@@Rekko82 And the second year, if he didn't win it again by saying something even more profound, he'd have won it 50% of the time. That's like... half.
Never bet money against anyone who gets to set the rules. Mathemeticians might stack the deck more subtly, but letting the other guy set the rules is just begging to have the deck stacked one way or another.
@@nathanbrown8680 Lee Trevino put it very eloquently. if someone bets you the ace of spades will jump out of a deck of cards and spit cider in your ear. Dont take the bet unless you want an ear full of cider.
In case you're wondering, the expected value for the length of the longest streak in 20 flips is in fact 3.65, so having a run of 4 in a row every time, while not random, is still expected. If you had to bet on a longest length, that's what you should bet on.
@@iidtxbc they're saying that just because something is random doesn't mean its jumbled. Like if you have to randomize a sequence consisting of A, B, and C the sequence will not always lack repeats. We fall into the trap of think that random means the next result needs to be different from the previous result but thats hardly ever true.
Yeah, thanks for that. I was just reading up on it on Wikipedia. Interesting. So is this related to people thinking that if some other fool has played a slot machine for some time and left it, that it is now "primed" to pay out? Or similarly, that if a person feeds a slot machine all day, goes to get more quarters, and comes back only to find some other slob put in one quarter and hit that jackpot, that the first guy's quarters "primed" the machine?
@@xyzct Well, a slot machine is a poor example, in that those things are not actually random. Indeed, inside many machines, there's actually a "payout" dial. You can set the machine to return, say, 5% or 10% or 15% of its takings. And this will modify the machine's behaviour to pay out, if it hasn't paid out in a while, and has dropped below the "payout" dial's percentage value, and in the other direction, it'll hold onto the money and not pay out when paid out too much. So, in fact, gamblers talking about "primed" machines are not wrong, but only because these machines are, in fact, not truly random. As I like to point out, look at Las Vegas. The most extravagant city on the planet. You really think that its owners are fairly gambling its continued existence on the back of a genuinely random process every single night? All these games are rigged. It's just easier to spot with some of them than others. The easiest to see how this "rigging of the game" works is Roulette, because it lays out the arithmetic right in front of you. Just compare the odds against the payouts. Odds of a single number: 35 to 1 (or 2.85%) versus payout on a single number: 2.7% (European) or 2.6% (American). And the more the game is played - by ANY player, as this is irrelevant to the house, as long as they're always players playing - then the closer the actual outcome gets to the theoretical results and that 0.15% or 0.25% difference guarantees the house an overall victory. Let's create a similar game. You ante up a pound and we roll a dice. If you guess the number on the dice, then you win £5. If you get it wrong, then I keep the pound. The more we play, the closer to theoretical odds the actual results will tend towards. So, at that limit, what's really going on here is that you're giving me £6 for every £5 I give you, and I'm up a pound. As long as people keep playing my game - and, from my perspective, it's perfectly irrelevant whether it's one person playing over and over again, or a different person each time - I'm slowly racking up all those £1 profits into a very sizeable "college fund" for the kids. None of these games are actually truly random. They're just rigged to give off the appearance of such. But, if you think about it, of course these businesses are not playing fair - as they'd be intrinsically risking their ability to pay rent, feed the family and continue to exist every single night. And that's no way to run a business. You wouldn't remain in business long, if that were truly your business strategy. Of course it's totally rigged. Just look at the mansions that the casino owners live in, compared to the shitholes that addicted problem gamblers can't afford to pay the rent on.
@@klaxoncow Thanks for the reply. Yes, I understand everything you said here. So let me modify my examples to include fictional random slot machines. Are those examples then manifestations of the Reverse Gambler's Fallacy?
Everything i find about "reverse gambler's fallacy" is exactly the same principle as the gambler's fallacy. The notion that past events influence future ones in random sequences. Protip: they don't (ツ)
It wouldn't need to be a trick double-headed coin to get that result with me, all it would require is that there be incredibly dire consequences for me if tails doesn't come up once.
This guy is one of my favorite numberphile "hosts". Its amazing how many people do not understand randomness but think they do. Wish there were more numberphile videos dealing with random/psuedo-random topics!
Randomness is amazing. On this topic, I recently read up on kolmogorov complexity and I loved it. I'm pretty sure it would make a great numberphile video too! Keep up the good work Brady, cheers from France.
I remember having an argument about coin-flipping with a friend a couple years ago. It's not only interesting from a mathematical point of view, but also a psychological one. We get so caught up thinking about the likeliness(or lack thereof) of any particular n-length sequence when adding an element, we end up forgetting that every other possibility is equally (un)likely... When you really take a step back from the exercise of "mental coin flipping", it's silly to realize how we ACTIVELY INTRODUCE PARAMETERS for generating said sequences, crushing the whole concept of randomness right then and there. Such a fun exercise in analytical versus intuitive thinking. And wonderfully explained, too!
Poker players, who can gain an advantage if they can be unpredictable, use lots of tricks to try to generate randomness free of this kind of bias. Tricks include things like the position of the seconds hand of a clock, or color of the cards that have been dealt.
I think that’s bs, better to just choose the slightly better option. I’m never in a spot where I truly feel both options are exactly the same value. So why give up ev for the sake of balance?
This is literally how computers generate "random" numbers too, except they use the number of milliseconds since January 1st, 1970. Basically, you just described pseudorandom generation from a seed value.
You made an excellent find in Simon, Brody. I've seen this done with my own eyes in a school assembly with real coins. 800 kids tossed coins and anyone tossing tails was out. By the end one kid had tossed seven or eight heads in a row. My statistics teacher 50+ years ago explained that one way of writing down a random sequence is to write 'HHHHHHHH...' because it's just as likely as any other sequence. I particularly like Simon's point about DNA sequences.
Carlos Navarro are you in a coma? Considering how many times you use the word love, I speculate you are clueless as to what it is. Love.. pfft. Easy to answer.
it's called "Memorylessness". in a true random system, every single result doesn't care about all the previous ones, so it can potentially give the same result forever
Indeed, but if we somehow has a magic ability to suddenly conjure a string of 20 coin flip results, it would also work the same without talking about memory. If only.
My instinct was to create a sequence based upon the odd/even position in the alphabet of each letter in the caption at the moment when you asked for it. A moment later, I realized for the first time in my life that all of the vowels are odd. Zoinks!
@@SaudBako cannot be as it is a fallacy, with some hindsight bias we can see pattern of course, and we can even sort of try to predict it and get confident about it, but it is just randomness, and it behaves the way that is opposite to patterns...
If Thanos really wiped out half the universe, chosen randomly, there would be planets where no one died, leaving an untouched planet, and planets where every last living being died, leaving an abandoned planet.
Depends on how he chose who died and who lived. He could've pooled all living beings in the universe like you suggested or he could've chosen randomly within each planet or even within species. There are a few ways to get to that 50% dusting.
@@wurttmapper2200 true, the method would most likely be pseudo-random but the other theme of Thanos' plan was balance. If a planet is unaffected by the snap, then his rebalancing would have failed. If a planet is left devoid of life, then his plan also failed because the intent was to preserve life for a longer period of time not end it completely.
Wurtt Mapper Thanos has always go to a planet and wipe half of that planet. So it would be innate to his wish that, he would wipe half of each planet randomly.
I came up with an interesting problem a while ago that I think relates to the topic in this video. Since I am not a mathematician, I have no idea how to approach it. Maybe someone could enlighten me? Anyways here's the problem: A string of 1s and 0s can be generated in two ways. One way is to choose either a 0 or 1 for the next character of the string. The other is to decide how many times you want to put a 0 or 1, depending on which one you start with, and then alternating between 0 and 1, each time choosing how many times you want to repeat that number. An example: Method 1: Choose 1 Choose 0 Choose 0 Choose 1 Choose 0 Choose 1 Choose 1 Result: 1001011 Method 2: 1x 1, 2x 0, 1x 1, 1x 0, 2x 1 Result: 1001011 As you can see, the resulting string is the same. Now suppose, using method 1, we generate strings in which each character has a 50/50 chance of being a 1 or 0. How would you use method 2 to generate strings that are statistically indistinguishable from those generated by method 1? I suppose you need to randomly choose the first digit in method 2 and also have the condition that you can’t write a digit 0 times. Thank you for your input!
In random binary sequence A streak of N has the probability of occurring proportional to 1/2^N. To make the second method have the same distribution as the first one, you pick streak of 1 with probability 1/2, streak of 2 with probability 1/4, 3->1/8,4->1/16. etc.
You basically have to use method 1 to generate the length of the streaks to make method 2 the same as method one. This would result in those streak probabilitys mentioned above. (1/2^streak_counter) . It would be the same as method one, because method one also alternates between 0 and 1 after ending a streak with a random length.
He's one if the few guests where his videos seem to get better and better. I didn't care for then much at first but the last several have just made me like him more each time.
For anyone interested, the designers of Winamp or Windows Media Player or some such software had to deal with this when the e-mails criticizing the shuffle function of their player just kept coming in. People would complain about how the player played songs that were right next to each other ALL THE TIME!!1 In reality, it was coded to perfect randomness but what people really wanted with shuffle was to get songs far away from each other, so eventually they actually coded a "controlled random" kind of shuffle, which did exactly that.
That bit at 7:04 is only telling part of the story. To me, the more fascinating thing is, that if you flip a coin 4 times, all 16 of those outcome patterns are equally likely. There are way more ways to get two heads and two tails than there are to get four of a kind, but only one way to get them in a specific order. Once you understand that, a lot of things about randomness make more sense.
@@ObjectsInMotion So how come I always hear about it *outside* of schooling and such? Seriously, whoever has been trying to do that for centuries, like the school cirriculum creators? They've been doing a *horrible* job of it. (Imo, would be nice to see what a proper cirriculum looks like.)
When I first intuited the gamblers fallacy it was by realising that 5 heads in a row is exactly the same chance as HTHTH or THTHT its just one permutation and not special in any way
His laugh reminds me so much of a childhood friend that moved away when we were still kids which is the reason for me betting on him winning aside from the fact that he as a featured guest was proposing to play the game in the first place.
This just reminded me of an Apple keynote years ago, where their "huge" innovation of the moment was an option make the randomness of iTunes' shuffle feature more or less random. Basically limiting the streaks of picking the same artist/album in a row. What a gratifying watch that was...
This reminds me of the time Apple had to change the "randomness" of the shuffle function that iPods had. The people felt that it wasn't "random" enough because of the streaks that made them listen to some songs many times. Funny.
I wanna see this exact theory, but with 2 people involved ; 1- The first person chooses between heads or tails and writes down the answer, 20 times; 2- A second person chooses if the first person's choice is a win or a loss, and writes down the answer 20 times also. I think this could show us how much randomness is created by removing the factor that the people by themselves are choosing over preset subconscious filters. I'm pretty sure that with theses conditions, it is very unlikable that you would be able to predict nearly as well as you did with one person choosing. I don't know about you but I'm pretty curious about that ! BTW, I just found this channel yesterday and I'm enjoying this content very much ! Very talented and passionate hosts ! Simple easy to understand explanations ! PS: sorry for any grammar error or syntax gore !
in the beginning of numberphile around 2014(?) they used the brown paper just because it was spacious, and the marker just because it shows up really well on camera. over time the brown paper became somewhat of a symbol for the channel because they always use it.
Schilling's 1990 paper on this is pretty cool, and this idea of streaks on coin flips has motivated a cool way of assessing and quantifying systematic deviation between data sets and between data and fits called CorMap. It's pretty cool!
Wow. I played along, and out of my 20 imaginary coin tosses, the first 10 go EXACTLY like Brady's ones. How?? (I also have 2 more streaks of 3, but not any longer ones. It is an interesting topic :) )
10:25 ... This is a lovely point. I remember hearing it expressed as "biology is its own shortest description". Or generalized, far-from-equilibrium (that is, chaotic) dynamical systems are their own shortest description. That means each of us is our own shortest description ... a beautiful thought. Wonderful video, guys! Well done :-)
Simon is such a a jolly fellow, really proves that even for complicated math you can still have fun with it. (Also: Kinda surprised not a single school kid picked like only tails because you know: kids)
But... what ALGORITHM is Simon using in his head to determine when he should raise the stakes and by how much? In this example, he went to $20 on the fourth guess. If he had lost that individual wager, what would he have done next and why? He seemed pretty confident that he would walk away the winner by the end, so I'm sure he has some sort of methodology. I need to know!
This has to be based on psychology and empirical studies rather than pure mathematics or pattern recognition. Humans generally have a certain tendency to simulate randomness, and if you know what it is you can exploit it.
Any sequence that you can name is potentially a random sequence. The randomness of a sequence is a property of how it is generated, not what it is. Some sequences are more likely than others. Simon was playing the odds in his betting because Brady's sequence is unlikely, but that doesn't mean it's impossible for that sequence to be generated randomly. In fact, one of the higher-order tests of random sequences is that they sometimes fail lower-order tests of randomness. When I was generating the random sequence for my WEP key (112 random bits) I got a run of 13 zeroes in a row, and I almost couldn't bear to use it because it doesn't "look random" enough but I was flipping four fair coins, so I managed to overcome my prejudices.
@@jonathanguthrie9368 But i understand your point ! Don't get me wrong, we are just arguing on word definition. I know I do follow your definition of randomness. I have a question for you, Would you classify the pi digit of random, Even if we can generated them from a known algorithm ?
@@twistedsim Random means unpredictable. If you can predict the next digit by some means, then it is (by definition) not random. The thing is, I don't think our positions are that far apart. If I am understanding the way that Simon is betting, he's looking for a run of two and betting that the next one will break the streak. So, the 21st "coin flip" is hard to predict in this case, but the ends of runs of two are not. As far as your question about the digits of pi, that is a very interesting question. I thought I knew what answer to give, and then I thought about it and I wasn't sure. The other day I was watching a video that touched on randomness. I don't remember the details, but the point was that some sequences can be treated as random from one perspective when they are perfectly deterministic from another. I had to stop and think about what that implied, and I'm not sure it's helpful. Your question led me to think about the book of random digits that Rand put out a while back. Is it random? I mean it says so on the label, but I bet you can always predict the next one given a long enough sequence of digits from the book. If you have the book, that is. How about this: If you list all the digits of pi that sequence is not random because you can always "predict" the next one, but if you have a list of some of the digits of pi, they are random because I would expect that every finite sequence of digits would appear infinite times in pi. Of course, that's a conjecture. Proving it is well beyond my ability.
The digit sequence of pi can be generated randomly, used to purposely do math involving pi, no ofc its is not random, but if you ran a (pseudo)random-generator(since we can't actually make a true random generator) enough times eventually at some point it will generate the sequence of pi (within the amount of digit we make it generate ofc), this could happen on the first run, or it could happen after a million runs, or ever later, and when that does happen then yes the pi like sequence would be random, it is ALL about the context, not the sequence itself
This does not only apply to predicting the future, but also to explaining the past. We have a tendency to see patterns that do not exist and to seek causal relationships where there are none.
Finally someone with the same idea I have, and to tell you he tried his best not to ridiculously overcomplicate the explanation. I tried explaining the same thing to my friends but no way the even tried to think about it.
To check if Simon was right, I ran the following script: from random import choice outcome = [choice(['H', 'T']) for _ in range(20)] print(outcome) and got ['H', 'T', 'T', 'T', 'T', 'H', 'H', 'T', 'H', 'H', 'H', 'T', 'T', 'T', 'T', 'T', 'T', 'T', 'T', 'T'], that is, a strike of 9 consecutive tails. He's right.
"Half is pretty significant when we're talking about probabilities, right? It's like... half."
Get this man the Nobel of Mathematics.
It's like half skill but only 50 percent luck... Or 51/49‽ 48/52.. 53/47 maybe😧 It might vary dependant on the cola-
He would be the first to get it. You know like like first then. LOL
@@Rekko82 And the second year, if he didn't win it again by saying something even more profound, he'd have won it 50% of the time. That's like... half.
From my experience in gambling, 50:50 are the WORST odds.
but is it the bigger half, or the smaller half?
Never bet money against a mathematician, especially if he gets to set the rules.
Casinos are the mathematicians.
Never bet money against anyone who gets to set the rules. Mathemeticians might stack the deck more subtly, but letting the other guy set the rules is just begging to have the deck stacked one way or another.
escpecially when he bets 99.99$ more than you exspected
@@nathanbrown8680 Lee Trevino put it very eloquently. if someone bets you the ace of spades will jump out of a deck of cards and spit cider in your ear. Dont take the bet unless you want an ear full of cider.
I wouldn''t be surprised if most of casinos automatically blacklists all the better known mathematicians and people who has math degrees
Excellent video once again, Simon's enthusiasm is contagious
Very very true hahahaha
this is the last place I would've expected to find you, hi anyways
11:53
To me, one of the best videos ever on numberphile. Randomness is random by definition yet we cannot really understand it nor accept it. Beautiful.
The fallacy would actually take 10% Luck
20% Skill
15% Concentrated power of will
5% Pleasure
50% Pain
And a 100% Reason to Remember the Name
for only a select few
🤣🤣🤣🤣
@@danielblank9917 ymfah?
😂😂😂
🤣🤣
Brady just got *SCAMMED*
Scam school
@@ypn.official or Modern Rogue now
This is like when my brother said to pick up a random card of the deck, I picked the very top one and he said to me that I have to be serious.
His trick would not work
😂😂🤣🤣🤣🤣
"Randomness is Random"
"Half is Half"
Next up on Numberphile:
"One is Not Two"
“An integer is an integer, you can’t just say it’s a half!”
"1 is not a Prime"
Pi is 3, e is 3, Infinity is -1/12
What's done is done. It is what it is, but a man's got to do what a man's got to do.
They actually did that already in dividing by zero video
In case you're wondering, the expected value for the length of the longest streak in 20 flips is in fact 3.65, so having a run of 4 in a row every time, while not random, is still expected. If you had to bet on a longest length, that's what you should bet on.
His laughter, especially after he wins the 100 is brilliant.
I would have wagered the mortgage on the house on the last bet. I read about this in a book.
Published by Random House.
How did you know?
Is that some kind of double pun?
random is not mixed up. Good point
I also loved "randomness is lumpy" and plan to use that whenever possible.
Whod'a thunk
I didn't quite get the meaning of "random is not mixed up", if you see my comment, please drop your comment.
@@iidtxbc they're saying that just because something is random doesn't mean its jumbled. Like if you have to randomize a sequence consisting of A, B, and C the sequence will not always lack repeats. We fall into the trap of think that random means the next result needs to be different from the previous result but thats hardly ever true.
random need not be mixed up* maybe?
Do the REVERSE GAMBLER'S FALLACY next time, please! It will blow people's minds.
Yeah, thanks for that. I was just reading up on it on Wikipedia. Interesting. So is this related to people thinking that if some other fool has played a slot machine for some time and left it, that it is now "primed" to pay out? Or similarly, that if a person feeds a slot machine all day, goes to get more quarters, and comes back only to find some other slob put in one quarter and hit that jackpot, that the first guy's quarters "primed" the machine?
I have not heard of this! Cool. Now I don't know if I want to read about it, or wait with the spoilers until he makes a video about it...
@@xyzct Well, a slot machine is a poor example, in that those things are not actually random.
Indeed, inside many machines, there's actually a "payout" dial. You can set the machine to return, say, 5% or 10% or 15% of its takings.
And this will modify the machine's behaviour to pay out, if it hasn't paid out in a while, and has dropped below the "payout" dial's percentage value, and in the other direction, it'll hold onto the money and not pay out when paid out too much.
So, in fact, gamblers talking about "primed" machines are not wrong, but only because these machines are, in fact, not truly random.
As I like to point out, look at Las Vegas. The most extravagant city on the planet. You really think that its owners are fairly gambling its continued existence on the back of a genuinely random process every single night?
All these games are rigged. It's just easier to spot with some of them than others.
The easiest to see how this "rigging of the game" works is Roulette, because it lays out the arithmetic right in front of you. Just compare the odds against the payouts.
Odds of a single number: 35 to 1 (or 2.85%) versus payout on a single number: 2.7% (European) or 2.6% (American).
And the more the game is played - by ANY player, as this is irrelevant to the house, as long as they're always players playing - then the closer the actual outcome gets to the theoretical results and that 0.15% or 0.25% difference guarantees the house an overall victory.
Let's create a similar game. You ante up a pound and we roll a dice. If you guess the number on the dice, then you win £5. If you get it wrong, then I keep the pound.
The more we play, the closer to theoretical odds the actual results will tend towards. So, at that limit, what's really going on here is that you're giving me £6 for every £5 I give you, and I'm up a pound.
As long as people keep playing my game - and, from my perspective, it's perfectly irrelevant whether it's one person playing over and over again, or a different person each time - I'm slowly racking up all those £1 profits into a very sizeable "college fund" for the kids.
None of these games are actually truly random. They're just rigged to give off the appearance of such.
But, if you think about it, of course these businesses are not playing fair - as they'd be intrinsically risking their ability to pay rent, feed the family and continue to exist every single night.
And that's no way to run a business. You wouldn't remain in business long, if that were truly your business strategy.
Of course it's totally rigged. Just look at the mansions that the casino owners live in, compared to the shitholes that addicted problem gamblers can't afford to pay the rent on.
@@klaxoncow Thanks for the reply. Yes, I understand everything you said here. So let me modify my examples to include fictional random slot machines. Are those examples then manifestations of the Reverse Gambler's Fallacy?
Everything i find about "reverse gambler's fallacy" is exactly the same principle as the gambler's fallacy. The notion that past events influence future ones in random sequences. Protip: they don't (ツ)
Starts off with a big action sequence and then becomes formulaic.
”A bit like this video."
lol
Thanks man...can't wait to bankrupt my friends
(Gets bankrupted.)
Think of all the kids that Simon has bankrupted xD
(Doesn't have friends.)
So just because the guest is a J e w, the episode had to be about coins?
Hopefully your friends don't watch Numberphile
Just bankrupted my siblings. more of these pls. i need money.
Today I learnt:
Random is Random
Half is Half
But did you learn why?
@@possibilityspace - Close enough!
@@SakosTechSpot - I'm happy with just learning 'something', most of the videos I'm just confused.
Half of what is half?
Can confirm.
Am random.
I flipped a coin 20 times and got HHHHHHHHHHHHHHHHHHHH.
In retrospect, I probably shouldn't have used a trick double-headed coin.
It wouldn't need to be a trick double-headed coin to get that result with me, all it would require is that there be incredibly dire consequences for me if tails doesn't come up once.
Damn, you got a lot of head
Give me a head
Edgar, is that you?
Got us the first half, not gonna lie
I really like Simon, he explains perfectly what he was talking about and was pretty funny
This guy is one of my favorite numberphile "hosts". Its amazing how many people do not understand randomness but think they do. Wish there were more numberphile videos dealing with random/psuedo-random topics!
I love his laugh.. and the fact that he's laughing so hard about something like this!
Randomness is random
Infinity is infinite
Two plus two is four minus one that's three quick mafs
- numberphiles
50% is like, half.
Roses are roses
Violets are violets
Diego Sanchez - Wow, fifty percent?! That's almost fifty-one percent!!!
Lol! Its MAFS!!
Randomness is amazing. On this topic, I recently read up on kolmogorov complexity and I loved it. I'm pretty sure it would make a great numberphile video too!
Keep up the good work Brady, cheers from France.
I think this is my favorite Numberphile video ever. I love Simon Pampena's personality so much.
LOVE IT!!!!! Great laugh at the end! Well done! My favourite numberphile contributor!
I remember having an argument about coin-flipping with a friend a couple years ago. It's not only interesting from a mathematical point of view, but also a psychological one. We get so caught up thinking about the likeliness(or lack thereof) of any particular n-length sequence when adding an element, we end up forgetting that every other possibility is equally (un)likely... When you really take a step back from the exercise of "mental coin flipping", it's silly to realize how we ACTIVELY INTRODUCE PARAMETERS for generating said sequences, crushing the whole concept of randomness right then and there. Such a fun exercise in analytical versus intuitive thinking. And wonderfully explained, too!
Don’t gamble, kids.
very good video lollllll love this guy and the way he laughs cheers me up
And randomness is very LUMPY!
like semen
So is quantum theory: that's its nature, besides jitteriness of course
Poker players, who can gain an advantage if they can be unpredictable, use lots of tricks to try to generate randomness free of this kind of bias. Tricks include things like the position of the seconds hand of a clock, or color of the cards that have been dealt.
Yep. My watch comes in handy when I'm looking to mix up my play.
I think that’s bs, better to just choose the slightly better option. I’m never in a spot where I truly feel both options are exactly the same value. So why give up ev for the sake of balance?
This is literally how computers generate "random" numbers too, except they use the number of milliseconds since January 1st, 1970.
Basically, you just described pseudorandom generation from a seed value.
@@Johnny-cz2wv How do you decide when to bluff?
I did a card experiment regarding allowing dealers to split cards or not. I found I won most if I don't allow.
Simon seems like such a nice guy and these two really make some entertaining videos!
You made an excellent find in Simon, Brody. I've seen this done with my own eyes in a school assembly with real coins. 800 kids tossed coins and anyone tossing tails was out. By the end one kid had tossed seven or eight heads in a row. My statistics teacher 50+ years ago explained that one way of writing down a random sequence is to write 'HHHHHHHH...' because it's just as likely as any other sequence. I particularly like Simon's point about DNA sequences.
And this, is why you better choose a long and easy memorable password than a short and complicated one.
This is by far my favorite Numberphile video
Carlos Navarro are you in a coma? Considering how many times you use the word love, I speculate you are clueless as to what it is.
Love.. pfft. Easy to answer.
it's called "Memorylessness". in a true random system, every single result doesn't care about all the previous ones, so it can potentially give the same result forever
Indeed, but if we somehow has a magic ability to suddenly conjure a string of 20 coin flip results, it would also work the same without talking about memory.
If only.
My instinct was to create a sequence based upon the odd/even position in the alphabet of each letter in the caption at the moment when you asked for it. A moment later, I realized for the first time in my life that all of the vowels are odd. Zoinks!
I love this guy.
The point is that randomness is not anti pattern.
In other words, just because a process is random doesn't mean it would exclude oganization.
but randomness is anti pattern.
@@otakarbeinhauer Last year I meant to say: patterns do have a place and a probability in random sequences.
@@SaudBako I agree
@@SaudBako cannot be as it is a fallacy, with some hindsight bias we can see pattern of course, and we can even sort of try to predict it and get confident about it, but it is just randomness, and it behaves the way that is opposite to patterns...
@@anoirbentanfous
Organization is a subset in randomness
I love how he nonchalantly admits to hustling small children XD
simon you need to make more videos. I love your enthusiasm. U usually crack me up.
If Thanos really wiped out half the universe, chosen randomly, there would be planets where no one died, leaving an untouched planet, and planets where every last living being died, leaving an abandoned planet.
Depends on how he chose who died and who lived. He could've pooled all living beings in the universe like you suggested or he could've chosen randomly within each planet or even within species. There are a few ways to get to that 50% dusting.
Alberic Ponce de Leon That wouldn't be random then.
If the population of the entire universe is in the quadrillions then the chance of you knowing someone that died is infinitesimal.
@@wurttmapper2200 true, the method would most likely be pseudo-random but the other theme of Thanos' plan was balance. If a planet is unaffected by the snap, then his rebalancing would have failed. If a planet is left devoid of life, then his plan also failed because the intent was to preserve life for a longer period of time not end it completely.
Wurtt Mapper Thanos has always go to a planet and wipe half of that planet. So it would be innate to his wish that, he would wipe half of each planet randomly.
Thank you for all the satisfying animations and sound effects. It's highly appreciated.
I came up with an interesting problem a while ago that I think relates to the topic in this video. Since I am not a mathematician, I have no idea how to approach it. Maybe someone could enlighten me? Anyways here's the problem:
A string of 1s and 0s can be generated in two ways. One way is to choose either a 0 or 1 for the next character of the string. The other is to decide how many times you want to put a 0 or 1, depending on which one you start with, and then alternating between 0 and 1, each time choosing how many times you want to repeat that number. An example:
Method 1:
Choose 1 Choose 0 Choose 0 Choose 1 Choose 0 Choose 1 Choose 1 Result: 1001011
Method 2: 1x 1, 2x 0, 1x 1, 1x 0, 2x 1 Result: 1001011
As you can see, the resulting string is the same.
Now suppose, using method 1, we generate strings in which each character has a 50/50 chance of being a 1 or 0. How would you use method 2 to generate strings that are statistically indistinguishable from those generated by method 1?
I suppose you need to randomly choose the first digit in method 2 and also have the condition that you can’t write a digit 0 times.
Thank you for your input!
In random binary sequence A streak of N has the probability of occurring proportional to 1/2^N. To make the second method have the same distribution as the first one, you pick streak of 1 with probability 1/2, streak of 2 with probability 1/4, 3->1/8,4->1/16. etc.
You basically have to use method 1 to generate the length of the streaks to make method 2 the same as method one. This would result in those streak probabilitys mentioned above. (1/2^streak_counter) . It would be the same as method one, because method one also alternates between 0 and 1 after ending a streak with a random length.
In method 2, do you have to alternate H & T, or can you roll 3xH, 2xH, 1xT for HHHHHT?
I love the ending of the video.. very sharp and funny.
When he asked me to flip a coin in my head 20 times, I immediately thought, 20 heads.
What would be incredibly unlikely, is if someone went through life without witnessing anything incredibly unlikely happening.
when i have to come up with a sequence of coin tosses in my head, sometimes it happens that a coin lands on its edge!
He's one if the few guests where his videos seem to get better and better. I didn't care for then much at first but the last several have just made me like him more each time.
13:20 Brady steals the $120
Congrats, you're one of the few commenters that noticed that! Most of the others seem to have missed that part...
For anyone interested, the designers of Winamp or Windows Media Player or some such software had to deal with this when the e-mails criticizing the shuffle function of their player just kept coming in. People would complain about how the player played songs that were right next to each other ALL THE TIME!!1 In reality, it was coded to perfect randomness but what people really wanted with shuffle was to get songs far away from each other, so eventually they actually coded a "controlled random" kind of shuffle, which did exactly that.
That bit at 7:04 is only telling part of the story. To me, the more fascinating thing is, that if you flip a coin 4 times, all 16 of those outcome patterns are equally likely. There are way more ways to get two heads and two tails than there are to get four of a kind, but only one way to get them in a specific order.
Once you understand that, a lot of things about randomness make more sense.
A tip for creating random sequences from Marcus du Sautoy is to use the digits of 'pi' or 'e' to make your choice
"Half is pretty significant: it's like... half."
Mathematical quote of 2018?
Random is random.
I have watched this so many times, it's great.
By merely informing people of this you'll inevitably change the patterns of choice yeah?
MickyR absolutely, so reinforcing the point that humans are so far from random it’s silly.
But they'll still be patterns.
You think the gamblers fallacy is new? People have been trying to inform the public on this for centuries one youtube videos going to change nothing.
@@ObjectsInMotion So how come I always hear about it *outside* of schooling and such?
Seriously, whoever has been trying to do that for centuries, like the school cirriculum creators? They've been doing a *horrible* job of it. (Imo, would be nice to see what a proper cirriculum looks like.)
No.
this title and thumbnail gives off major tim and eric vibes
1:52 when do you achieve that laughter
When I first intuited the gamblers fallacy it was by realising that 5 heads in a row is exactly the same chance as HTHTH or THTHT its just one permutation and not special in any way
I always set the seed to 638474946383 because having the seed the same everytime is just as random as having any other seed.
I know you're joking but this goes completely against what was said in the video and I wonder what prompted you to say it.
@@kuro13wolf Leaving clued for the ARG.
His laugh reminds me so much of a childhood friend that moved away when we were still kids which is the reason for me betting on him winning aside from the fact that he as a featured guest was proposing to play the game in the first place.
Bob Ross looks well
Happy little probabilities!
I scrolled through the comments just to see if someone had mentioned Bob Ross.
@@123coolmik And here we are! Nice to meet you 👍
@@andie_pants you mean happy little probabilitrees
Showing some love to you guys
This just reminded me of an Apple keynote years ago, where their "huge" innovation of the moment was an option make the randomness of iTunes' shuffle feature more or less random. Basically limiting the streaks of picking the same artist/album in a row. What a gratifying watch that was...
This reminds me of the time Apple had to change the "randomness" of the shuffle function that iPods had. The people felt that it wasn't "random" enough because of the streaks that made them listen to some songs many times. Funny.
Well, shuffle means a permutation of the songs, so you'd probably want to listen to them all, not just in the original order.
I wanna see this exact theory, but with 2 people involved ;
1- The first person chooses between heads or tails and writes down the answer, 20 times;
2- A second person chooses if the first person's choice is a win or a loss, and writes down the answer 20 times also.
I think this could show us how much randomness is created by removing the factor that the people by themselves are choosing over preset subconscious filters.
I'm pretty sure that with theses conditions, it is very unlikable that you would be able to predict nearly as well as you did with one person choosing.
I don't know about you but I'm pretty curious about that !
BTW, I just found this channel yesterday and I'm enjoying this content very much ! Very talented and passionate hosts ! Simple easy to understand explanations !
PS: sorry for any grammar error or syntax gore !
Imagine if this guy was significantly less smart, that's what ALL of my friends are like.
6:04
Min freaking blown by smth so simple...
Brilliant masterpiece of a video as always, man
What is it about mathematicians and sharpies?
in the beginning of numberphile around 2014(?) they used the brown paper just because it was spacious, and the marker just because it shows up really well on camera. over time the brown paper became somewhat of a symbol for the channel because they always use it.
They imitate Trump..
Nothing. It's just this channel.
Mathematicians usually use computers or chalk.
One of Simons best videos. Very nice.
I didn't know that randomness is random. I've learned something new today.
This video was so great! Loved your guys' banter!
Mr. Pampena's laugh is delightful! Also, wonderful Numberphile video!
Schilling's 1990 paper on this is pretty cool, and this idea of streaks on coin flips has motivated a cool way of assessing and quantifying systematic deviation between data sets and between data and fits called CorMap. It's pretty cool!
All the coin flips I did in my head were heads. That's weird.
All the coin flips I did in my head landed on their sides. That's weird.
@@futurestoryteller "SSSSSSSSSSSSSSSSSSSS" - caller always loses if he says head or tail! XD
Please trade in your brain for one with real coins
@@VanessaMagick only $599.99 for replacement brain coins sold separately
Maybe if you did them in your tail, they'd be tails.
Simon is absolutely my favorite guest on this channel. He rules.
Wow. I played along, and out of my 20 imaginary coin tosses, the first 10 go EXACTLY like Brady's ones. How??
(I also have 2 more streaks of 3, but not any longer ones. It is an interesting topic :) )
10:25 ... This is a lovely point. I remember hearing it expressed as "biology is its own shortest description". Or generalized, far-from-equilibrium (that is, chaotic) dynamical systems are their own shortest description. That means each of us is our own shortest description ... a beautiful thought. Wonderful video, guys! Well done :-)
Great video
Simon Pampena es un tío genial!! Contagia su entusiasmo!!!
I love Simon
WE WANT MORE SIMON!
"I'm gonna try and make money...."
>Gives money
>Can only break even in best-case scenario
Simon is such a a jolly fellow, really proves that even for complicated math you can still have fun with it.
(Also: Kinda surprised not a single school kid picked like only tails because you know: kids)
But... what ALGORITHM is Simon using in his head to determine when he should raise the stakes and by how much? In this example, he went to $20 on the fourth guess. If he had lost that individual wager, what would he have done next and why? He seemed pretty confident that he would walk away the winner by the end, so I'm sure he has some sort of methodology. I need to know!
This has to be based on psychology and empirical studies rather than pure mathematics or pattern recognition. Humans generally have a certain tendency to simulate randomness, and if you know what it is you can exploit it.
Simon is such a cool guy, bring him more on numberphile
"you owe me 20 bucks" reminded me of Django unchained when he kills the sheriff
spoilers
11:53 Best laugh ever!
Finally! Early for a numberphile video!
Brady has found the most amazing group of people to hang out with! They all seem like people I would grab a drink with!
Wait, brady sequence is a random sequence, just not an uniformly distributed one.
Any sequence that you can name is potentially a random sequence. The randomness of a sequence is a property of how it is generated, not what it is.
Some sequences are more likely than others. Simon was playing the odds in his betting because Brady's sequence is unlikely, but that doesn't mean it's impossible for that sequence to be generated randomly. In fact, one of the higher-order tests of random sequences is that they sometimes fail lower-order tests of randomness.
When I was generating the random sequence for my WEP key (112 random bits) I got a run of 13 zeroes in a row, and I almost couldn't bear to use it because it doesn't "look random" enough but I was flipping four fair coins, so I managed to overcome my prejudices.
@@jonathanguthrie9368 So you are saying to me that you can precisely guess which side Brady gonna choose for the 21th coin? :)
@@jonathanguthrie9368 But i understand your point ! Don't get me wrong, we are just arguing on word definition. I know I do follow your definition of randomness.
I have a question for you, Would you classify the pi digit of random, Even if we can generated them from a known algorithm ?
@@twistedsim Random means unpredictable. If you can predict the next digit by some means, then it is (by definition) not random.
The thing is, I don't think our positions are that far apart. If I am understanding the way that Simon is betting, he's looking for a run of two and betting that the next one will break the streak. So, the 21st "coin flip" is hard to predict in this case, but the ends of runs of two are not.
As far as your question about the digits of pi, that is a very interesting question. I thought I knew what answer to give, and then I thought about it and I wasn't sure. The other day I was watching a video that touched on randomness. I don't remember the details, but the point was that some sequences can be treated as random from one perspective when they are perfectly deterministic from another. I had to stop and think about what that implied, and I'm not sure it's helpful.
Your question led me to think about the book of random digits that Rand put out a while back. Is it random? I mean it says so on the label, but I bet you can always predict the next one given a long enough sequence of digits from the book. If you have the book, that is.
How about this: If you list all the digits of pi that sequence is not random because you can always "predict" the next one, but if you have a list of some of the digits of pi, they are random because I would expect that every finite sequence of digits would appear infinite times in pi. Of course, that's a conjecture. Proving it is well beyond my ability.
The digit sequence of pi can be generated randomly, used to purposely do math involving pi, no ofc its is not random, but if you ran a (pseudo)random-generator(since we can't actually make a true random generator) enough times eventually at some point it will generate the sequence of pi (within the amount of digit we make it generate ofc), this could happen on the first run, or it could happen after a million runs, or ever later, and when that does happen then yes the pi like sequence would be random, it is ALL about the context, not the sequence itself
This does not only apply to predicting the future, but also to explaining the past. We have a tendency to see patterns that do not exist and to seek causal relationships where there are none.
So 20 is like 2^4.33? So the most likely longer streak is between 5 and 4 in a 20 Laplace set?
Superb example of human natural thinking!!
Thanks for this viddy!!
Easy money!
I love Simon's presentation style!
yay! I love Simon!
Finally someone with the same idea I have, and to tell you he tried his best not to ridiculously overcomplicate the explanation. I tried explaining the same thing to my friends but no way the even tried to think about it.
Title: Randomness is random.
Yes, the floor here is made out of floor.
Loved it! Keep’m coming!
function randomNumber() {
return 4; // chosen by fair dice roll
}
To check if Simon was right, I ran the following script:
from random import choice
outcome = [choice(['H', 'T']) for _ in range(20)]
print(outcome)
and got ['H', 'T', 'T', 'T', 'T', 'H', 'H', 'T', 'H', 'H', 'H', 'T', 'T', 'T', 'T', 'T', 'T', 'T', 'T', 'T'], that is, a strike of 9 consecutive tails. He's right.