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
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.
@@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.
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.
@@michaegi4717no, you shouldn’t understand all theory before engaging in risky investments. You really only need to know base level statistics and Kelly criterion to make money.
It was physics, not chemistry. Try to regain the wonderment you once had, and applying this video to investing will enhance your ability to make decisions over a large number of entries
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.
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
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.
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.
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.
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?
there's that amazing book named 'Fooled by Randomness' where it is explained that among many other good tactics expert stock traders say 'let some one else get the last dollar' which seems aligned to this Mathematical corollary, that if one attempts to win it all, such tactic is far more dangerous than just walking away before it's too late.
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*...
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.
@@Kashlarthemagicman _"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."_ - So you guys are aware of the issue and still do it. Damnit. Believe me people find it more intimidating to read what is essentially single digit hash keys in place of actual variable names.
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
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
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...
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
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.
Did you never compute sums with binomial coefficient before ? The sum at 20:52 and the expected value of a binomial is easy and the k(n,k)=n(n-1,k-1) is a well known identity. Thoses two things are easy for first year math student.
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.
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)
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.
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 :)
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".
@@gbBaku 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.
@@gbBaku 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.
@@gbBaku 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
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
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.
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.
The concept in this video is too abstract for an investor and market never allows him to maximize his profit because other investors, then, would be forced to maximize their losses ! So, a wise investor settles for whatever profit comes to him and prepare for the next game. He has to prepare for death also ! However, I should add finally that the knowledge of statistics of the author is superb !
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.
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?
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
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.
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.
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.
I thought the other means was just people throwing random stuff that felt like a mean and call it a day. Never thought they're all connected systematically
@@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
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.
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 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.
@@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
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"
At small accounts i always yolo the trades for example 500 to 1000 and once i start accumularing bigger account like 5k to 10k i would lower my risk. If you have big enough account having just 5 more winners per month at 2 percent risk will net you 10percent profit per month which will be enough to cover expenses and grow your account. Imo hardest part is actually making high win ratio. If tou have high win you can grow your account slower with lower risk but eventualy you make big money since we are compounding.
What a very specific audience this video is targeting… it’s way too basic for anyone who actually does finance math (explaining random variable, mean, etc) but probably too mathy for general audience who just want a simple bitesize explanation of Kelly criteria.
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
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.
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...
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 🤩
@@jazzyj2899 I don't know a shorter explenation than with this video, plus some aspects of how prices are defined in stock markets. But maybe we can limit it to your specific aspect. Maybe I'm able to answer your specific question. Why do you think that daytrading is a good way to invest your money?
I have been trading stocks and in the first 100 days I have used my entire account all in on each day trade. My win rate is 92%. My gains are 22.14% growth per month. With stocks you have the added benefit of indicators and patterns and if you can buy only when stocks are oversold they are bound to go back up. I have a daily pattern that wins 92% of the time. This has become my full time cashflow in just under 4 months. One more note on stocks is that they really don’t go to $0 if you buy the top companies. The risk of Meta stock going to $0 for example is infinitely less than the risk of anything else. So even the losses are minimized risk as stocks typically grow in value and you can stop losses quickly with one click to exit losing trades.
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
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
@@monkeybobvery well said I was very tempted to leave an AI generated reply to your comment
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.
@@michaegi4717no, you shouldn’t understand all theory before engaging in risky investments. You really only need to know base level statistics and Kelly criterion to make money.
Kid just wanted to explain what he learned yesterday at class.
It was physics, not chemistry. Try to regain the wonderment you once had, and applying this video to investing will enhance your ability to make decisions over a large number of entries
Serious and elegant explanation of the Kelly criterion, no Ferraris, no fancy stuff, no fake, thank you, you earned a new suscriptor
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 think it’s cool that you provided so much for the creator to consider :)
Ok chatgpt u can rest now
lost af but watched the whole thing
Same
very little people can watch these things and not get lost at all
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
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.
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.
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!
Not possible.
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?
there's that amazing book named 'Fooled by Randomness' where it is explained that among many other good tactics expert stock traders say 'let some one else get the last dollar' which seems aligned to this Mathematical corollary, that if one attempts to win it all, such tactic is far more dangerous than just walking away before it's too late.
Sir, these were the best 30 minutes I spent in RUclips all of my life. Thank you so much!!
Fr
Bro the insurance company stealing money from you joke got me. I subscribed. Good work.
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.
18:41 The range of Y is actually given by {-1, Inf, 1, 1/2}.
Thanks for the great video!
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
@@Kashlarthemagicman
_"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."_
- So you guys are aware of the issue and still do it. Damnit. Believe me people find it more intimidating to read what is essentially single digit hash keys in place of actual variable names.
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
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
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...
Why a fraction and not the full thing
7:48 Now this gives a new way to look at am gm inequality
So mean of order a is greater than mean of order b if a > b
Nice!!
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!!
Didn't realize I was so uneducated til I watched this video.
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.
would have appreciated a conclusion
There are too few views on this excellent video
10:29 it should be proportional to the mean quadratic speed rather than the square of the mean speed. Huge difference
Did you never compute sums with binomial coefficient before ? The sum at 20:52 and the expected value of a binomial is easy and the k(n,k)=n(n-1,k-1) is a well known identity. Thoses two things are easy for first year math student.
This is a great video as a proof of the Kelly Criterion. Congratulations
Just incredible. Well done!
So what is the answer
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? 😀
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)
@@ПрудиславВладиславович So use 2x leverage? But that's not really sustainable long-term, unless you invest in a leveraged ETF
Does maximising losses guarantee profit? I hope so.
Yes just keep gambling and you will win big i promise
18:25 If Y = 1/X, then when X is 0, Y should be undefined, not 0.
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
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 :)
Visit statquests
18:28
Are we just casually saying that 1/0 = 0 ?
6:28 r > 0 not 1. Any value over 0 is positive gain.
I know i learnt this in high school 7 years ago , but this is so much clearer hahaha
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".
@@gbBaku 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.
@@gbBaku 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.
@@gbBaku 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
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
Critique: switching microphones every sentence was very distracting.
Bro if you are distracted by a slight change in voice you are the problem!
Hello, may you provide further clarification on how you reached the conclusion at 15:45? Thank you
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.
The concept in this video is too abstract for an investor and market never allows him to maximize his profit because other investors, then, would be forced to maximize their losses ! So, a wise investor settles for whatever profit comes to him and prepare for the next game. He has to prepare for death also ! However, I should add finally that the knowledge of statistics of the author is superb !
i like your ring theory video waiting for zero divisors 2
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.
It's a shame youtube doesn't let me like this video more than once.
I would like to see more on this topic
5:25 can someone explain me this graph ?
I wish I already understood everything. It'll take me a few years or more to understand all of it. Do you have courses?
This just covered my 6 month prob stats course in 30 minutes lmao
Is "abstractify" actually a proper REAL word, per language authorities? Or is it just another one of those words that's "creeping in"?
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
With a 1:1 rrr & I trade once a day can I risk 25% of my account per trade with out blowing it with a 70% win rate?
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
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
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.
Look up binomial distribution
Is there an online calculator to find the right percentage allocation?
What's the answer?
Wondering how this could apply to selling oout the money options
Conclusion?
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.
The house always wins lol
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.
I actually used this method to win a local church lottery.
I thought the other means was just people throwing random stuff that felt like a mean and call it a day. Never thought they're all connected systematically
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
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.
The world would be so much nicer if humans were naturally good at statistics and probability
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
Can one deduce to always hedge as a solution?
Solution: Get too big to fail, have tax payers cover the bill, and then give yourself a nice Christmas bonus.
1:05 Money printer go brrrrrr
Well said
Marx had nothing to say about wealth.
He was all about private property, not personal property.
I understood that even if ways to maximize your profit are presented to you. They are so not understandable that I better stop try investing at all.
3:25 sudden ASMR
ok, so you want to maximize final profit, not average profit. Is this a .... "duh!"?
Yea i just follow price action and sentiment...i make good money doing that :D
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"
At small accounts i always yolo the trades for example 500 to 1000 and once i start accumularing bigger account like 5k to 10k i would lower my risk. If you have big enough account having just 5 more winners per month at 2 percent risk will net you 10percent profit per month which will be enough to cover expenses and grow your account. Imo hardest part is actually making high win ratio. If tou have high win you can grow your account slower with lower risk but eventualy you make big money since we are compounding.
Why I feel that I am dumb after looking this video?
because its maths masturbation
Why does the voice keep changing really interrupts the flow of the vid
I really wish I understood this.
Interesting math. & Ka-ching, huh?
What the hell am i doing to do with all these livers and kidneys?
What a very specific audience this video is targeting… it’s way too basic for anyone who actually does finance math (explaining random variable, mean, etc) but probably too mathy for general audience who just want a simple bitesize explanation of Kelly criteria.
23:48 had no clue this guy was lying haahaha
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
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
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.
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...
Thanks
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 🤩
could you explain for the layman?
@@jazzyj2899 I don't know a shorter explenation than with this video, plus some aspects of how prices are defined in stock markets. But maybe we can limit it to your specific aspect. Maybe I'm able to answer your specific question.
Why do you think that daytrading is a good way to invest your money?
I have been trading stocks and in the first 100 days I have used my entire account all in on each day trade.
My win rate is 92%.
My gains are 22.14% growth per month.
With stocks you have the added benefit of indicators and patterns and if you can buy only when stocks are oversold they are bound to go back up.
I have a daily pattern that wins 92% of the time.
This has become my full time cashflow in just under 4 months.
One more note on stocks is that they really don’t go to $0 if you buy the top companies. The risk of Meta stock going to $0 for example is infinitely less than the risk of anything else.
So even the losses are minimized risk as stocks typically grow in value and you can stop losses quickly with one click to exit losing trades.
Thats why I dont follow the Kelly% on my KPI.
Gambling is illegal in some countries
Most Fortune 500 companies maximize profits and most keep growing