Randomness is Random - Numberphile
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- Опубликовано: 17 дек 2018
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Наука
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
"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?
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?
😂😂😂
🤣🤣
"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
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
😂😂🤣🤣🤣🤣
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
Brady just got *SCAMMED*
Scam school
@@ypn.official or Modern Rogue now
His laughter, especially after he wins the 100 is brilliant.
Starts off with a big action sequence and then becomes formulaic.
”A bit like this video."
lol
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.
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
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?
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?
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.
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.
Sounds about right. For fun, I played the exercise by also choosing 20 flips. Although I had no streak longer than 3, my guesses did contain two separate instances of the 3-streak patterning (after my opening heads on flip one, I penciled in 3 tails in a row, and then later one, opted for 3 heads in a row with flips 15-17).
As an aside - even though the exercise is clearly intended to be done in real time, as the predictor's expectations will be based upon whatever strings of initial seeding he's given, I still found it kind of impressive that he accurately predicted 70% of my flips, most notably with the opening 4 being spot on, and then - starting on flip 10 - he would go on to score another 6 in a row. He erred on my final flip, but I think that's largely due to the fact that he couldn't analyze what I'd given to him up to that point. I would otherwise expect him to have a statistically much better than average chance of getting it right.
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
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)
I love his laugh.. and the fact that he's laughing so hard about something like this!
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.
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!!
I really like Simon, he explains perfectly what he was talking about and was pretty funny
And randomness is very LUMPY!
like semen
So is quantum theory: that's its nature, besides jitteriness of course
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
And this, is why you better choose a long and easy memorable password than a short and complicated one.
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.
But it doesn't.
I love how he nonchalantly admits to hustling small children XD
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.
When he asked me to flip a coin in my head 20 times, I immediately thought, 20 heads.
very good video lollllll love this guy and the way he laughs cheers me up
I think this is my favorite Numberphile video ever. I love Simon Pampena's personality so much.
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...
I love this guy.
LOVE IT!!!!! Great laugh at the end! Well done! My favourite numberphile contributor!
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!
simon you need to make more videos. I love your enthusiasm. U usually crack me up.
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
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.
Thank you for all the satisfying animations and sound effects. It's highly appreciated.
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.
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!
Simon seems like such a nice guy and these two really make some entertaining videos!
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.
This video was so great! Loved your guys' banter!
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.
"Half is pretty significant: it's like... half."
Mathematical quote of 2018?
Random is random.
A tip for creating random sequences from Marcus du Sautoy is to use the digits of 'pi' or 'e' to make your choice
I have watched this so many times, it's great.
Don’t gamble, kids.
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
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.
1:52 when do you achieve that laughter
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.
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.
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 didn't know that randomness is random. I've learned something new today.
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.
WE WANT MORE SIMON!
What would be incredibly unlikely, is if someone went through life without witnessing anything incredibly unlikely happening.
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.
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.
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!
One of Simons best videos. Very nice.
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.
"I'm gonna try and make money...."
>Gives money
>Can only break even in best-case scenario
Loved it! Keep’m coming!
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 :-)
Mr. Pampena's laugh is delightful! Also, wonderful Numberphile video!
Great video
loved this thanks for posting!
Man what a great episode, I love how they enjoyed it
the statement "that sequence is not random" is a bit strange, since a random generator CAN produce any sequence with the same likelyhood. it is just that this KIND of sequence is less likely than others.
Yes it could be random, but the fact that he could predict it this well means that he either got lucky or that there's a pattern.
@@Swarm_ i know. my point is basically that every pattern can be the product of a random "mechanism" (guess a mechanism i per se not random, but you probably get what i mean - a random "cause" ? )
would be nice to have a more detailed explanation / definition of what it means to be random in maths
@@davejacob5208
randomness is if you cant predict it. With that said the definition depends on our knowledge. The question is if there even is somethin like true randomness. What would an omniscient person say?
I think he means that this sequence doesn't seem to be generated from a uniform random process
@@Rithmy that is most likely not the definition IN MATHS. since there are no causes to describe in maths. nothing to "predict".
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.
I really like this episode! Would love to see some more info on this, but I guess I might have to crunch the numbers myself.
I love Simon
Finally! Early for a numberphile video!
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...
I love Simon's presentation style!
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.
This is actually an interesting thought.
This is what separates* theoretical probability from experimental probability.
sepArate
In theory there's no difference between theory and practice, but in practice there is.
@@Ogrecrusher I prefer this one: "The difference between theory and practise is significantly bigger in practise than in theory."
@@RBuckminsterFuller Thanks, I was wondering why spell check highlighted that.
@@nicfink5310 I think this is much better "There is no difference between theory and practise but the difference is more apparent in practice than in theory."
Simon is absolutely my favorite guest on this channel. He rules.
My new fav numberphile video!!!
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 :) )
So 20 is like 2^4.33? So the most likely longer streak is between 5 and 4 in a 20 Laplace set?
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.
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)
Title: Randomness is random.
Yes, the floor here is made out of floor.
yay! I love Simon!
this title and thumbnail gives off major tim and eric vibes
thanks brady... I commented on last video bring back simon pampena and he did it!
he definately looks like a mathematician .
"you owe me 20 bucks" reminded me of Django unchained when he kills the sheriff
spoilers
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
I keep coming back to this video BC I love it and love these 2 guys
Casinos: make millions and cost gamblers a fortune
No gambling person ever: "I'm starting to see a pattern here..."
What the actual heck, I made a computer program to do 20 flips for me, and it came up with
"HTHTHHTHHTHTHHTHTHTT"
THERE'S NOT EVEN A SINGLE STREAK OF 3, LET ALONE 4 LMAO
what are the chances of that lol
EDIT: the fourth time I ran it, it came up with a streak of seven tails in a row lol
EDIT 2: the seventh time I ran it, it came up with TEN tails in a row. Nice
Well done!! Thanks for setting it up, running it, & sharing those results!
I'd say around 2,1%
Ecl1psed276
I checked, about 0.7% if I actually did it right
@Alexander
Their pseudo-randomness is still more random than people would usually come up with unassisted.
I did 20 runs of 20 flips. Of those, only 3 had a maximum run of 3 or shorter, and 10 had a maximum run of 4 or shorter - the longest run was 8.
Also only 8 had a split of 10/10 or 11/9, with 7 having a split of 13/7 or wider, up to 15/5.
Could someone explain to me how did he get to that number at 6:18, plz? I'm not that great at combinatorics, even though it doesn't seem to be that hard to calculate this one...
Victor Pessanha all also thought it would be easy at first glance, but it’s not. Untill someone can prove me wrong
Janus 1305 indeed! This counting part of combinatorics can be pretty frustating sometimes as well. I mean, since there can be so many possible outcomes it's quite easy to eventually get lost/tired if you're not 100% as to how to properly even begin the counting
For a start, for a seq of 20 coin tosses, write 0 if two consecutive tosses are equal, and 1 otherwise.
So you get a string of 19 bits.
Now the question becomes: how many 19 bit seq such that there are no 3 consecutive 0
Such seq would need at least 6 1s. First you fix the number of 1s in the seq, then you count how many ways to allocate the 1s to prevent a streak of 3 0s.
2**20 is pretty small, could've easily calculated it on a computer
Simon is such a cool guy, bring him more on numberphile
Brady has found the most amazing group of people to hang out with! They all seem like people I would grab a drink with!