[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 16 KB, 254x380, 1387691819523.jpg [View same] [iqdb] [saucenao] [google]
6241976 No.6241976 [Reply] [Original]

Can someone explain probability to me?

If you flip a coin 100 times, the results will be around 50/50.

But what if you flip it and it comes up tails 20 times in a row. Doesn't that mean the probability of the next flip being heads is increased? Why not?

>> No.6241981

Each event is independent. It may seem like since you just got 20 tails, the next should be heads. But that's actually a logical fallacy. The results of those other flips aren't effecting the outcome of your next flip. The coin doesn't know you just flipped it 20 times, it's a coin. It just spins in the air and lands on a random side.

>> No.6241983

>>6241981
/thread

>> No.6241984

>>6241981
This always fascinates me. You can flip tails 100 times consecutively, and there will always be a chance that the next flip will be tails. I think the factor of being unknown is what attracts people to gambling.

>> No.6241986

OP, that is a common mistake and the reason that Las Vegas is so rich/successful. Each flip of a coin has a 50/50 probability for either side. And every flip of a coin is an independent event, as the previous flip does not affect the new one. You may think that with 20 tails, it's due time for a heads. However, this is something called "gamblers fallacy" and is not true. The event of 20 tails is very rare and just a matter of luck.

>> No.6241990

>>6241984
what attracts people to gambling is the idea that you can get something for nothing. how many math students do you know who buy lotto tickets?

>> No.6241992

>>6241990
> how many math students do you know who buy lotto tickets?
infact none

>> No.6241998

It doesn't take a degree in mathematics that a zero in a trillion gazillion billion is a pretty low probability

>> No.6242008

There was once an event where someone rolled like 23 or something blacks in a game of roulette, and then decided to all in on red because he had rolled so much black that the next roll was surely to be a red.

Probability is a fun thing, it really messes with intuition, especially with gambling: if you get a prize that says you will win 1/4 of the time, that doesn't mean that if you get 4 prizes you assure a win, what it means is there is a 1-(3/4)^4[chance of losing] or 1-(81/256) or 175/256 or about 68.36% chance of at least one of those prizes winning, which is much less than what it seems like it should have been, since grabbing 4 seems like it should have assured victory, but you still have over a 30% chance of losing.

>> No.6242014

>>6241976
If the events were all tied together, it would seem more so. In fact, if you look at the concept of coin flipping instead of the independent event of a coin flip, then that means there is exactly a 1 in 1267650600228229401496703205376 of not flipping a single heads in 100 turns.

>> No.6242024

>>6242008
You know ... I hit 14 losses in a row in bitcoin roulette doubling my bet every time, never playing that bullshit again

>> No.6242025
File: 32 KB, 480x357, 39966-rosencrantz_amp_guildenstern_dead.jpg [View same] [iqdb] [saucenao] [google]
6242025

>>6241984
If you get tails 100 times,
Id be checking that coin.

>> No.6242035

>>6241981
But the probability of the event of 21 consecutive tails is 0.5^21 right? So why wouldn't your 21st coin flip be more likely to be head?
Enlighten me please, I'm always terrible with probability.

>> No.6242040

>>6242035
My take for this is that, regardless of the probability for 21 consecutive tails (A), the event of *20 consecutive tails* (B) already happened. So the probability for the 21st coin flip is P(A|B), which is just the probability of a regular coin flip.

>> No.6242042

>>6241976
You're confusing the probabilities of the 21st flip alone vs the whole series of 21 flips. Plug in n=21, k=21, p=1/2 to this and you get the latter:

http://en.wikipedia.org/wiki/Binomial_probability#Probability_mass_function

>> No.6242144

>>6242042
Thanks to everyone for their input. It really put things into perspective. I googled "gambler's fallacy" and it was really insightful, explaining everything and where the term originated.

I've recently been playing online poker (not real money!) and have been victim to this phenomenon as well.

http://en.wikipedia.org/wiki/Gambler's_fallacy

>> No.6242748

Yea, well, we are talking about a mathematical model of reality. It's not a logical fallacy to say that your next flip is influenced by your last. It just that that sort of reasoning doesn't usually fit reality well.

>> No.6242806

>>6242035
Basically
It's unlikely that you'll get 21 heads in a row, but it's still a 50/50 chance to get a another head after your 20th flip

>> No.6242839

>>6241976

>Can someone explain probability to me?

Probability means that whatever you are expecting is a lie.

In all probability, someone somewhere at some point in time has done a coin flip test and gotten an unusually high amount of tails results.

Probability, calculating averages, is basically working with false information and hoping for the best.

You get the most mileage out of it when planning long term events in advance.

>> No.6242865

>>6241990
I do, I buy a s $1 scratch ticket time to time.

>> No.6242873

>implying probability isn't what we use when we don't know exactly how each variable in a system is related to each other

>> No.6242880

>>6241981
>Each event is independent.

Actually quantum physicists have shown that the result of a coin flip does slightly alter the outcome of the next flip.

For instance if you get heads, the chances of getting heads again is .999.../2

>> No.6242882

>>6241992
lol, I had math professors who were gambling addicts lol

>> No.6242888

>>6242880
lel

>> No.6242961

Alternatively, if earthquakes are expected to happen every 200 years, and one hasn't happened in 600 years, then saying "it's due" is correct. Because if the true probability really is 200 years, then it will have to happen somewhat soon to keep on that same probability percentage.
This is different than a coin flip because there's a geological reason why earthquakes happen so often.

>> No.6242977

Side note that probably isn't too relevant. But if you flip a coin and get heads 20 times in a row then the way you're flipping them or the coin itself is probably biased.

>> No.6243028
File: 2 KB, 585x423, 1387753518511.png [View same] [iqdb] [saucenao] [google]
6243028

You can actually understand this. The problem here is that the shrinks involved in the ansewring of such question are refusing to involve the dimension called time. It does mean the probability of the next flip being heads is increased. You seem to be unsure of both statements. The chance of rolling heads twice is 1/4. The chance of rolling heads 3 times is 1/8. What is the chance of rolling heads 21 times, no breaks? 1/2097152. The chance of not rolling heads 21 times is 2097151/2097152. It is like someone forgot it and went saying I had a laugh and a diploma anyway. Events are not independent, that is what you tell yourself when you don't know what happened before. It is a fucking rare event, I played money poker enough. As complexity rises rethoric on theory gains weight, well, just do the math twice, I am a math major myself. Stop calling yourself a retard and the long term outcome will answer the doubts. These odds doesn't change while you breath or someone writes something on a board.

>> No.6243572

>>6242880
can you provide a source for this

>> No.6243598

>>6242880
>can't tell if bait

>> No.6243608

>>6243572
>he doesn't know .999... = 1

>> No.6243882

>>6242873
Didn't this notion go out when frequentism came in?