Gambler's Fallacy vs Regression toward the Mean

[@erikthompson584]

I enjoyed your video, but unfortunately the following statement you made is NOT true: "Tails will appear at some point to compensate for the previous heads." Later you say verbally that the universe will produce more tails to compensate for the first 15 heads, but we just don't know when that will happen. Again, false. As you know, previous flips have NO BEARING WHATSOEVER on future flips. So to suggest that the universe will EVER compensate for the previous flips is absolutely not true -- that statement suggests that the universe cares what happened in the past. It doesn't (with coin tosses at least). Here's a more accurate way to describe what is most likely to happen after your first 15 flips: the most likely result for the future flips is a 50-50 mix of heads and tails. Period. To calculate your expected result, you'll add the new 50-50 split to your previous 15 heads. So if you plan to flip a hundred more times, then when considering the new total of 115 flips, the most likely result for the future is 15 + 50 = 65 heads and 50 tails, which means out of 115 flips, you are most likely to have 65/115 = 56.5% heads and 50/115 = 43.5% tails (NOT 50-50!!!). If, after your initial 15 heads, you flip a million more times, then your most likely outcome is 15 + 500,000 = 500,015 heads and 500,000 tails, which means you are most likely to have 500,015/1,000,015 = 50.000075% heads and 500,000/1,000,015 = 49.999925% tails (NOT 50-50!!!). The more times you flip, the more your original 15 heads will be DILUTED and the ratio will approach 50-50. This is what you meant by your statements. However it's NOT accurate to say that the universe will eventually compensate for your first 15 heads. No matter how many times you flip, you should never expect the universe to care what happened earlier. It's more accurate to say that the universe is most likely to DILUTE your past results, but NOT COMPENSATE for them. Now, technically speaking, there is a CHANCE that the universe might compensate for the past -- the universe MIGHT deliver 15 fewer heads over the long run so that eventually you have a perfect 50-50. But that outcome is LESS LIKELY (!!!) than the outcome that the universe just gives you 50-50 from this point forward and you never actually reach a perfect 50-50. Does that make sense?

[@abdulrahmansamir9056]

nice.

[@hEmZoRz]

Exactly my thoughts when watching the video. Came to the comments to see whether someone had pointed this out already, and sure enough, someone had. It's a shame your comment is buried so deep down here and few people will ever see it.

[@darshan5044]

should be pinned

[@cherubin7th]

In nature most things are not independent. Dices and coins are artificial.

[@MrWitchtrials]

Seen many complicated explanations of this but yours taught me the most, i.e. that regression affects the next series of events and not namely the next event.Excellent!

[@NormalizedNerd]

Yeah...exactly the point!

[@charimuvilla8693]

There seems to be a regression to the mean fallacy as well. If the coin lands on heads 20 times in a row some believe that it's more likely that there will be more tails in the next 20 flips "to balance things out". That's still very wrong but It's harder to explain why.

[@BigDataRPG]

Finally, great content is recommended to me on KZbin =] Thank a lot

[@NormalizedNerd]

Glad you loved it 😍...

[@MrMexc]

what if you've now flipped a completely fair coin 14,999 times, all heads. now the probability of any 1 flip is still 50:50, as will be the 15,000th flip. But regression to the mean says eventually the total will balance out to a 50:50 as well. doesn't this imply there is an infinitesimally slight increase in probability gained for a tails flip after each consecutive heads so that the regression to the mean occurs? and if so, would that then not be a 50:50 probability?

[@NormalizedNerd]

No, the probability of heads won't increase even a bit. The point is regression toward mean doesn't tell you anything about the immediate next flip. All it says is if you flip the coin 14999 more times then we should see an increase in number of tails. Suppose you are the one who got 14999 consecutive heads. Then you give the coin to me without telling me the outcomes of 14999 flips. Now I start flipping. Will the coin change it's probability to favor tails on my first flip? NO IT CAN'T. All you can say is I'll probably get more tails than you in my course of 14999 flips.

[@newbielives]

@@NormalizedNerd i feel this comment is clearer than the video, thank you

[@newbielives]

@@NormalizedNerd but lets say i was going to bet on all 14999 flios by you shouldnt i bet tails every time because even you said we should see an increase in tails. Im now confused again

[@vishy099]

@@NormalizedNerd but we could have said that also at 6k or 7k heads and the future would have gone against that expectation. Where am I going wrong? Or maybe it's just imprudent to keep believing the coin is a fair one after those many (6k or 7k) heads on a trot?

[@bogdar2019]

Gfeat stuff, man! Very clear

[@johnchen2963]

if I were taking a multiple choice test(a,b,c,d) and didnt know anything do I a. choose my favorite letter and fill out the entire test with that letter b. guess randomly for each question my thought for a. is that maybe something to do with regression to the mean so that best case scenario I get close to 25 percent accuracy correct my thought for b. is that regression to the mean doesn't matter and its like the gamblers fallacy so each question you guess is still 1/4 therefore 25% getting it right each time

[@NormalizedNerd]

Take two situations... Case 1: You don't know anything and you are purely guessing every question. Both the methods will earn you 25% of the total marks. Actually, the gambler's fallacy won't appear here because after guessing a question, you are NOT told the actual answer to that question. So, you have no knowledge of the past 5 questions before answering the 6th one. Case 2: You have studied and answered 5 questions correctly but stuck at 6th. You saw that all the answers to the past 5 questions were (c). Here, you might fall into the gambler's fallacy thinking that the 6th question is very unlikely to be (c) again. You should just guess randomly instead of avoiding (c).

[@x-act]

​@@NormalizedNerd This is in a situation where the universe is writing your exam- teachers usually mix up answers, and some smart teachers even give all a's or all b's to confuse students. You have a much better chance of guessing right if you properly asses your teacher's phycology and past experience- or you could just study.

[@MambaMentality24943]

@@NormalizedNerd For case 2, it makes sense to avoid option. (c). Given that answers to most test questions are approx 25% of each choices, it is fair to assume uniform distribution. Yes, it applies to only when n tends to infinity, but in practical life, there is no infinity. Hence, it makes sense to take this approximation. If you do not believe me, try tossing coins without using any simulations, you'll get what I mean :)

[@Matthew-ez4ze]

Excellent explanation. The coin has no memory. The roulette ball has no memory. Gamblers will always lose to the law of large numbers.

[@NormalizedNerd]

Exactly!

[@fjbvghjvv2291]

Try telling that to my dad, all youll get is "ask any gambler" and then he will try to convince you the falacy is true.

[@andreiandrei7775]

the gambler's fallacy is only valid when the experiment is completely unbiased. You can bias coin flips when you know how to throw it, not to mention casino games

[@klaik30]

This does not make sense to me. You make a distinction that the prediction that is logically sound is that the "next round of 10 flips is expected to have less than 10 heads" and then you say "please note that nowehere does it say that it should expect more tails". How does this make sense? If the set is expected to have LESS than 10 heads then by definition that means that the next set has an increase in tails as if there are less heads, a tail has to replace it. Obviously it doesnt guarantee but it PREDICTS that there should be a regression to the mean. If the next set is more likely to have less heads then obviously that set contains a larger amount of tails and I should therefore pick tails as the distribution will be more "in favor" of tails.

[@AP-dw6nf]

I don't agree. The fallacy is a fallacy itself and comes down to explicit semantics. investopedia: "occurs when an individual erroneously believes that a certain random event is less likely or more likely to happen based on the outcome of a previous event or series of events" wikipedia:"if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future." The word 'future' implies an un-predefined range where regression to the mean will occur wherein the subset is more likely to contain more of the correction spins than the last say 100. Thereby the gambler is right the next should contain more of the opposite spins. Though there is no guarantee on which spin- nonetheless they are right. What is true of a group then should be true of the subset and the gambler is right on the next spin it is increasingly more probable for an interruption to occur

[@ayushmanbt]

You should have said... Stay random stay safe. Anyways nice vidoe. Participated in the survey, though I thought the coin is clearly biased... Not a single tail for 15 times is quite unbelievable. If there were 1 or 2 tails I would have selected at random

[@NormalizedNerd]

Haha nice line. To make the gambler's fallacy more prominent I had to give 15 heads :3

[@cuzmariosaidso]

Heads

[@TradingAlien]

Wrong. Dead wrong. 🤦 You should pick tails, the one that is 'behind' statistically... Regression to the mean and the so-called Gambler's Fallacy are the same principle. Claiming 1 is correct and the other not, is non-sensical and self-refuting. The only difference is the number of instances you consider (1 with the G-Fallacy and multiple with the regression), but if the chances changes over a string of multiple instances, it MUST then also be true to that it's different for individual instances. It simply is a small difference as there is always a non-zero chance of the string of unexpected results to continue (in theory ad infinitum). However, with each instance, you get asymptotically closer to 0 - or in other words - with each instance, the chance of getting an outcome to interrupt this unexpected result (in this case tails) grows, and eventually comes close to 100% (99,9999999 etc)

[@TradingAlien]

*You can even calculate your chances* (and find online odds calculators, just Google it). The chances of the first outcome is 0,5 (50%), chances of getting a repeat is 0,25 (0,5x0,5), next one also repeating is 0,125 (0,5x0,5x0,5) So if the chance of the repeat is shrinking with each coinflip, the chance of the other outcome (tails in your example) is increasing with each coinflip. Also notice what you are arguing when you deny this; you are saying the chance of a string of 15xH = 16xH (and 17xH and 100xH)... If that were the case, it would be just as likely to not regress to the mean and go on forever repeating H as it would be to be broken. The Gambler's Fallacy is false. It's not a fallacy. However, the difference between 15xH and 16xH is very small statistically, so the only relevance it has, is if you plan to play multiple (potentially many) consecutive flips and double your bet every time you don't hit (which is very costly, very quickly and people who do this with Roulette, often fail because there's a table limit, that often doesn't allow for more than 7-10 double-ups, because of the minimum required bet compared to the max bet)

[@VinayKumar-mk7qn]

@@TradingAlien He says that probability of getting a head at 16th trial (given that first 15 trial shows head) = probability of getting a tail at 16th trial (given that first 15 trial shows head) I hope you get it

[@10xGarden]

Shit, I fell into the freaking Fallacy]

[@10xGarden]

It was such a gamble as a video

[@NormalizedNerd]

Yeah you did 😂...Will try to make more 😍

[@dodobird809]

So if I fall and break my ankle and then get in a car crash and then fall down stairs, it doesn't make me more likely to get into harvard? 😭 It just means something good will happen sometime in the future

[@NormalizedNerd]

No it just means...if you try to go downstairs again and again, you should fall less often 😂😂

[@QuizmasterLaw]

if you are intentionally alluding to the paradox of material implication then you win a plate of green moon cheese