6. Monte Carlo Simulation

[@splashd]

The sign of a good teacher--I landed here by accident, stayed for the entire lecture, and understood all of it...

[@leixun]

*My takeaways:* 1. History of Monte Carlo Simulation 0:56 2. Monte Carlo Simulation 3:23 - Example1: coins 6:03 - Variance 10:00 - Example2: Roulette 11:00 3. Law of large numbers 18:40 4. Misunderstanding on the law of large numbers: Gambler's fallacy 19:48 5. Regression to the mean 22:42 6. Quantifying variation in data: variance and standard deviation 30:14 - Always think about standard deviation in the context of mean 35:10 7. Confidence level and intervals 36:00 8. Empirical rule for computing confidence intervals 39:27 9. Assumptions underlying empirical rule 43:40 - mean estimation error is 0 - Normal distribution 10. Probability density function 46:25

[@dr.mohamedaitnouh4501]

thank you Mr. Lei

[@leixun]

Dr. Mohamed Ait Nouh you’re welcome :)

[@pajeetsingh]

Thanks Mr. Lel

[@leixun]

Pajeet Singh you’re welcome

[@imrs07]

Thank you Mr. Lei

[@sitrakaforler8696]

00:00 Monte Carlo simulation is a method of estimating unknown quantities using inferential statistics. 06:48 Variance affects confidence in probability predictions 13:09 Law of large numbers: Expected return of fair roulette wheel is 0 over infinite spins 19:23 Understanding the Gambler's Fallacy and Regression to the Mean 25:16 Regression to the mean is a statistical phenomenon where extreme events tend to move towards the average with more samples. 31:11 Understanding variance and standard deviation for computing confidence intervals. 37:37 Understanding confidence intervals and the empirical rule 44:04 Probability distributions can be discrete or continuous, and are described by probability density functions. Crafted by Merlin AI.

[@hamidrajabi8775]

I've never met him, but he taught me python years ago. we should be grateful for such giving human beings.

[@kepstein8888]

This is a true teacher. He actually explains the concepts instead of just scribbling equations on the board.

[@cly5570]

Couldn't agree more. I am hooked.

[@lidarman2]

Why MIT is a top school. I love that MIT allows anyone to watch these for free.

[@IonidisIX]

COULD NOT AGREE MORE!!! He is truly amazing. Suddenly the Stats I did on a Data Science Coursera course start to make sense. A couple of more lectures by him and I will have everything sorted out in my mind... My God. Some lecturers just Got it and some just Don't.

[@benphua]

I wonder how much time and effort was made to ensure every word was meaningful and carefully stated (just been through a course with a lecturer who knew his stuff but mostly winged it which was one of the biggest wastes of my time). I also noticed not a single 'um' or 'uh' which is amazing.

[@cbarlow3]

@@benphua Well, I noticed four "ums" or "uhs" in second 0:35 to 0:45 alone, but I agree the lecture is very clear.

[@pepegallardo4060]

Watching Prof. Guttah teaching is a joy. A true inspiration for those of us who also like teaching and want to do better

[@mikebernard8535]

For those looking for some visuals of how a Monte Carlo simulation works, see the second half or so of lecture 7 on Confidence Intervals.

[@francissydnor7891]

MVP

[@przemysawniedziela4631]

Thanks a lot, that was what I was looking for!

[@bharathsf]

Which playlist??

[@kenerwin5198]

This guy is such a fantastic teacher. I would love to have him in person, thanks again for uploading the video!

[@zZE94]

Have him for ... breakfast?

[@antoniomoraes1741]

@@zZE94 Ken really sounded weird ahahahha

[@DaviSouza-kq7xz]

He prolly would love have you in person too, for sure.

[@dennis1836]

At the university where I studied all teachers were also fantastic teachers until the exam. Afterwards they were all a**h****.

[@iPergjakshem]

I came here for the Monte Carlo simulation but got unexpectedly thus far the best explanation for simple concepts like Variance or Standard Deviation

[@27eharkness]

Not what I was looking for, but couldn't help but watch the entire video. Well done sir.

[@vydaniel]

same

[@SuperFreelibya]

The same!

[@danielschaben]

I love random walks through youtube

[@GaoyuanFanboy123]

wanted to know what a monte carlo simulation is but I guess ill revise some stats intuition ¯\_(ツ)_/¯

[@3ndr3wmusic56]

@@GaoyuanFanboy123 hahaah same xD

[@habeebyusuf7037]

this man right here is a true teacher, understands the subject topic deeply and speaks passionately

[@robertkelleher1850]

For those that may be confused, he misspoke at 23:36 "taller than average" should have been "taller than the parents". In the case that parents are shorter than average, it is expected that their children will be taller than them, not taller than average.

[@mdcamp00]

Some of the best explanations of statistics I’ve heard. Does a great job of breaking down concepts.

[@nikolavalizadeh133]

Unfortunately, during my studies at Bachelor and Master, I never had such great real professor. Thanks so much for sharing such great video.

[@ridhikakhanna6383]

After watching this lecture, I wish I was smart enough to get into such elite schools and be taught by such passionate teachers. Respect!

[@dxhunzai]

But you have access to MIT open courseware

[@durgeshkinnerkar2826]

Brilliant lecture. I can binge watch Professor John Guttag's lectures. Amazing.

[@commandofaku]

An instructor of the highest caliber; clear explanations, projects a seemingly universal likeable and fair personality, low intensity approach. Good hire MIT!

[@JebBradwell]

I love professors who make mistakes and make corrections accepting help from students.

[@aayushkhanal5564]

What a beautiful way to explain a concept. Starts with something so simple and gradually builds up to the more complex part, also delivers the lecture in a way that even a tiny bit of boredom can't creep in.

[@nmeyer1112]

At 8:30 he misses implications of Bayes theorem - if you observe 52 heads from 100 flips, it is still much more likely that the coin is fair than biased. Because as he mentions, there are many many more fair coins and dice our there than weighted ones. The probably you have to assess is P(52 heads | coin is fair) * P(coin is fair) vs P(52 heads | coin is biased) * P(coin is biased). Far more likely that it is fair.

[@rishabhsinha4765]

My thoughts too

[@Timehotosunlena]

the frequentist approach would work too

[@owenmurphy2275]

Should of done better in highschool and went to MIT. This is great. A true teacher

[@tawlguy123]

I really love the teachers at MIT. I have watched a ton of lectures from them and all have been great

[@NazriB]

Lies again? Support Indonesia Malaysia

[@JohnSmith-he5xg]

Thanks for addressing the apparent contradiction of the Gambler's Fallacy vs Regression to the Mean ~25:00 in. I'd always thought these 2 were in opposition, but guess I'd never heard (or thought of it) in the right frame of reference.

[@OlumideOni]

This is the best lecture I have ever seen on statistics. It wasn't even what I was looking for but couldn't take my eyes off it till the end. Thank you Professor! Thank you MIT!

[@papasmurf9146]

Excellent presentation. Don't know why KZbin presented the option of the video, but watched until the end. Very gifted professor. The only thing that I can think to improve it is to repeat the question from the audience so that the question is picked up on the recording.

[@batatambor]

One observation, the code returns totPocket/numSpins, which is in fact return per spin, not the expected return in %. In the exemple in particular since the bet is 1, numSpins equals the total value payed to play, hence the expected return in %. If you change the value of the bet, the output is not right.

[@georgejetson9801]

I love these old school professors. They are true masters.

[@GeneralZhang]

Good lecture overall but there is a bug in the code at 14:32 and 15:25 -- playRoulette should instead print 100 * totPocket / (numSpins * bet). The output in his example only looks correct because `bet` is 1. If `bet` were 2 and `numSpins` were 1, it either prints "-200%" or "7200%" (obviously you can't lose more than 100% or win more than 3600%).

same thought. Should have divided the bet amount to calculate the percentage

[@ractheworld]

Isn't he the most adorable teacher ever? Great job walking your audience through the material!

[@yusuffarah351]

Great teaching style. Small number of teachers can teach such concise and clarify. I learn a lot from the great educators.

[@user-js5tk2xz6v]

27:30 But if we start counting from the beginning of the series, when we have 5 blacks in row, then the next black would change the series of 5 into the series of 6 ,which is more extreme. Can't I think this way ?

[@isaacspark]

Wow..... He truly explained what monte carlo simulation in 50 min. Thank you Prof.

[@guestimator121]

+Isaac Park I've heard everything but a Monte Carlo here. Confidence intervals, regression to the mean, Gambler's Fallacy etc, but not much about Monte Karlo and its many alghorithms.

[@GbUnLimiteD]

26:53 Great answer to make the difference between gambler's fallacy and regression to the mean clear!

[@rorisangsitoboli4601]

Regression to mean is not the same as Gambler's fallacy in that Regression to mean basically says after an extreme event you are unlikely to get a successive extreme event. Gambler's fallacy says it is definite to get successive extreme events. Gambler's fallacy falls into the trap of assuming the events are dependent/correlated (linearly +ve/-ve). That is not the case in Fair Roulette.

[@d.v.faller9251]

Excellent lecture. Prof. Guttag is a great teacher. Thank you. Every course or lecture I have watched in this MIT Open Courseware has been superb. Thank you to the teachers and to MIT for posting.

[@alperensayar9679]

Hayatımdaki en iyi üniversite dersiydi.Thanks Prof J. Guttag

[@jordanfox840]

I feel like the slide at 22:00 is a good opportunity to introduce probability notation, since in English the second sentence sounds really misleading. The first sentence is P(26 consecutive reds). The second sentence is P(26 consecutive reds | the FIRST 25 are red). Strictly speaking the second sentence is grammatically incorrect, what the professor means is "Probability of a single roll being red, given that the last 25 were red." This makes it WAY easier to understand that rolls are not correlated. What is written on the slide makes it sound like there are 26+25 rolls taking place.

[@LaureanoLuna]

39.07 That a result will lie within an interval with probability 95% doesn't mean it will be within that interval 95% of the time. Probability cannot be directly translated into percent of times.

[@xichenjiang7799]

Hint: Playing on 1.25 speed is ideal for this video.

[@AbdulRabChachar]

Thanks. :))

[@samvandhapathak2167]

2x for engineering students in south asia

[@Matze27396]

For an foreign student from germany like me - 1.0 speed is good. But for all native english speakers i think he speaks quite slow.

[@mlsivaprasad]

But 1.0 speed is too good.

[@pipertripp]

pro-tip, mate. Thx for the time back.

[@rasterbate87]

Makes even high level material understandable to a neophyte. That's the mark of a skilled educator.

[@CodeJeffo]

Wonderful professor. So casual but I believe what the students learn will stick with them forever.

[@fabbiotec]

WANTED MORE ABOUT MONTE CARLO, but he is such an amazing teacher that I got stuck anyways!!!!

[@acesovernines]

Brilliant lecture...brought me back memories of school. Just one mistake @45:46 (perhaps oversimplification - discrete random variable need not have "finite" number of possible values, it can also be "countably infinte" as in Poisson). Again, I'm not trying to be a smart-ass...but this is an important consideration

[@dirkvanmaercke8469]

The slide at 25:05 is wrong ! For a system without memory (like a roulette), the past has NO EFFECT on future events. Therefore, the probability of any event remains the same, even after the occurrence of an extreme event. That means ; after an extreme event the system is exactly in the same state as it was when we started the game. After a sequence o 10 reds, the probability of getting a red at the next trial is just 18 ou of 37. Some people lost a lot of money in Monte-Carlo the day "red" turned up 26 times in a row. When doing Monte-Carlo simulations be careful of so-called "cyclic" random number generators. From a mathematical point of view, be aware that variance on the estimated mean value tends to zero as the number of trials increases, but the variance on the number of events does not. Check any good book on probability.

[@kasra545]

Finally understood what statistics is about after 10 years of endeavour! Thanks so much!

[@howardlam6181]

Trying applying it to obtain Lebsegue Integral. See, you probably have understood nothing.

[@harshabhogle1020]

Kasra Keshavarz your face shows how stupid you are

[@AbhishekSingh-pp1ks]

Howard Lam. It is “Lebesgue”

[@IonidisIX]

Suddenly the Stats I did on a Data Science Coursera course start to make sense. A couple of more lectures by him and I will have everything sorted out in my mind... My God. Some lecturers just Got it and some just Don't.

[@paulorufalco]

12:47 "win some lose some, it's all the same to me" Lemmy

[@BULLSHXTYT]

What a great introduction course that is simple to understand yet extremely powerful to student.

[@squashplaya0313]

23:33 this should be corrected to --> if the parents are shorter than average, the children are likely to be taller than the parents ( not taller than average).

[@wedeldylan]

True

[@SadatAbdela]

That was wonderful Sir, Big respect from Ethiopia. Please record lectures for people like me watching from remote.

[@quakerparrotandlovebirds1138]

As roulette dealer I am interested in how smaller bankrolls and length of playing sessions affect these numbers. Hold percentage for Roulette is much higher than 3% in our Casino. Most likely 20%+

[@happywednesday6741]

@22:15 the wording of the last sentence was confusing and made it sound like the opposite of reality! 😅 How it is written makes it sound that it's a 50% chance to get 26 consecutive reds, if the previous were 25 black...The correct statement is just to say, if you had 25 reds in a row, the 26th spin is still 50% to be red regardless of what happened previously as all spins are independent of one another (Gamblers Fallacy to think otherwise). Also how do you get 1/67,108,86*5* for a power of 2?

[@syncopowerstations]

I love a professional, whether he be a doctor or a scientist, who has the confidence and grace to admit that he makes an honest mistake.

[@davidwilkie9551]

Very good introduction of how the e-Pi-i conception of probabilistic Calculus by Pi circularity numberness/orbital is a dualistic +/- possible Infinite Sum, Normal/orthogonal self-defining "e", metastable +/- singularity convergence to zero difference, balance of frequency constants in Totality.

[@satoshinakamoto171]

such respect for these fantastic teachers

[@keyaamarsee9631]

Thank you for this great lecture. You explain it so well. I was looking for Monte Carlo Simulation but ended up watching the whole video.

[@bayesian7404]

He is such a great teacher on multiple topics. After this course I plan to finally take Linear Allgebra.

[@dragoda]

The roulette and coin flip needs to input other variables: maybe the next turn of the roulette the dealer spins the wheel harder or slower, or the balls shoots out of the fingers faster or slower. When you flip a coin maybe the thumb throws the coin harder or slower or you raise the hard to high and the results change. So, despite the simulations, in real life the odds are different. But, who has infinite time to flip infinite coins to confirm the mean value of 50% in a coin flip :)

[@williamlewis8773]

Under what conditions is "conformity to expectation" distinct from "regression to the mean" ? When are these phrases used equivalently ? by whom , and why ? In what ways does the use of statistically derived results differ between the population of typical social engineers and the population of physically science theorists , and "Why?" ?

[@paulmctaggart6947]

Had this same lecture in PSYCH Stats class at CofC. Learned a lot and this was fun to watch again

[@petterhemnes768]

Great professor! A slight hiccup on 23:38; I believe he meant to say if the parents are both shorter than average it is likely that the child will be taller than their parents (not average).

[@alvinsihombing18]

Thank you Prof. Guttag & MIT.

[@RedShipsofSpainAgain]

At 38:02, I believe there is a typo: The confidence interval should be between -6.8% and +0.2% (not +9.2%). We get this because the avg return is -3.3% and adding +3.5% for the upper bound of the CI would yield 0.2%

[@Enigma758]

He corrects that at 38:34

[@acool6401]

Thought I was dreaming or hallucinating and then was wondering why didn’t anybody see that? Good Catch! 👍🏼

[@pajeetsingh]

Thank you Professor Guttag and thank you late Stanislaw Ulam.

[@maeric522]

Can someone explain about the regression to the mean? If the first 10 trials are all red, why the second 10 trials will be less extreme, i.e. fewer than 10? If according to the gambler's fallacy, the independent property, the second 10 trials should have a MEMORYLESS property, why the second 10 trials must have fewer red?

[@davidjohansson1416]

His explanation of regression to the mean is slightly confuzing. Because the main point is that the number of samples increases. (Is this true?) in other words as like Law if large numbers, as sample converge to population varinace around mean will be smaller. NOT that there is an influnce.(i.i.d. Events).

[@dark_all_day9311]

Extremely Based series of lectures. Top tier professor!

[@jorgeriveramx]

Small mistake in minute 23:36 I'm sure what he meant to say is the child would be taller than the parents, but instead said taller than the average which makes no sense.

[@toddmarshall7573]

21:42 2^26 is 67108864. The proof (that 865 is wrong) is left to the student.

[@mikepiazza2000]

I feel like I with no prior knowledge just intuitively already understand all of this and use it in daily life. Cool to hear it's basis though and a more technical presentation

[@fritsvanzanten3573]

22:10 I understand (I think, I hope) that concept of independence, but then it is said we assume the wheel is not rigged. But is this assumption justified after 25 consecutive reds? Probably yes, things like this happen (and we don't forget them for decades), but on the other hand, at how many consecutive reds should we become suspicious?

[@fritsvanzanten3573]

But, regarding the following example, will my results in the next semester be independent from my results in this one?

[@wentaoqiu4072]

Ok, he is really good 33:45, how I hoped to have a prof. like him back in college.

[@franklipsky149]

the next toss is independent of the previous toss ;but there is a different question that can be asked :what is the probability of of x tail(heads) in a row=1/2^x .Two completely different betting strategies

[@rajjain7628]

That is what they call a gamblers fallacy.

[@BlacksterVFX]

Congratulations, you just fell for the Gambler's Fallacy...

[@longn.8804]

I love the sense of humour of the instructor. A great lecture indeed!

[@tjo8529]

Thank you for the great lecture. One question....at 39:00 I see it saying "The return on betting a pocket 10k times in European roulette is -3.3%". Was that based on the Monte Carlo sim? I ask because there are 37 pockets on a European roulette wheel. If you win it returns 35 to 1, plus your original wager, for 36 units returned on a win. 1/37 = 0.0270, for an expected return of -2.7%, or 97.3% (depending how you look at it) on European roulette. Thanks again for the awesome info...

[@creedrituel]

This is what is used to determine results of A/B testing folks, i had to learn this on the fly at my job

[@GPCTM]

proper: denoting a subset or subgroup that does not constitute the entire set or group, especially one that has more than one element.

[@MM-uh2qk]

Thank you Professor John guttag. You're a great teacher and reading your book --"introduction to computation and programming with python" has been a great experience thus far. Please, if you don't mind could you clarify me on this: When is an event said to be truly random? Or better still do we have truly random events? Randomness implies causal nondeterminism and from my little knowledge that's almost nonexistent. Events that yield uncertain outcomes are better delineated as predictively nondeterministic which doesn't imply that they are random but in stead reveals the limitations of our probing instruments and/ or statistical technique in unsheathing the nature of such events and correctly predicting their future states. No event to me qualifies as random, the outcome of coin flips, die throws could sufficiently be predicted to very high degrees of accuracy if only we could be patient enough to understand the physics of the processes - the coin/ die initial position, throwing/ flipping force, air drag, et cetera. So what processes are random?

[@rafaelalvesdasilva6013]

Momoh Mustapha your question is very interesting and very deep. The only truly random variables that I know of are those that describe a microscopic system in Quantum mechanics. If you measure the spin of an electron for example you have a 50% chance of getting spin up or down, there's nothing we can do to predict If we're getting spin up or down before we measure It and that's not a tecnological limitation that's a limit Nature itself imposes to us.

[@timelyrain]

I had the same question, I had to somehow answer it myself as I never found simple and satisfactory answers online. I first imagined a fully deterministic universe, but we humans have limited observability. Therefore, our observations would be noisy hence can be described as random because of its non-explainable nature. The hard part is to come up with specific distributions (such as uniformity) from which we would like to sample whenever we want; however, as far as I know, we humans can never find exactly such technique because confirming that a found phenomenon conforms a certain distribution takes infinite samples. We have to settle on "close enough". For your information, computational statistics often use deterministic methods to calculate samples; no randomness here.

[@QqJcrsStbt]

A base ballbatter is a complicated example. Not independently random, player could be injured, getting divorced, loosing his house, about to be sacked or close to making his bonus. Over a season there will be more factors at work, such as different pitchers and weather conditions, more random but still not perfectly independent random. It is likely that data here will be skewed since the worst batter can do no worse than zero. A great average (above average) is 0.4. A batting average of 1.0 is theoretically possible but I doubt that it has ever been achieved over a career or even several seasons. Maybe in a single game or a one season carreer (odd to quit with that record short of serious injury or jail). It is very hard to prove that data is truely random by sampling even if it is. There are many ways though to prove that it is not random. Note; 36 Fair, 37 Europe and 37 US spins, not 35 are required. If you win on every one you will be asked to leave.

[@ronaldjensen2948]

14:32 Either his understanding of the FairRoulette script is not good, or he is misspeaking. totPocket is the amount won, not the number you get right, betPocket does not return 0, it returns the negative bet playRoulette is missing the final parameter "toPrint" in the definition on the slide playRoulette's expected return does not correctly calculate because it does not use bet size 40:45 code is incomplete and looks wrong, too. :(

[@ucctgg]

no

[@GeneralZhang]

Yes, good lecture, but the code is buggy. playRoulette should instead print 100 * totPocket / (numSpins * bet). The output in his example only looks correct because `bet` is 1. If `bet` were 2 and `numSpins` were 1, it either prints "-200%" or "7200%" (and you can't lose more than 100% or win more than 3600% of your bet in one spin).

[@sarkersunzidmahmud2875]

What's the main difference between the law of large numbers and the monte Carlo experiment? Monte Carlo is using the law of large numbers to run the experiment? Why do we need the monte Carlo experiment if we know the characteristic of the law of large numbers? Can anyone tell?

[@geniusmode-set-2-winacadem77]

Great lecture, awesome teacher. Concepts were explained really well.

[@ravishanker785]

Correction, At 21:52 its 67,108,864

[@mozeeen1]

How the 68% was calculated for the probability of value between -1 and 1 in the last example?

[@JonathanKandell]

Love your Data Table hack at 2'. Thank you for that!

[@Tyokok]

it says monte carlo simulation, but it's talking about distribution, conf interval. nice teacher tho

[@mpadlite2925]

As already stated a great lecture by a great lecturer. Though I be!ieve he misspoke @23.33. when he regarding "regression to the mean" said that "two parents who are shorter than the average, likely would have a child that is taller than THE AVERAGE", which (I believe) is incorrect. What I think he meant to say is that "... They are likely to have ahold that is taller THAN THEM"... And thanks again for making this and so much other fantastic content freely available :} Brgds

[@TimTheMusicMan]

What is the purpose of the MC simulation? Where is the advantage if a user implements it? Whatever advantage it serves for the user (gambler), isn't there any equal advantage to the house?

[@annakh9543]

he is so funny, i wish i had such professors

[@MJ-iy4fb]

I give this professor two thumbs up. I like his style. Good presentation also. A hardy bravo zulo to the man.

[@nikolaosbeglitis5508]

Nice. Can I just argue something, there is always an example with coins but I don't think I have ever heard someone just adding a disclaimer that tossing a coin is not a random process. In theory, if you could start the tossing under the same initial conditions you would get the same outcome. So it is possible to get an infinite number of heads if you just manage to toss the coin the same way an infinite number of times (i.e. with the same initial conditions). I don't think that would be too difficult to achieve either. An example of a true random process is nuclear decay of radioactive atoms.

[@Ricocase]

Would love to see this for craps. Why apply mean to abnormal data? The median might be more accurate.

[@gustavogodoy5823]

Wow... fantastic lecture by Prof. Guttag... Thank you and congratulations.

[@psinity]

thanks lord for these free lectures

[@northdot9]

In the slide "Gambler's Fallacy" it reads at the bottom: "Probability of 26 consecutive reds when the previous 25 rolls were red is:" The wording is poor in my opinion. Does it mean: "What is the probability of the next roll being red?" Or Does it mean: "What is the probability of the next 26 rolls being red?" Or maybe : "What is the probability of 26 consecutive reds occurring in the next roll if the previous 25 rolls were red?" Based on his answer I think that the question should have read: "What is the Probability of the next outcome being red when the last 25 outcomes where red?" And then he goes on to talk about it being independent after this question. He didn't establish at the beginning that the outcomes were independent.

[@PRT976]

If all mathematic teachers taught like this in classes, I'm pretty sure the amount of those who grew up hating math would have been a lot less. Very clever way of teaching by giving scenarios, explaining them with mathematical concepts, without diving too quick to the expressions or formulas which not everyone is ready for.

[@epicmarschmallow5049]

if all mathematics teachers taught like this, nobody would know any maths

[@keneben]

Thank you Sire. I hope you're okay wherever you are

[@williamlewis8773]

What does the choice of "standard units of measure" used in the measurement of a phenomenon have to do with the "size" of the reported number that is used to represent the result of a statistical test ? How are do distinct populations differ in the ways they impute "meaning" to the size of a reported numerical result ? How do answers to this question differ between societal recipients of the report and individual persons for whom the report may be intended ?

[@nataliyaka3214]

I think that explaining the gambler fallacy should take into account how the gambler thinks. The gambler thinks that one rare event has to compensate by another very rare event, counter to the one the gambler just experienced. In fact, the counter-event is as rare as the currently observed one, and is not likely to happen, well, because it is rare as well! What is likely to happen is a less rare event, rather than another extreme one. Would that be one of the ways to explain the gambler fallacy?

[@ihgvjihnfgiobvhdegui]

23:32 If the parents are shorter than average then the child will likely be taller than the parents, but not taller than average.

[@666HeroHero]

He probably just misspoke.

[@bibekgautam512]

yup. It would be gambler's fallacy to say that.

[@cleverclover7]

caught that too. just a slip of the tongue.

[@milachaparro4128]

Yeah, slip of the tongue, one of those is not worth to correct at the momento because are understood right away

[@tillw9730]

I think he meant the average of their height