2 prize doesn't come from a 50% chance. It comes from a loss. The $4 prize comes from a 50% chance. So the expected value should be $2 down the whole column.
ok smart guy. what percentage is the first $2?
Me: I'll pay $10 to play this game
Also Me: loses on the first flip 😭
Am I missing something here? It's not pay per turn, you elect how much you want to pay once for potentially "infinite turns". So pay 1c and watch your investment blossom.
This game would be a racket in practice for anything more than pocketchange since most people would already be out of the game by $4. Betting $2 on a roulette wheel and going all-in on your number coming up twice in a row would have better odds for a better payout.
Puts in another $10 and still loses
@@sergeant5848 yes, you are missing something here. You need to pay $10 for every new run.
@@StRanGerManY Nowhere in the first 5 minutes (i didn't bother to check the rest) does the video say you need to pay $10 per turn (or at anytime any value other than your initial wager). It implicitly asks how much would you pay for the privilege to play. Because I know the "trick" to this trick, I'd pay 1c. Even if I lose on the first round I'm guaranteed $2. If this is not the expected behaviour of the game, then Vsauce2 failed to explain the trick properly.
the problem with the game IS NOT the moral expectation.but that fact that in real life you can't really play infinite amounts of times.
If you pay 10$ 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$.
Exactly!! Thank you
1:33 *”if things go really well, then things go really well.”* -vsauce2
best quote ever
We all know that in reality after ∞ flips you go home with -1/12 coins
I love Vsauce2 and 3 but micheal explains things in a way that makes me immediately get them where I feel here I’m hearing an explanation that’s 20 steps ahead of where I am watching it for the first time, don’t get me wrong I love it but what can I say micheals the best
"If things go really well..... Things go really well."
Makes sense to me
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
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.
10:12 "The other party [must] be comfortable with potentially infinite loss. And... no one is cool with that, so..."
Oh, Kevin Kevin Kevin.
Is this how Mr Beast funds his videos
Damn, Kevin is carrying the Vsauce brand on his back right now. With Jake not uploading in months and the chance of Michael returning to make videos anytime soon being super low cause of Mind Field, Kevin's all we've got!
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.