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/sci/ - Science & Math

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6684817 No.6684817[DELETED]  [Reply] [Original]

I have coworkers who literally believe that the probability of a coin flip changes based on previous flips. They think if it's heads 9 times in a row, it's more likely to be tails the 10th flip.

We all know this is ridiculous. They won't believe websites. I want to shove this in their face because they're so adamant that I'M being the idiot in this "debate." What can I do? Is there a super smart guy on Twitter who might answer if I tweet that I have a bet about that? Maybe Neil Degrasse Tyson?

>> No.6684826

>>6684817
>They won't believe websites.
>super smart guy on Twitter
>Neil deGrasse Tyson
Impending elitist tempest.

>> No.6684834

Will they believe a book? The gambler's fallacy should predate the internet.

Fucking old people and their books

>> No.6684839

the thing is neither of you have an advantage in coin flipping with or without the knowledge.

>> No.6684875

Why don't you just demonstrate it for them?

>> No.6684894

>>6684875
Gambler's fallacy wouldn't have existed if it could be demonstrated away.
>>6684817
Tie them up in your basement and keep them there until they can describe in detail how exactly the coin remembers the previous flips.

>> No.6684899

>>6684817
People that set in their beliefs are nearly impossible to set straight. IMO, your best bet is to bring in a statistics professor or a statistician from some big, well known organization. Even that's not really likely to work.

>>6684875
>coin lands heads
"but it was still more likely to land tails"

>> No.6684902

Just tell them to look up independent events versus dependent events.

Why are you working so hard to enlighten these ignorant individuals? You're working so hard to do them the favor of educating them.

>> No.6684931

>>6684817
So wait, theres a 50/50 chance it flips heads/tails. So if you flip a coin infinite times, does that mean that at some point youll be flipping heads a million times in a row and the other way around? But its 50/50 so its impossible right?

>> No.6684935

>>6684931
It's called a mathematical coincidence.
And yes, I know measuring probability is faulty and retarded.

>> No.6684938

>>6684931
See the Infinite Monkey Theorem

>> No.6684943

>>6684931
it's quite possible and will occur many times during your infinite journey.

>> No.6684948

>>6684817
>They think if it's heads 9 times in a row, it's more likely to be tails the 10th flip.

But that's a statistically correct assumption?

>> No.6684971

>>6684948
so before all the coins are flipped, i tell you you have to choose either 9 heads then 1 tails, or 10 heads in a row, you think one of those is more likely than the other?

both are very unlikely, but given that you already flipped the first 9 heads, that doesn't change the odds for the last one

>> No.6684972

>>6684817
>We all know this is ridiculous.

No it's not. You're just an idiot frequentist.

>> No.6684981

>>6684817
People tend to not like being told they're wrong. Why are you out on some kind of autistic crusade to become hated among your peers, and over such a trivial issue too?

Just let them believe what they want, even if it's incorrect, and drop it. It's their loss if they ever go to a casino.

>> No.6684982

>>6684894
>gambler's fallacy wouldn't have existed if it could be demonstrated away
if you can't think of a way to demonstrate this with a simple experiment you should think about it more, it can easily be demonstrated and that's a very important concept. "it can't be demonstrated" makes it sound like magic hocus pocus

>> No.6684989

>>6684972
so you're one of those people who doesn't know the first thing about probability and statistics but still talks about "idiot frequentists?" where did you get that from, xkcd or some blog?

>> No.6685071

>>6684981
Ahh yeah, the old autistic trolling. 1/10 0 creativity but got me to respond.

Maybe in your literal autistic group of peers will proving someone wrong make them hate you, not so among normal people though.

>People tend to not like being told they're wrong

Exactly. Especially bad when you know you're right 100% :)

>> No.6685106

>>6684817
Truth is, if you flip 9 times and get 9 heads, it's more probable that you'll get heads the 10th time, because the coin is apparently unbalanced.

Seriously, do this:
Flip some coins and bet on the outcome. Nine in a row will take hundreds of flips, so aim for something smaller, like three in a row.

Flip and keep track of the outcome. Each time you hit three heads (or tails) in a row, bet them some amount of money that the next flip will be heads (or tails) and tell them that they should give you odds (like say 3:2 or so), since they're so certain that the next flip is more likely to be tails (or heads).

>> No.6685126

>>6684817
Probability and statistics is one of those things a person either 'gets' or they don't

You're wasting your time.

>> No.6685132

>>6684948
How is that statistically correct? If we hold that the coin is fair then the chance of tails is 50% at all times. If we say that the chance is unknown and look at our sample distribution, then we should conclude that heads is more likely than tails. But there is no reason to state that tails is likely in the next flip.

>> No.6685133

Explain how gambling odds work if they're retarded and need to know that, and then gamble with them.
Get a coin, keep flipping it until it hits heads 4 times in a row, then bet them that it will be heads again (o em g miracle) and make money off them. Make like a 2 to 1 bet, because obviously it's 1/32 chance that a coin will flip heads 5 times in a row, so 2 to 1 is pretty generous for them.
Eventually they'll realize how much money they lost and admit that you're right. Or they'll say you have a loaded coin, so make sure you use one of theirs.

>> No.6685134

>>6684972
In this case, both frequentists and Bayesians would agree that tails is not more likely. You have no idea what you're talking about.

>> No.6685290

>>6685133
What's funny is they're huge gamblers too.

>>6685106
>Seriously, do this:
>Flip some coins and bet on the outcome

But thanks guys, this suggestion is perfect and actually realistic to try. Loving it.

>> No.6685295

Sit down with them and have a nice, long discussion about delusions we take for reality and how they can impact us when we constantly rely on them as fact.

He's not ready to handle the fact that coinflip odds, and everything he has done with association to those odds, have always been and always will be 50/50

>> No.6685326

"Fair coins" don't exist.

I've flipped coins and got the same side every time, or got alternating sides, depending on how I flipped it.

The way a coin toss works is that one person flips, and the other person calls it in the air. That makes it like a game of rock-paper-scissors, but with no possibility of a tie. If either person chose randomly, the outcome is random, and both are motivated to be unpredictable to the other.

A person flipping a coin, with the desire of producing a random outcome, who gets a long string of the same face, is likely to change his flipping technique, particularly if he stops to think about it.

Don't confuse conventions of probability hypotheticals with actual truths about the world.

>> No.6685335

>>6685326
1. True, but the difference between a real life coin and a fair coin is negligible.
2. An unfair technique doesn't make the coin unfair.
3. There is nothing in the hypothetical that isn't the same in the real world. Even if there were something, it wouldn't matter, because it's a hypothetical.

>> No.6685356

>>6684817
Do some bets with them.
Make sure to use faux logic with them, so like "since the last 5 flips were heads, it is a 5x chance that the next will be tails, So the bet is 5:1 amount if i win.

>> No.6685359

>>6685335
Rubbish, on all three points.

A "fair coin" in probability is a coin that, when flipped, will produce heads or tails with equal probability in a purely random fashion.

Flipping a real coin in such a way as to make an unequal probability means it's not a "fair coin" in the sense meant in discussions of probability.

As I've pointed out, real coins are known to not normally be "fair coins", which is why one person flips and the other calls. This prevents the flipper from biasing the result by intentionally flipping one side or the other.

>> No.6685370

>>6684817
it's called gambler's phallacy
google it
</thread>
really: </thread>

>> No.6685377

>>6685356
this
maybe make it 3 times in a row or even 2 times to be more achievable, and do this several times.

>> No.6685395

>>6685370
is it a big, throbbing phallacy?

>> No.6685422
File: 1.15 MB, 796x829, coin flipping machine.png [View same] [iqdb] [saucenao] [google]
6685422

>>6684817
The crazy thing is, they are sort of right here. By the very physics of the coin flip, it's 1% more likely at minimum that the coin will land on the face it was launched from.

Pic related shows a machine that's capable of flipping a coin to heads ~100% of the time from the study "Dynamical Bias in the Coin Toss," linked below

>>6685335
>>1. True, but the difference between a real life coin and a fair coin is negligible.
Wrong: The bias is more than the house edge in many casino games.

http://econ.ucsb.edu/~doug/240a/Coin%20Flip.htm

http://statweb.stanford.edu/~susan/papers/headswithJ.pdf

>> No.6685449

>>6685422
Yes, the difference between .51 and .49 when it comes to using a coin to randomly determine something that one would use a coin for in the first place is negligible.

>> No.6685469

I understand The Gambler's Falacy, and that previous coin flips don't effect future coin flips. But there's something about it that makes me confused, and maybe it's why other people deny the Gambler's Falaccy.
Okay, so let's say the chance of flipping heads 9 times in a row is 1/50 (pulling numbers out of my ass here). And then flipping heads 10 times in a row is 1/100 (again, ass pulled number). So if 10 heads in a row is less likely than 9 heads in a row, how is it still the same chance for that 10th head? It just seems like it would matter, but like I said, I know it doesn't, because obviously the coin is not remembering anything.

>> No.6685517

>>6685422
But which side do you launch from next? That is also essentially random. So it is 50/50 even when you take that bias into account.

>> No.6685521

>>6685469

You don't really understand the fallacy if you're confused by it, I'd say you're just aware of it.

In any case, yes, 10 heads in a row is less likely than 9 heads in a row, but in this case we already know you got 9 heads in a row, so it's just a matter of whether that last coin lands heads, the probability for which is 1/2.

Honestly though I don't know what you're trying to convey and it doesn't really help that you're pulling the numbers out of your ass.

>> No.6685526

>>6685469
>So if 10 heads in a row is less likely than 9 heads in a row, how is it still the same chance for that 10th head?
What is the chance of getting 9 heads in a row and then a tail? 1/100.

So you see, getting a tail or a head after the 9th head is still 50/50. The reason getting 10 heads in a row is unlikely is not because it's the same thing 10 times, it's because you are naming a very specific event among 100 different events that could happen. 9 heads and then a tail is just as specific. A head then tail then head then tail, etc is just as specific.

>> No.6685572

>>6685526
Oh, and just to be clear, it's not 1/100, it's 1/2^10.

>> No.6685573

>>6685526
>9 heads and then a tail is just as specific

Thank you, that actually answers my question. I don't know why I didn't realize that.

>> No.6685574

>>6685526
>1/100
>implying

>> No.6685575

>>6685574
See >>6685572

>> No.6685582

>>6684817
It's not an incorrect assumption. Given enough coin flips on average you should get almost the same amount of tails and heads. So while the probability of either heads or tails is still 50%, the probability of 10 consecutive heads is less than 50%. But this only works with large amount of coin tosses.

Think of it this way, the distribution of 10 consecutive heads throughout the history of the coin states is not the same as the distribution of 3 consecutive heads.

What they are doing, is trying to apply the law of large numbers to 10 coin tosses. This is clearly wrong.

>> No.6685584

>>6685582
>It's not an incorrect assumption.
No, it's an incorrect assumption.

>So while the probability of either heads or tails is still 50%, the probability of 10 consecutive heads is less than 50%.
Yeah, but the probability of 9 heads and then a tail is exactly the same as the probability of 10 heads. You just fell right into the Gambler's Fallacy.

>> No.6685586

>>6685521
>but in this case we already know you got 9 heads in a row

But what about that problem where someone doesn't know the two genders of someone's kids, but does know that one of them is a boy. And /sci/ says the chance of both kids being boys is 1/3, not 1/2 like you'd think. Because they say the original options were:
BB
BG
GB
(removed because irrelevant - GG)
And I thought they basically were saying that the added information that one was a boy (or that you did in fact get 9 heads already), didn't affect the chances. I don't know shit though, this is just what I read on here.

>> No.6685589

>>6685586
the difference there is you don't know which of the two children is KNOWN to be a boy. if i say child 1 is a boy, what is the chance that child 2 is a boy, then it's 50/50.
if i don't specify which is known to be a boy, then like you said it's 1/3 that they're both boys given that information.

>> No.6685590

>>6685589
and that's because "child 1 is a boy" is more specific than "one of them is a boy;" the first covers the cases BB, BG while the second covers three cases, BB BG GB.

>> No.6685591

>>6685586
Totally different problem. The condition "one of them is a boy" and the event "both are boys" are DEPENDENT events. If both are boys then by definition one of them is a boy. So the condition effects the probability of the event.

Coin flips on the other hand are independent events. The result of flip one has no effect on the probability of the result of flip two.

>> No.6685592

>>6685589
Yeah, I was just realizing this myself. I do see how they're slightly different, because you've got the two individuals to take into account, rather than one linear set of coin flips. (or something like that)

>> No.6685596

>>6685592
and to apply it to the coin problem, if i flip 10 coins and look at them, then i tell you 9 of them came up heads, what is the probability that the last coin was heads?
the answer's no longer 1/2 in that case (it's 1/10) . "9 of them came up heads" is much less specific than "the first 9 came up heads", as there are 10 different ways for that to happen.

>> No.6685597

>>6685590
>>6685591
Thanks, I understand it a lot more now.

>> No.6685602

>>6685586

The difference is in how ordering affects the problem.
When someone says "at least one is a boy" (or "at least one is heads"), where it occurs in the sequence doesn't matter, so there are more valid sequences in the problem space.

Consider the difference between predicting that you will get exactly 9 heads in a row followed by a tails, and predicting that you will get 9 heads and 1 tails in any order in a sequence of ten.

>> No.6685612

>>6685584
You are correct, I fell for it.
Maybe your explanation will help OP's situation.

>> No.6685633

>>6685133
no, youre actually getting 2:1 odds for a 1:1 chance. not 1/32 because the first 3 flips are given

>> No.6685642

Make a gamble with them.

>> No.6685650

>>6684817
>Neil Degrasse Tyson
Look how much hate he got over his stance on transgenic crops. If you got NDT to explain why the gambler's fallacy is actually a fallacy, they'd only receive strengthened resolve and a newfound vitriol for science. Such is the cognitive bias of the inferior mind.

Also, get a different job, anon. Seriously, what the fuck? You're most likely in the wrong social stratum. /sci/ watches and judges

>> No.6685651

>>6684817
Also >inb4 probability doesn't apply to coin flips because mechanical systems are inherently deterministic

>> No.6685848

If I ever learned anything from /sci/, it's that when the host reveals tails, you win 2/3rds of the time by switching whatever you picked before.

>> No.6685868

>>6684948
Yeah, I believe so too (but I know I'm on the wrong side of this).

>>6684971
I think the question would be "what is the likelihood of getting 10 heads in a row" and maybe not "what will be the next draw".

>> No.6685902

>>6685650
Pseudoscience is where you go to get moral judgements, science is for making measurements and predictions, not about watching and judging, are you by chance the same zealot kook who keeps insisting that psychology is science?

>> No.6685905

>>6685902
>are you by chance the same zealot kook who keeps insisting that psychology is science?

>0/10, must troll harder

>> No.6685938

How would the coin remember its previous flips?

They're right in that 10 heads in a row is extremely unlikely, but so is every other combination. Each flip is still fundamentally 50/50 probability.

This is how casinos stay in business.

>> No.6685967

>>6684971
> given that you already flipped the first 9 heads, that doesn't change the odds for the last one

actually it increases the likelihood of the coin being biased for heads, but only very slightly.

>> No.6685974

>>6685967
That's a lie.

>> No.6685987

>>6685974
>unbiased coin should randomly select either side
>toss coin 9 times, all heads
>hmmm... the coin might biased
>toss coin 99 times, 78 heads
>hmmm... the coin is certainly biased
>toss coin 9999 times, 8102 heads
>the coin is biased and I can give a reasonably accurate statement as to how badly.

Its like you don't know how statistics actually works.

>> No.6685990

>>6685974
>what is a priori knowledge

Do you even Bayesian statistics, anon?

>> No.6685991

>>6685987
>>hmmm... the coin is certainly biased

It's incorrect to draw that conclusion. It might be biased, but just flipping it is not a valid way of discovering whether it has bias.

>> No.6685994

>>6685991
The chances of it not being biased at 100 flips are vanishingly small with those results. Increasing n by flipping it many more times is exactly how you confirm the bias.

>> No.6685996

>>6685991
>law of large numbers

>> No.6685997

>>6685994
define "vanishingly small"

>> No.6686000

>>6685994
But still existent

>> No.6686041

Your coworkers are simply plebs

>> No.6686044

>>6684982
What I meant to say that you can't convince a fallacious gambler of the gambler's fallacy by demonstration, because they, for instance, can spend a fortune in a casino without learning a lesson, hence the name. Because to them it's about a belief, and they'll find a way to handwave it.
IMO it is easier to provoke them into contemplating his belief and discovering that it stands on flimsy assumptions.
So rope & chains, dungeon, rats for breakfast until you've analyzed the damn thing.

>> No.6686073

>>6686000
sorry, meant to say 'almost certainly'

>> No.6686097

Make a bet with them - flip the coin until you get 9 in a row then flip one more time and if it lands on the same side they give you 51 bucks, otherwise you give them 50 bucks.

>> No.6686254

>>6684817
The way it was explained to me why this is confusing was that the probability of flipping 50 heads in a row is .5^50, but the chance of flipping a heads each time is always 50-50. So people tend to be actually talking about the probability of flipping 50 heads when they think they're talking about each flip.

I find it's always one of those define your words before you argue and everyone tends to agree a lot kind of things.

>> No.6686281

>>6684943
An infinite amount of times even

>> No.6686340
File: 9 KB, 291x300, pcoin.jpg [View same] [iqdb] [saucenao] [google]
6686340

>>6684817
What now?

>> No.6686489

>>6686340
So it's 1/3 the 1% of the time as opposed to 1/2 the rest of the time?

How would something like that even work

>> No.6686539

>>6686281

Not necessarily.

The coin COULD show heads an infinite amount of times.

Infinity doesn't necessarily mean that every thinkable combination occurs.