Mathematics of Maximizing Profit in Gambling/Investing - Kelly Criterion
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- Опубликовано: 30 май 2024
- In this video, we introduce the Kelly criterion which is the formula that gives optimal risk that maximizes the long term profit, and we will proceed to derive the formula in a nonstandard way.
The necessary prerequisite materials like random variables, transformations of random variables, expected value, generalized mean are introduced in the video.
Links:
Proof that E(B) = np
proofwiki.org/wiki/Expectatio...
Wiki page which has detailed information about the median and the mode of the binomial distribution
en.wikipedia.org/wiki/Binomia...
geometric mean is the limit of the power mean as the power goes to 0
planetmath.org/derivationofge...
Chapters:
00:00 Intro
03:18 Problem Statement
04:51 The Kelly Criterion
06:36 What is an Average?
11:53 First Step towards the Model
13:30 Random Variables
16:00 Expected Value
18:05 Transformation of Random Variables
20:20 Random Variable for the Problem
22:26 Median of Random Variables
29:15 Mode of Random Variables
31:18 Geometric Mean of Random Variables
Music🎵:
Track 1: Make a bet - BGM President • [브금대통령](도박/긴장/Casino) ...
Track 2: Confusion in my mind - BGM President • [브금대통령] (방황/혼란/Emotion...
Track 3: Aurora Currents - Asher Fulero • Aurora Currents - Ashe...
Track 4: The Confused Mind - BGM President • [Royalty Free Music] T...
Track 5: YOLO - BGM President • [Royalty Free Music] 복...
Track 6: Forest_Sage - PeriTune • 【無料フリーBGM】幻想的なヒーリング「Fo...
Track 7: Soul Searching - Causmic • Soul Searching
Corrections:
18:22 Y=1/X should be 1/X if X ≠ 0 and 0 if X = 0
21:59 E(R) = (1+r)^n, not (1+r)^20
20:52 Here is what the computer did!
First you start out with the sum from k=0 to n of (1 + tr)^k * (1 - sr)^(n - k) * Binomial(n, k) * p^k * q^(n - k)
and then you can combine some terms because a^k * b^k = (ab)^k, getting
the sum from k=0 to n of (p + ptr)^k * (q - qsr)^(n - k) * Binomial(n, k)
Then, due to the binomial theorem, this is simply equal to ( (p + ptr) + (q - qsr) )^n
And with a little simplifying you finally get (1 + ptr - qsr)^n :D
Amazing work!! That was much simpler than I thought!
Thanks man
i don't understand but i have to learn it
When I clicked, I expected to learn something about investing. But only 11 minutes into this video, you've covered- Maths, Statistics and Chemistry
Yeah, but you shouldn't do any risky investment without understanding all theory. But you can summarize: as long as you are not willing to lose most of your invested money, you should try to stay as safe as possible. Try do build up a diverse portfolio and stay away from all investment strategies that try to rely on finding the right time to buy or sell. This holds especially true for all those daytrading stuff.
There's a reason physics PhD's can become highly paid quants. The math works, and the math doesn't care where you apply it; it's the same.
This video does a really good job of:
- explaining the algebra behind concepts like mean, median, mode
-showing math equations and formulae and what their terms represent
-going in depth on the math behind statistical and probabilistic principles
The editing is solid, although as people have pointed out, the audio recording on your mic has two different settings which is a bit jarring. The animation and overall visuals are excellent.
This video does a very poor job of:
-explaining basic algebra and calculus in a way that is comprehensible to people not well versed in math or who are just very much out of practice (like me!)
-giving a conclusion or interpretation to all of the concepts presented.
You can't leave the interpretation of a mathematical equation up to the viewer. This isn't a stats class in university. This is infotainment! I'm now going to go watch how the Kelly Criterion is interpreted elsewhere on RUclips so I can actually draw conclusions on it and base my investing behaviour on those conclusions. I understand your hesitancy to do so yourself as you don't want people to make bad choices based on your advice, but I still feel like you could have done more to explain what the criterion implies without giving investing advice.
I really appreciate the effort you took to make this video and as I said, there are many positive points, I hope you can appreciate my feedback as constructive, as no offense was meant. Maybe I'm not the target audience, but I strongly feel like an interpretive conclusion was missing in this video.
I'm dumb with math, and I English isn't even my first language, yet your explanation is so clear I can understand all of them. Amazing job!
If you have one bad bet, your leverage is gone and you're immediately in debt and in a bad place. On average you'd be fine, but if you bet *everything*...
It's a first passage problem
If you bet everything, you are not using the Kelly criterion.
lost af but watched the whole thing
I am thoroughly impressed and grateful for the quality of your videos. Recently, I have been voraciously studying probability theory, statistics, and machine learning. Your videos explain things so well that I had to say something. By the way, I did not want to use RUclips's 'Thanks' feature-- I would much have rather subscribed to a Patreon or donated to you directly, but this was the only option, as I looked for other ways to support you! Thank you so much for your videos. They have completely taken priority over some of my lecture notes, the next chapter of Murphy's PML book that I'm on, and several videos by other creators. A few key videos of yours are next on my list for rigorous study thanks to the incredible bandwidth of knowledge transfer you provide. I also love your presentation style, with occasional humor and very well-placed context for certain problem solving decisions.
Thank you so much for your donations
Why does this sound exactly like an ai generated response...🧐
@@atheoristspointofview7059 Because, to increase the chance of quality output, AI is told to default to formal prose like you'd find in an article or a letter, and not how people talk or text. This person wrote this like a letter. But that isn't surprising because they apparently put a lot of thought and effort in before even writing the comment. So, to me, it makes sense they wouldn't skimp out on the effort of writing the comment either. And, same as making a handwritten thank-you note, the appearance of formality and effort is itself part of trying to communicate gratitude.
@@monkeybobthat made me laugh
It was really cool to see that there were four different types of averages.
He actually showed an infinite amount of averages if you watch again.
Great video! Thank you so much that was great at elucidating so many scary stats and probability concepts in one nice, clean mathematical umbrella! Did a better job in 30 minutes than half a semester of courses
Very well explained. I use this concept to allow my trading bots to adjust Risk by thinking of the history of wins/losses as the changing probability, so it doesn't bankrupt me if market conditions become unfavourable or if there's faulty logic that I didn't perceive.
How did you create a trading bot?
There’s no easy answer for this. I have years of experience in programming multiple languages, I’ve been trading for years, and I combine those skills to do what I do.
@@rickym2847 Find a pattern/strategy in the market, make it objective, hire a programmer to create it. I've got about 7 of them.
@@rickym2847 I forgot, math is very important, but how important really depends on how complicated you want to make things for yourself.
I do aerospace engineering and I applied my knowledge in mathematics for trading too. I have a basic grasp of coding so I code indicators and things like that. I have created a document which contains all of the mathematics required to beat proprietary firms in trading indices specifically. The reason for trading firms is because the market is almost completely random, the firms give us an edge and the slight trend of indices gives an edge also. I would like to contact you since I see you are clearly not like other retail traders who fail (which I suspect is 99.999% of them). I can give you my number through email?
Sir, these were the best 30 minutes I spent in RUclips all of my life. Thank you so much!!
Fr
math would be so much more understandable/accessible if mathematicians just used whole words/phrases to define variables instead of single letters. Like why do i need i hold in my head "r = risk" can you just say "risk"? what do you gain by abbreviating every little detail?
i'm sorry if i sound annoyed or obnoxious but for me it's so much more easier to grasp the full concept of what is being explained when i don't have to hold all these little bits of translation in my head at the same time. I'm sure there's some level efficiency gained by growing the mental muscles of holding multiple definitions in ones brain at a time. but there is such a thing as over abstracting variables to be placeholders that could mean anything.
this video seems really cool but i honestly just don't have the capacity to retain all these definitions just to understand what "p(w) * r / t - s" means. maybe my brain just works different or i'm dumb, idk maybe i'm just a software engineer who is so used to thoughtfully named variables that this level of abstraction just feel esoteric.
To attempt to give a constructive response/roughly answer "what do you gain by abbreviations every little detail", I think there's a few things:
1 - visual space:
Often, math expressions end up including many more variables and operations chained together than eg. programming expressions, so writing variables out as full names would produce a massive amount of text that many people would find more intimidating to read.
(Personally, I would agree that the programming approach of splitting more complex blocks into a collection of smaller, more readable expressions is a more generally effective solution to this problem, and you do see this in math also to some extent.)
2 - abstraction is a tool:
You mention "over-abstracting variables to placeholders that could mean anything". Most mathematicians see this as a very beneficial thing to do, for a few reasons.
2a - reusability: if you can map two systems onto the same placeholder structure, you can use the same analysis for both, and most mathematicians find it easier to recognize these patterns when thinking of them in threes more abstracted terms.
2b - (not) remembering definitions:
With how mathematicians approach things, I think, maintaining awareness of variables definitions isn't actually something it's seen as useful to do. When manipulating a set of expressions, really all you need to keep track of is just the datatype of each variable, and the actual definitions only matter at the very end when you're plugging stuff in for evaluation.
2ca - definitional flexibility:
Often, it's not clear what descriptive variable name to give something. If you have a particularly nasty expression and want to pull past of it out as a separate variable definition to make it easier to handle, you might have no idea what an appropriate intuitive name for that part would be.
2cb - definitional specificity:
Often, giving a descriptive variable name is seen as a bad thing, since it may get mixed up with other uses of the term, and promote misuse or misinterpretation. "Average", as demonstrated in this video, is a great example of such a term: someone could easily write "avg" to mean geometric average and have it misinterpreted as meaning arithmetic average.
HOWEVER - agreeing with you:
Many sources do lean on symbol conventions to what I would agree is an unhelpful extent. My background is in electrical engineering, and physics texts are absolutely notorious for this; even worse, physics and EE texts disagree on some conventions, such as calling sqrt(-1) i or j.
Overall, I would say the high degree of abstain and abbreviation popular in math is a very useful tool, but really could stand to more heavily lean on multi-statement formatting and declarative clarity.
High degree of abstraction* typo in last line
This video gave me a lot to think about including the intuition of putting my money under my mattress.
Well, only the house wins in a casino, and in capitalism you only win by betting on average perpetual* growth. (Perpetual* meaning while capitalism lasts)
The other ways to make reliable gains are to bet on crisis happening, but that needs a lot of data analysis.
You can do better than your intuition tells you, but not by a lot. In fact the more you have the better you can hedge. Funny how that is. It's almost like if the system that favours those that have inherently less risk of losing is favoured by them.
Excellent explanation, a link to this video should be posted under all those investment strategy videos, especially all those daytrading scams.
If you don't understand every aspect of this video, you should stay away from daytrading.
If you understand the whole video, you will most probably don't want to do daytrading 🤩
Very nice video, thank you! I think the proof of equivalence with maximizing the geometric mean can be much simplified by expressing the random variable ln(G) as a function of the ransom variable k, the number of wins
This is a great video as a proof of the Kelly Criterion. Congratulations
Thanks for the video, I enjoyed all the examples and metaphors in the beginning. I think it would be great if you had more in the second half. And especially to wrap up the video, some examples would have been great to drive the point home.
Actually, this also explains a lot of reinforcement learning based algorithms and other branches .. nice video
I found a counterexample for the continuous case:
let X be a standard normal distribution N(0,1) which has one mode at X = 0
then Y = ∛X is a transformed random variable, and the real cuberoot is monotonic,
but the probability density function of Y is
f(x) = (3/√(2π)) Exp[-x^6/2] x^2 which has 2 different modes
Beautiful job!!
So i really disliked statistics class. This video, while i still have some dislike towards statistics, I want to relearn all of it again. Seems that statistics, out of all the branch of mathematics, is the most applicable in day to day life. Math class should teach more of the different types of mean, and how they can be used to solve questions from elementary school level to industrial real world stuff. It's not like it's the best, just another way of thinking the same issue and i find it really intriuguing
thanks for the video :)
Solution: Get too big to fail, have tax payers cover the bill, and then give yourself a nice Christmas bonus.
soooo in conclusion…
Yeah, same. Kkkkkkkkkkk.
In conclusion, if you understand all these concepts, find the appropriate tool to use for appropriate situation, then investing is no longer gambling in the everyday sense. It is not and never will be as simple as "follow these simple steps to get rich quick".
@@gbBakuryu I mean, he begins with “even though the expected value is positive, doesn’t mean I should bet 100% repeatedly”. Which is obvious. So, what amount should I bet. Maybe I’m just dumb, but I don’t think he responds this question in any part of the video.
@@gbBakuryu the problem is that i dont understand the concepts because i
can’t speak math. if u used real words and not numerical gibberish it would make sense.
@@gbBakuryu when did i ever say i think following simple steps will get me rich quick don’t fucking put words in my mouth mate fuck u. i know u think ur smarter than me because i type like this and i critiqued u but it is actually u who is so stupid than u underestimate others and overestimate urself because u know which numbers go in what orders to make x=z or whatever the fuck. can u please just get off ur fucking high horse and tell us in human words what the fuck ur talking abt. what is the ideal level of risk that would increase returns without leading to eventual implosion? or is such a thing nonexistent? please explain in words and symbols that arent these niche fucking mathematical calculations thrown up on the screen. or do we not deserve to know unless were math gigachads like u? r u a fucking gatekeeper? wanna keep specialized knowledge and wealth out of the hands of the filthy fucking degenerate masses huh?
we dont get to know what u think if we didnt take fucking college calculus? fuck u. the way u responded to me was patronizing as fuck. i know exactly what type of person u r. midwit fucking pseudointellectual ‘expert’cuck
0 to the power of 0 is 1. 0 to positive powers is 0 because multplying by 0 gives you zero. But 0 to the 0 is an empty product: you start with 1 and then don't multiply by anything. Also, the limit of x to the y as (x,y) approaches (0,0) doesn't exist, so there isn't a way to define this with its limit. I hope that helps.
Is 0 to the power of 0 1 the reason why the universe exists? 😀
There are too few views on this excellent video
i like your ring theory video waiting for zero divisors 2
20:52. The easiest way to do it is evaluate it using binomial theorem:
You just multiply
- p^k multiply (1+tr)^k together to get (p + ptr)^k
- q^(n-k) multiply (1-sr)^(n-k) together to get (q-qsr)^(n-k).
Then you just have E (n over k) * (p + ptr)^k * (q-qsr)^(n-k) = (p + ptr + q-qsr)^n = (1 + ptr - qsr)^n
I wish I already understood everything. It'll take me a few years or more to understand all of it. Do you have courses?
what happens if the "average" is in the beneficial range but one, or more, local mean is negative? To put it another way : imagine a scammer who runs a "clean" game until a big spender arrives then influences the odds to his own advantage ... but no so much as to reduce the overall average below the inflection point.
Real world, re the casino odds, the best math for casino gambling is DON'T DO THAT. Which I'm glad to see you opened with.
Hey, I'm a little confused at 26:03 . The median was 4 and so everything above 4 is at least half. But why is everything below 4 and 3 at least half as well?
Everything down to 3, so 3 and above
Nice job, mate! How did you edited your beautiful videos? Lemme know that
For combining the video and audio? Not sure. For making the video? To me it looks like Manim. No link since it will probably get nuked, but it’s the first result when you google "Manim"
16:43 This has been bothering me, how did you come up with and calculate the number of times a six 6 would be rolled if a die is rolled ten times? I’ve been trying to calculate and figure it out, but I’m coming up different answers.
Is there an online calculator to find the right percentage allocation?
consider holding your microphone at a moderately-constant distance away from you. There are weird times where your one part of a sentence sounds as if you were in a room, and the others sound good.
Wondering how this could apply to selling oout the money options
If there's a game where you double or lose your bet on a fair 50% chance, you can come out on top by doubling your bet each time, but if you start at $10 and lose an unlikely but possible 5 times in a row, your next bet is $320 - you lose when the next bet is more than you have. I wonder if a similar strategy could work for a game with negative R, but with hilariously large increases in bet that would be unsustainable in real life
This was a long way to go about saying, as many papers have already written about, just use a fraction of kelly, 1/2 or 1/4 whatever youre comfortable with really...
So.....what's the best strategy for the S&P500?
Using the data, he calculated, that there is 59% of winning by using strategy "sell at 2х or at 0,75x.
Now the question is what part of your portfolio you should invest.
Another part of the video was about the Kelly's formula:
r = P/S - Q/T. P =59%, S=0.25. Q= 41% T = 1.
0.59/0.25 - 0.41/1 = 1,95.
For this tactic you should use 1,95x of your current portfolio.
If u want to use any another strategy, you should analyse the data previously, count the w/l percent's and count wich parts of portfoilo u should use)
@@user-bs9yw3dp5r So use 2x leverage? But that's not really sustainable long-term, unless you invest in a leveraged ETF
3:01
If the expected value is positive why will I eventually lose everything?
In other words Why does act of maximizing expected payout lead to long term ruins?
Let's say we flip coins. Heads I get your bet. Tails I pay you twice your bet. A game you would want to play as often and with as much money as you want which is very bad for me.
Now next we assume that I own unlimited money.
In this case you might think that you want to bet all of your money every single time, but you would be wrong.
Let's say you have 1k $ saved. You bet. You win. Now you have 3k $. Now you bet 3k $. This time you lose. That was bound to happen eventually. Just bet again - oh wait, you don't have anything left. You should have become a millionaire, instead you lost everything. But with your strategy to become a millionaire you would have had to win 6 times in a row, that's very unlikely. If you only bet half of what you have, then you get to play much more often and thus abuse the game much better and have a much better chance at becoming a millionaire.
Okay, let's dial back: Same game, you own 1000$. This time you only bet 500$. You win. Now you have 2500$. You bet 1250$. Lose. No problem, you still have more than you started with and even if you lose the next two games you are still likely to become a millionaire. Now you want to bet 625$. I refuse. It's a terrible game for me. Darn, maybe you should have bet everything after all.
One more thing: In the first scenario you could have gotten very lucky and become a millionaire. Let's change the rules 1 more time to make it more obvious: You tell me your strategy and then we run through 1000 bets before you get to change anything. If you bet everything every time, then you might get incredibly lucky to have won an equivalent of the whole universe in gold at one point and I'd be still standing there, smiling, knowing that your not even close to not losing everything to me (and most likely I won't have to reveal to you, that I do actually not own infinite money and in fact not even the equivalent of the universe in gold, although that's much less). But if you just calculate the expected value, then you might get the idea, that betting everything every time is a great strategy.
The expected payout is skewed by super improbable but gigantic returns.
Playing at maximum risk is like playing one game where you have 1/2^N chance of winning 3^N times your bet, and 1-1/2^N of losing your bet.
The main issue is that the law of large numbers does not apply here : the variance of this game grows much faster than N, the expected value is thus meaningless.
@@jeanf6295 Yes I understand what you are saying and thanks for pointing that out.
But over here in the given example, the probability of winning P(W) is 0.59 which is pretty high. So why is such a high risk-high reward strategy detrimental, even after such a high probability of winning statistically speaking?
Obviously practically you won't risk all your money in a bet even if chance of winning is 99% because if you lose [However unlikely] you will need to live on the roads.
Take a game where flip a coin heads you 10x your money tails you lose everything. It's always optimal to play one more time but playing this optimal strategy will lead to losing everything. The longer you play the expected value grows and eventually you lose it all
@@jeanf6295yeah it creates a paradox. Where you should in theory play forever to get an infinite amount but with a probability that approaches 0, and a probability that approaches 100% that you lose it all
I don’t get it. What is the percentage of the stack that I should bet? The formula must have the expected value and the percentage only. Right? There is a lot of variables in the final formula.
you have to worry about the discrepancies in your estimation of the odds because if you mess that up, then the kelly critereon stops working. in general though you want to give a conservative estimate of the probability. then put that into an online calculator that will solve it automatically.
It's a shame youtube doesn't let me like this video more than once.
3:25 sudden ASMR
Conclusion?
Does maximising losses guarantee profit? I hope so.
Interesting math. & Ka-ching, huh?
6:28 r > 0 not 1. Any value over 0 is positive gain.
The problem with probability is that it is nearly impossible to honestly estimate it reliably. Yet mathematical people throw them around with such confidence it gives the naive impression of accuracy.
medieval peasant brain
In some cases it's easier than in others. In investing, the probabilities are all estimates, but in casino games the probabilities are all part of the game. The odds of getting 21 in blackjack or of the ball landing on black in roulette can be known exactly
When you say mathematical people, do you mean people who over estimate their skills in mathematics? You and I probably don’t disagree that there is an underlying “real probability” to an event that we might not be able to directly measure and there is the perceived probability that we can measure through taking multiple outcomes of the event and dividing the positive outcome by the total number of outcomes. But there are fields of study that discuss this exact thing. I’m pretty sure the overwhelming majority of stem students (and other degrees as well) have had a class that discusses that. It might not be common knowledge but it’s not a secret either. I think it’s equally naive to say that you definitely know the probability of something after 10 trials as it is to say that “you don’t know what the probability is” after hundreds or thousands of trials when all of modern science is built on the off chance that we got the real probability wrong.
it really isn't in literally every gambling game, you know why? would you as a casino risk losing money on your games? you control the probability so that it's in your favor, or else you will go bankrupt.
for example in the roulette there are 37 slots, half black half red and one green, so if you choose a color the probability of it appearing is less than half percent. it is mathematically proven in the law of large numbers and the central limit theorem that eventually with a big enough sample the estimated average will be distributed as a normal distribution
(assuming indipendence between the elements of the sample and given that the elements of the sample have the same distribution, which both hold true) with average equal to the one of the distribution of each element of the sample and variance equal to the one of the distribution of each element of the sample divided by the number of elements of the sample
in simple terms
you have to know:
how the probability is distributed for each element of a sample (probability as a person of winning a certain numbers of games choosing reds = binomial distribution of average k*p where k is the number of trials and p is 1/2-1/37)
that there is not a big number of influences from one player and another
that a lot of people will play that game (more than 30 usually to apply the law)
you will be mathematically sure (very low variance since it's devided by the number of players) to gain money as the casino since the average, which is usually referred as the "expected value" will be on your favor, and it cannot be any other way, luck does not apply to large numbers
(i wrote all of this because i have nothing to do and took probability and statistics)
@@CalebTerryREDIn investing, not only are probabilities obtained through estimates, but since the financial markets are complex adaptive systems, even the estimating criteria changes. In other words, you're actually trying to bet not on the current criteria, but on the expected price-dictating criteria of when you'll close the position.
Brb gonna go make a fortune
Hey diddle diddle,
The Median's the middle.
You add then divide for the mean.
The Mode's the one you see the most,
And the Range is the difference between.
4th grade flashbacks
Critique: switching microphones every sentence was very distracting.
Bro if you are distracted by a slight change in voice you are the problem!
Can one deduce to always hedge as a solution?
The word "dice" is plural. One may refer to two or more "dice", but not to one "dice". The singular of "dice" is "die".
🎉
🤓☝
Although you are correct historically, dice is accepted as singular and is very commonly used in academic literature. Language changes.
@@eak74 Believe it or not, I am well aware of changes in the language. Although it may be a losing battle, I believe in arguing against such linguistic monstrosities as "very unique" , and "one dice". I have already accepted as fait accompli the singular "they" but I avoid it when possible.
and this is why french is a bad influence. not because of this exact word, but because it proves that it opened the gates to words with the same mental value as a dried bog
The world would be so much nicer if humans were naturally good at statistics and probability
Hello, what i need to study to understand the math of this video,? I want to learn how to compute gambling edge.
Algebra, simple probably and sequences and series are essential. Understanding conditional probably, optimisation and sensitivity analysis will also help but aren't essential as he explains it quite well.
A lot, but this is only statistics. There are assumptions behind statistics. One of them is of an assumption of a "stationary process". You won't find an "interesting" and "strict" one in your lifetime hence all the statistics has its time validity intervals. All the known stationary processes have already been exploited. These, who got there first turned the field into some oligopolies. The "interesting" ones are subject to a fierce competition and some occasional "upsetting of the chessboard", so to speak. In other words, the "interesting" statistics are valid within some time framework which might be as small as a dozen milliseconds... nanoseconds even (HFT).
You need some good approximation of an underlying dynamical system to be able to make reasonable guesses about statistics and time intervals.
The beauty of mathematics lies in the fact, that these, purely mathematical, considerations apply in a multitude of other, non-financial situations, say, biological evolution.
23:48 had no clue this guy was lying haahaha
I actually used this method to win a local church lottery.
What's the answer?
18:25 If Y = 1/X, then when X is 0, Y should be undefined, not 0.
3:00 I . . . don't understand? You win more than you lose, and when you do lose, you lose 75% less than you would win. So in what world do you lose all your money on average?
probability is confusing
you will eventually lose just once if you keep playing. If you all in, that guarantees that you lose everything that one time
You start with X money, and bet an amount B, either winning 2B, or losing B, (100% if you win, 100% if you lose, double or nothing).
If you choose your bet B to be X - all your money, you can either end up with 2X, or 0. From this point forwards, X is equal to either 2X, or 0.
In the former case, you can read this comment from the top down again and keep going. In the latter case, you have no money, and winning double of nothing leaves you with still nothing. If you start a game with zero, you end the game with zero. It is an endpoint, a black hole from which you will never escape.
If you played an infinite amount of games, you would end up with the exact expected value by definition. In an infinite amount of games, because there's always a way to reach zero, you will eventually hit it, and then play infinitely more, ending up with zero every time, bringing your average down to zero.
@@Asdayasman but you don't lose all your money in his example, only 25% of it. And it isn't additive, so losing 4 times in a row would only lose ~68% of your money, while winning four times in a row, which is more likely, will give 1500% more of your money back.
Although I am starting to understand, if there's a way to reach zero, you'll eventually find it given infinite time. But if money was allowed to be continuous, instead of in discrete $0.01, then it would be likely to blow up to infinity.
@@aguyontheinternet8436 My bad, I misunderstood the example, but you've got the point for sure - if there's a way to reach zero, you're gonna.
@@aguyontheinternet8436leverage/margin means ur playing with amount of money more than your own capital. Taking 4× leverage means ur betting 4 times the amount of money in your portfolio
Why I feel that I am dumb after looking this video?
because its maths masturbation
Most Fortune 500 companies maximize profits and most keep growing
ok, so you want to maximize final profit, not average profit. Is this a .... "duh!"?
Sick video, let’s make some money boys
Now I can become a trillionaire
commit to one trillion activities that can guarantee you one dollar
@@0MVR_0too bad it would take about 6500 lifetimes if you were paid $1 for every breath you take.
Why does the voice keep changing really interrupts the flow of the vid
Now no one can stop me from becoming billionaire 😅
great video, i really needed a refresher in stochastics, however i was confused by the comment about Karl Marx wanting equal wealth distribution, which is untrue
Gambling is illegal in some countries
You forgot in the civilized world you're never risking anything because of the existence of safety nets. As the name of the strategy Foods Stamps or Lambo implies!
What the hell am i doing to do with all these livers and kidneys?
let profits ride until they become losses
the key is having your losses actually be someone else's loss while you can keep the profits
The over recording sucks, it'd be nice if you just did the entire paragraph again.
Simulating complex probabilities on a computer is easier lol
shouldn't have called the curve a parabola.
Didn't understand a thing that happened
no i don't want to be the insurance company stealing money from people
3:40 math strikes again!
- How should we abbreviate RRRRisk? hmm.. r. What a great choice!
- What about Gain? ...n? g?.. t! Yes of course, Tgaint, perfect sense!
- Ok now we are at Lose, this should be easy. S for loSé
- But why? so that 5:04 everything fits neatly on the screen as pqrst!
- That completely throws me off! I've no idea what each letter is.
- It's ok we can spend some time to describe each and get familiar with them.
- Wouldn't all this be avoided if we use meaningful variable names?
*Insert Boardroom Suggestion meme where reason is thrown out the window*
I'll just go check if 3b1b posted anything new...
Gambler’s fallacy
8:16
tell me you never read kapital
without telling me you are still to misunderstand the concept of rates in surplus-value.
Marx did not care about perfect equality of distributions, the notion is just slander.
@@0MVR_0 😂😂🤣🤣
@@sebastian2zen you never read kapital
Irrational emotions and drunk people populate casino games... gambling is losing math is not necessary to avoid gambling 😅
It's a pretty evil empire.
Okay nerd tell me how to get rich at the casino and investing
I hear alot of math porn and little solutions
Um, you didn't include the fact that any major gambling or investing system is going to be rigged which reduces your probability of winning to 0.
Pretty sure that’s what he meant when he said “you’ll lose everything to the house” in the first minute of the video.
So what games should we be betting on bruh... and what should we be betting... that's what I'm here for
Hold your horses... Government specialists who you should put all your faith into. Say these numbers you are giving are wrong. Obviously they are not just paid idiots hell bent on stripping the poor of what little they have. I am being sarcastic...
Needlessly long, low information density
8:13 "imagine one person having three dollars, and another person having five dollars. If Carl Marx saw this, he would want to equally distribute wealth."
Nah, it would depend on which one of the people was Marx. If he had five dollars he'd say nothing. If he had three dollars he'd be saying the guy with five should give him two.
I will spit on Marx' grave the next time I'm in the capital.
This example isn't related to Marx at all
nothing to do with Marx
so you're busy spitting and the drivel lands on your shirt.
As a mathematician, I’ve never heard so much math with so little understanding behind it before 🤮
this is so unfocused, going in such random places compared to the premise. this is a bad video. im incentivised to skip through it, because of how all over the place it is
TLDR ... if you bet everything on a get rich quick scheme, you are likely to lose everything.
This is why theoretical traders can’t make it in the real world. Theory and praxis-heaven and hell!