/sci/ - Science & Math

>>10759439
there is a 100% probability that you are a brainlet. otherwise why would you create this thread. you are just insecure.

>>10759451
Sorry bro, I'm above 145 unlike most people on this board.

>there is a 100% probability that you are a brainlet
Statistically laughable in any case, you got filtered.

>>10759439
You should consider the probability of you becoming a useful member of society from spending exorbitant amounts of time posting on imageboards.

>Is probability the highest IQ filter?
It's why they say:

Lottery is a tax on stupid people.

>another IQ thread

>>10759439
>equating probability with randomness
I'm sorry, but you're a brainlet.

>>10759459
>145
that's you post on image boards
fag

>>10759439
Solve this

>>10759439
>randomness
define what you mean by this, don’t care if its bait someone explain precisely what you mean when you say this right now

>>10759687
Two distinct meanings:

1. Result determined by a constant statistical distribution( eg 50-50 for a coin ), which implies it could be an output of a deterministic function

2. Non-determinism

>>10759691
Would you be willing to explain what the second definition entails?

>>10759459
What a fucking embarrassing post. Imagine purporting to have 145 IQ yet being so insecure that you need to hide opposing viewpoints.

You're a fucking loser.

>>10759683
If we ignore the 1 outcome then the expected value per game is +4. Since the 1 outcome results in -x/2, the expected value is just -x/12 + 4.

E >= 0 implies 48 >= x, so when you have 49 or more coins the expected value of your next roll is negative.

Is this correct?

Probability, game theory, logic, decision theory all excellent brainlet filters. The point is not that one needs to study these fields to be smart: actually the opposite - the general and widespread absence of any understanding of even the basic principles of logic or rational ecision making is a testament to that, and is not something that can be learned very easily (c.f. the entire field of behavioral economics). In fact, studies have repeatedly found that classes on subjects like logic and inferential statistics actually don't improve your tacit understanding of logic or valid statistical inference (mainly they just improve your ability to answer test question about things like confidence intervals and hilbert style deductions).

>>10759683
>you will keep playing as long as the expected value of your next roll is non-negative
>((value of your next roll"))
Value does not equal coins, value equals the number of dots on the side of the die facing upwards. 1,2,3,4,5, or 6. None of these are negative thus you never stop rolling

>>10759683
>you decide that you will keep playing as long as the expected value of your next roll is non-negative
But that's dumb, there's simply no reason to ever stop rolling.
It's like playing the lottery for free, why would you ever quit?

>>10759728
You seem like you are getting at something else, forgive me for putting words in your mouth but isn’t this just another cognitive trait or faculty that is strongly associated with general intelligence and so is probably a result of genetic factors which are determined largely by pedigree and chance?

>>10759770
>pedigree

>>10759439
>Is probability the highest IQ filter?
I wouldn't say it's the highest, but it's definitely up there.
One thing I like about is the granularity of the filter can be tuned because the concepts get progressively more nuanced as you go.

Like absolute brainlets can't even understand expected value or the concept of independent trials.

But then there are trained brainlets who pride themselves on understanding expected value and will argue ferociously that a game where you're 50% to double up is the same as a game where you're 25% to quadruple up. That is, they don't understand risk of ruin / edge vs odds. Better still, they actually look down on people who do.

Or trained brainlets who get independent trials, turn it on its ear and watch the confusion. For example if you ask
>if 10 independent trials succeed 5 times, what is the probability that the probability of success is 5%?
You get all kinds of bizarre answers generally to the effect of "all success probabilities are equally likely no matter what you observed"

>>10759817
Amos and Tversky published the studies anon is referring to if people are wondering

>>10759827
Fuck daniel kahmeman and amos tversky i mean lol

what randomness happens in the world you brainlet? everything is cause and effect. fucking retard.

>>10759600
obligatory ennui pepe with collared shirt lamenting
>another IQ thread

Are you the same guy every time?

>>10759439
LOL we don't even really know what true randomness even is. Its just conceptual handwaving and has little to do with the computations done in probability.

>>10759885
>pepe
It's apu you newfag

>>10759683
42? The sum of the dots except one is 21, and losing half means the expected value reaches zero on 42.

It might be worthwhile to play a little longer though, as despite on relying on luck, you are virtually guarranteed to reach the 42 again.

>>10760188
oh, it's actually 40, I did add the one by mistake.

>>10759439
No it isn't very well correlated with IQ. Some high IQ people may be easily confused by this; autistic people on the other hand seem to be near completely immune.

>>10760192
My experience too in undergrad. I am the king of the autists in my program.

>>10759694
Collapse of the wave function,which is fundamentally non deterministic

>>10759830
Cause and effect doesn't imply non randomness

>>10759722
Expected value per game (ignoring the loss) is 20/6, which is smaller than 4, so you should play till you have 40 coins, not 48.

>>10759747
This

>>10759722
Nope

>>10759736
The brainlet filter works

>>10759747
Arbitrary condition that will be clear once you solve it

>>10760188
Nope
I stop when I accumulate X coins, the average reward for when I hit either one from 2 to 6 is (2+3+4+5+6)/5 = 4. Since this happens 5 out 6, the reward for each throw is 4 * 5/6. The cost is X/2 * 1/6. Given the condition that the cost needs to be higher than the reward for me to stop then:

(2+3+4+5+6)/5 * 5/6 < X/2 * 1/6

20/6 < X/12

X > 40

The next integer bigger than 40 is 41, so X = 41.

>>10760750
Perfect example of the brainlet filter in action, they learn a couple concepts and then apply them in a hamfisted way to every situation
The game has zero cost, so there is no reason to ever stop rolling, ever

http://www.elem.com/~btilly/kelly-criterion/

>>10759439
The human mind in general is pretty bad about handling probabilities.
Even though I know better I'll hit on 17 and be surprised when I bust.

>>10760464
This isn’t (non-deterministic collapse of the wave function) an effect of projecting some construct onto an observation with instruments or mathematical models?

>>10761007
>the game has zero cost

>>10759683
>expected value of your next roll
? Im assuming this means "At what amount of rolls is it statistically likely you roll a 1" which is piss easy, you stop at 3 rolls which is a 50% chance of not rolling a 1, barring if you roll a 1 for the first roll in which case you keep rolling forever untill you get a non 1 value, and continue rolling 3 more times after. Half of 0 isnt a negative value so theres not a clear and concise way to phrase the answer if my intpretation of the question is correct.

X= number of times dice is rolled 1 co secutively at the start
X+3 dice rolled before you should stop

>>10761194
other answer is if "value" is reffering to the sum total of gold you can gain. In which case, never stop rolling because there is no cost to play and its possible to get ridiculously high sums of gold from rare strings of non-1 rolls. Which makes actual sense from a non retarded hypothetical perspective but most hypotheticals have a retarded criteria.

>>10760750
Yes, I know, I corrected myself a minute later: >>10760190

>>10761229

It's actually 41, look again

>>10759439
I think so too. This is why you see so many people claiming remedies have so many cures. It's because they form wrong conclusions bases on weak correlations.

>>10759817
you are just a slightly more trained brainlet. so you shuffled through a kahneman and tversky book. big fucking deal. truly smart people don't hang out on anime boards calling each other brainlets a million times a day. that's all you do
>brainlet!
>no you are a brainlet, brainlet
>hey brainlet i am not a brainlet, brainlet
that /sci/ in a nutshell. you don't ever discuss anything interesting or prove that you actually know anything. you are here 24/7 to call each other brainlets. fucking underage faggots.

It's hard to really crystallize mentally. Getting into sportsbetting and investing has really opened my eyes to the existence of probability everywhere.

>>10761007
the game has a cost, its just conditional on rolling a 1

>>10759601
>>10759687
>>10759830
>>10759894
OP here. You guys are totally correct, there's no such thing as randomness. A better fitting word to describe it would be uncertainty.

>>10759439
Yes, lack of statistics understanding is also the main reason why social sciences are a complete shitshow.

>>10762281
based

>>10759439
>Measure theory: brainlet edition
>highest IQ filter

>>10762418
>Measure
>theory

>>10759683
5/6 you win an average of 4 coins
1/6 you lose half of the stack

4*5*2=40, whenever you have more than 40 coins your expected value is negative.


In actual game theory you should keep rolling the dice forever if possible.

>>10759817
>if 10 independent trials succeed 5 times, what is the probability that the probability of success is 5%?

0.95^5*0.05^5=very fucking low lmao
But the fact that it can actually happen will mislead the brainlets

>>10759722
>>10759736
>>10759683
>>10761194

>unironically proving OP to be completely right

>>10760750
>The next integer bigger than 40 is 41
no kidding, einstein
lmfao
I deliberately subtract marks from nerds like you when I mark exams, because I can

Ok faggots I'll give you a harder problem, try to solve this (hint: it's harder than it seems):

If you draw 5 cards from a poker deck what are the chances of drawing 4 kings and 1 queen?
The deck has 52 cards.
Cards withdrawn from the deck are not reinserted on it.

>>10759683
>>10759736
>>10761194
>>10762537
The challenge is shit since it doesn't clarify what expectation value you should consider. You might infer from context that they probably mean "expected profit", but it's not clearly spelt out.

>>10759459
That's about 4'9'', are you 5' or what

>>10759683
stop rolling when you have >5*(6!) coins

>>10759683
stop rolling when you have >200 coins

>>10762793
What other interpretation is there?

>>10759439
You are a biologist traveling through the rainforest when you are bitten by a rare and deadly venomous snake. You know that you only have a few seconds before you pass out and die. You also know that the female of a certain species of frog that inhabits this rainforest secretes the antidote to this venom on its back. Luckily you see a frog of this species a short distance in front of you sitting silently. You then hear a croak behind you and turn around. You see two frogs of this species the same distance in the opposite direction. You realize that you only have enough time to run to the first frog you saw or to the pair and lick their backs. You also know that females and males look identical, are in equal proportion in the population, and that only males croak. Which direction do you run and what is the probabily of survival?

>>10762793
>The challenge is shit since it doesn't clarify what expectation value you should consider.
Brainlet cope, the question is very clear.

>>10763010
You turn around and lick the 2 frogs, your chances of surviving are 2/3. If you choose the other option the chances of surviving are only 1/2.

>>10763041
Wrong.

>>10763048
You're either trolling or stupid.

https://www.youtube.com/watch?v=cpwSGsb-rTs

>>10759439
>tell humanities student that on average women are shorter than men
>he/she tells that she/he knows tall woman so my statement is untrue
i cringe every time about this "thinking" of brainlets
same applies to iq (psychology) and character features and racial differences

>>10763052
>it's on YouTube so it must be right
Did you consider that a frog which is sitting silently is more likely to be female than male? Once you do, you'll have to change your entire answer.

>>10763063
>Did you consider that a frog which is sitting silently is more likely to be female than male?
...

>>10763063
Don't worry, I knew I was right before I googled it.

>>10759439
>Is probability the highest IQ filter
Yes. But not in the way you think.

>>10763070
>not in the way you think
Elaborate

>>10763064
Do you disagree?

M = the frog is male
F = the frog is female
C = the frog croaked while you were listening

P(C|M) = x > 0

P(C|F) = 0

P(M|~C) = 0.5(1-x)/(0.5(1-x)+0.5*1) = (1-x)/(2-x)

P(F|~C) = 0.5*1/(0.5(1-x)+0.5*1) = 1/(2-x)

(1-x)/(2-x) < 1/(2-x)

>>10763065
If you know you're right then the answer should be the same when you take into account the probabily of a male frog croaking.

>>10763077
Lmfao...

>>10763077
Is this b8?

>>10763080
>>10763081
Chance the first frog is female = 1/(2-x)

Chance the pair contains a female = 1 - chance both are male

If frog 1 croaked then the chance it's male is 1. The chance frog 2 is male is (1-x)/(2-x).

If frog 1 didn't croak then the chance it's male is (1-x)/(2-x) and the chance frog 2 is male is 1.

So the overall chance that both frogs are male is (1-x)/(2-x).

This gives the chance the pair contains a female as 1-(1-x)/(2-x)= 1/(2-x)

So it doesn't matter which direction you choose, your chance of survival is the same. This is because you know the croak you heard had to come from a specific male frog while the other frog didn't croak.

>>10763080
>>10763081
Also I emailed Derek Abbott when I first saw the video and he agreed that the video is flawed. It's supposed to be equivalent to the boy-girl paradox but the animators screwed it up by changing the nature of the problem.

>>10763124
Further, if we assume that the three frogs we have seen are a representative sample then the chance of a frog croaking in the amount of time you were listening is 1/3. This means that P(C|M) = 2/3.

So our chance of survival is 1/(2-2/3) = 3/4. Pretty good.

>>10763010
Assuming the time is too short to expect all males to croak, and with no further knowledge about the frog's behavior, the chances are equal at 50%. One frog, vs two frogs, at least one of them male.

>>10763238
It's true they are equal but they shouldn't be 50% because that would imply the chance of a male croaking while you are listening is 0.

>>10759683
155

>>10759459
Your IQ is so high that you have to state it just to prove you are not dumb.
In fact, you are average at best

>>10762050
>you are just a slightly more trained brainlet. so you shuffled through a kahneman and tversky book.
Never heard of them, actually.
Of course, I understand that a lack of knowledge alone does not make one a brainlet.
The defining characteristic of the brainlet is that he refuses to admit what he doesn't know, and won't even entertain proofs to the contrary.

>>10762510
>But the fact that it can actually happen will mislead the brainlets
Precisely. And because this realization was a major epiphany for them, they mistakenly assume that others just haven't realized it yet.

>>10761148
>>10762105
>You start this dice game with no money, and you can play it as much as you like.
In other words, the game as a whole is free, even if individual rolls can cost you.

>You decide that you will keep playing as long as the expected value of your next roll is non-negative.
As already shown, this is a suboptimal strategy.

>At what point should you stop rolling?
>should
Had this said "will" or "would" (i.e. after you chose to use a bad strategy), the answer would be 41.
But since they specified "should", the answer is "never."

>>10763380
defining characteristic of brainlet is slow processing speed

>>10763383
probably this. the research all shows that iq positively correlates with reflexes, visual processing, comprehension, arithmetic skill, etc

>>10759683
the expected value is (2+3+4+5+6)/5 - current ammount/2 = 20 - current amount/2

this is zero when 40 = current amount. Doesnt this not mean that you should stop when you have 41 or more coins?

WHy is this wrong?

>>10759901
Apus are a subset of pepe

>>10763326
u mirin?

>>10763971
>you should stop when you have 41 or more coins?
>WHy is this wrong?
It's not.

>>10759683
Perhaps I've misread the question but surely you can't score below zero since it's impossible to receive a negative role?
the lowest you could possibly win is zero assuming you only threw 1s or some infintesimal fraction above zero if you threw multiple 1s after winning some coins.

>>10764684
Yes, it's a pointless game. There is zero total cost to play.

>>10759439
nope
multi-variable calculus and differential equations is typically the limit for people generally considered smart.

>>10759683
fiddy?

>>10764968
Yet half of /sci/ fails to solve simple probability problems.

>>10759708
The reason why this board sucks is because instead of discussing science and math, we have threads like this that will inevitably turn into intellectual dick measuring contests.

>>10762457
mfw there is even anime versions now

>>10762482 Assuming I don't have forever, the question is how long a wait is worth my while, depending on parameters not mentioned in the "challenge". If I get a million rolls a second, I could set the stop quantity at something much higher than if I get only one a minute, and have a reasonable expectation of catching a favorable run long enough to have a meaningfully larger payoff within a meaningfully short time-frame. In reality, we're always playing odds against time, even when instinct has anticipated what we're unable or unwilling to calculate.

>>10763010
You lick the single frog.

If you know one of the frog pair is male, the other will also be male the majority of the time, as chemicals (((they))) put in the water have turned the frogs gay.

>>10763010
Numerically, you have a 2/3 chance of survival with the two frogs, but Murhpy's law ensures that the female one will slip away if you're either too clever or too stupid, so the applied probability is still 1/2 because you have no way of knowing if this is a Murphy's law situation or not.

Luckily, you have a 50/50 chance of surviving with the lone frog, so adding the total system together your quantum probability of survival is 100% for the realities that you survive to experience. By exercising sufficient indecision, the universe will take both paths, and because something can't go wrong (quantum immortality) it won't, and you'll instinctively bolt at the last second to the worldline where you survive. The trick is making sure no version of you ends up experiencing the 1/7 probability that all frogs are male, because that will lead to an entirely different method of survival, possibly in an Everettian mangled world.

>>10767628
>as chemicals (((they))) put in the water have turned the frogs gay

>>10764968
intro stats and calc ii is the limit for most stemfags, this whole board is evidence we need to kick out most undergrads and fire most stem faculty

>>10759722
>>10759736
>>10759747
>>10761194
>>10764684
>>10762984
I love when /sci/ can't solve easy probability questions

>>10763010
Lick the one in front. It is known that >=1 of the set behind are male, and therefore even if it's 50/50 it is known that there has been no indication of the one ahead being male.

If you knew more about their behavior however, the pair may be a better option.

>>10759599
Except its a good investment during roll overs. But yeah listening to what other people say is great for 100 iq decisions

>>10768189
It's a good way to out high school students and underageb& in general.

>>10767117
That's a harder question. First, you should set the number of maximum rolls you're allowed to do. Once you have that you can start weighting the chances of rolling higher than what you currently have in X amount of rolls.

>>10768210
>Lottery is a good investment during roll overs
Spotted yet another brainlet in the thread.

>>10768210
>>10768513
Depends on lotery, but it might be true. It's a tiny loss compared to the possibility of a lifechanging win, so unless you already have a lot of money, lottery might be worth while, even though the expected return is below zero.

This is simmilar to: You get $10 million. You can either keep them or you can flip a coin and get either $30, or nothing. Mathematically, flipping the coin seems like a better choice, but since $10m allows you to live a comfortable life from capital gains alone, unless you can already live from capital gains, you should probably stick to that and not flip the coin.

>>10768210
>>10768513
Depends on lotery, but it might be true. It's a tiny loss compared to the possibility of a lifechanging win, so unless you already have a lot of money, lottery might be worth while, even though the expected return is below zero.

This is simmilar to: You get $10 million. You can either keep it or you can flip a coin and get either $30, or nothing. Mathematically, flipping the coin seems like a better choice, but since $10m allows you to live a comfortable life from capital gains alone, unless you can already live from capital gains, you should probably stick to that and not flip the coin.

>>10763010
When I try Bayesian modelling, where each frog has a prior probability of 0.5 of being male, and a male frog has a prior probability of p of being heard to croak, and you can hear the difference between one croak and two croaks, either choice has a 1/(2-p) probability of including a female frog.

>>10768570
Very good.

>>10768194
>Lick the one in front. It is known that >=1 of the set behind are male, and therefore even if it's 50/50 it is known that there has been no indication of the one ahead being male.
How does this indicate you should lick the one in the front?

>>10759459
>posting it on 4chan
definitly high IQ move

>>10763971
>Why is this wrong

>(2+3+4+5+6)/5 = 20

I guess this was a fake based on another one's answer

>>10768189
My gripe was with the wording of the question, it's fairly obvious that 41 is their intended answer but they can't formulate a question for shit

>>10768547
Spotted another brainlet.

>>10768570
Now try solving the problem by induction with 2 coins. Let someone flip them for you and only warn you whenever at learn one of them is tails. 2/3 of the times you're warned one of the coins will be heads.

Brainlets may not reply.

>>10769015
OK, that's different from the situation with frogs. With frogs, the more male frogs you have, the more likely you are to hear a croak.

>>10769015
>Let someone flip them for you and only warn you whenever at learn one of them is tails
This is different because it's not information about a specific coin. A croak has to come from a specific frog. If he only looked at one coin and saw that it landed on heads and told you, then it would be an analogous situation.

>>10769000
OK

Let's say you're in the middle of the desert, dying of thirst. You are given a 2500gallon tank of water. Will you keep it, or flip a coin to get either nothing or a 10000 gallon tank of water?

Let's say you asked on a home improvement board if you should attempt a fairly risky but quick job that you have not been trained to do. A pro tells you "forget about it I've been a roofer for 30 years and even I fell off a ladder once and hurt myself". Also out of hundreds of posters who saw your post, it only happened to that one guy. And you know that even though you don't have the skills or experience, for you it is a one time task. Unlike that roofer that has been on a roof a few thousand times and slipped only once. So taking the probabilities into account, would you heed his advice? Considering you have exact same equipment (a proper ladder to climb a 2 story residential home).

>>10769156
You missed the point, retard. I've studied economics and a fully understand the subjective nature of value. Now, also studied in economics, there's a cognitive bias that leads people to buy lottery due to overestimating the chances of winning.

>>10768547
>You get $10 million.
>You can either keep it
>or you can flip a coin and get either $30, or nothing.
>Mathematically, flipping the coin seems like a better choice
nani the fuck? what sort of maths did you use to come to this conclusion?
did you mean flip a coin for a chance to win another $10m-$20m vs losing your $10m ?

>>10770420
You obviously don't. The first few gallons are lifesaving. The thousands make no difference.

In lottery, saving $2 a week won't make any difference to anybody. Buying a ticket each week gives you a tiny chance of a lifechaing gains.

>>10770427
Yes, keep $10m, or flip a coin and get either nothing (lose those $10m) or get $30m ($20m extra on top of the $10m.

$10m, when reasonabyl invested may give you $400k a year, with inflation included. You basically don't have to work ever, if you really don't want to. So, it's either that, or flip between a slightly more comfortable life or going back to the grind. Which means, unless you're already rich, it's better to just keep the $10m.

>>10770552
Educate yourself, ignorant.

https://en.wikipedia.org/wiki/Expected_value
https://en.wikipedia.org/wiki/Prospect_theory

>>10759439
i like to consider myself pretty random tehehe ;3

>>10770592
>https://en.wikipedia.org/wiki/Expected_value

I know what it is. Obviously doesn't apply here, because the values are not linear. As in the example with the water - the first gallon is obviously far more valuable than the thousandth. You fail to take that into account.

>https://en.wikipedia.org/wiki/Prospect_theory

>The value function that passes through the reference point is s-shaped and asymmetrical. The value function is steeper for losses than gains indicating that losses outweigh gains.

People would not buy lottery if that was the case.

>>10770592
>https://en.wikipedia.org/wiki/Expected_value

I know that. Obviously doesn't apply here, because the values are not linear. As in the example with water - the first gallon is obviously far more valuable than the thousandth. You fail to take that into account.

>https://en.wikipedia.org/wiki/Prospect_theory

>The value function that passes through the reference point is s-shaped and asymmetrical. The value function is steeper for losses than gains indicating that losses outweigh gains.

People would not buy lottery if that was the case.

>>10770606
>People would not buy lottery if that was the case.
People overestimate the chances of winning the lottery. Explaining this to you feels like explaining calculus to my dog. Just accept you're a brainlet and swallow it.

>>10770801
Arguing is pointless because you're a brainlet who learned something and has no idea when or how to appy it.

>>10770801
>Arguing is pointless because you're a brainlet who learned something somewhere and has no idea when or how to apply it.

>>10770801
Arguing is pointless because you're a brainlet who learned something somewhere and has no idea when or how to apply it.

>>10770552
fair enough then
I suppose it also does not take into account that it is easier to earn more money when you already have it

>>10759683
Never, every roll there is always a 5/6 possibility of winning.

>>10771489

>>10759439
Is thing I struggle to understand the highest IQ filter?

>>10770937
>Arguing is pointless because you're a brainlet who learned something somewhere and has no idea when or how to apply it.
Exactly my thoughts on you, faggot. I have studies on the subject.

>>10773695
>thread proves OP is absolutely right
ebin

>>10759683
stop right away, gambling is sinful

>>10759439
Another RACIST thread!

>>10773708
>RACIST

>>10764404
But Apus aren't Pepes anyway you fucking retard.

>>10759683
the answer is literally in the question, unless you believe in "expected utility"

>>10773699
this, honestly a well done thread

If it is a good filter then why the fuck l are literally all IQ tests about pattern matching? None of them have any probability related problems.

>>10759683
NEVER stop playing... your income will only ever go up.

>>10773708
>Another RACIST thread!
dude .. . OP never said African Blacks have barely above retardation level IQs

>>10759459
145 with strength in what? Maths or verbal?