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Gambler's Fallacy

Anonymous Sun 09 May 14:06:11 2021 No.13103912 View Reply Original Report

Quoted By: >>13103935 >>13103951 >>13104146 >>13104315 >>13104329 >>13104610 >>13105773 >>13106007 >>13106706 >>13110015 >>13110114 >>13110152 >>13111706 >>13111822 >>13114107 >>13114130

If I toss a coin 6 times and it lands on heads those 6 times, if I assume it's not likely to land on heads a 7th time I'm committing a gambler's fallacy.

But if you consider all the possible variations of 7 coin tosses, only 1 of those contains all heads, while there are 7 variations of 6 heads and 1 Tails. Is it not logical to think tails is likelier?

Whats the fault in my judgement?

Anonymous

Anonymous Sun 09 May 2021 14:10:10 No.13103935 Report

Quoted By: >>13103950 >>13104488

>>13103912
If the coin is fair, it should be equally likely to toss HHHHHHH and HHHHHHT. Oftentimes you should figure that there is a heads and tails, so it is basically fair if you trust yourself to toss a coin properly.

Anonymous

Anonymous Sun 09 May 2021 14:14:27 No.13103950 Report

Quoted By:

>>13103935
But to also debunk your line of thinking, I will point out there are two variations accounting for your next move. If you dont account for your next move you did get a unique turnout with that many heads. But if you are predicting the next move there are only two outcomes, and both have as many heads. It is only logical to think one is likelier if you there is some bias, which is what you are expecting. Your reasoning is just to support your assumption.

Anonymous

Anonymous Sun 09 May 2021 14:14:49 No.13103951 Report

Quoted By:

>>13103912
>while there are 7 variations of 6 heads and 1 Tails.
You've already eliminated 6 of those possibilities though. It's not possible to get 6 heads in a row and have your pattern be HHTHHHH

Anonymous

Anonymous Sun 09 May 2021 14:16:08 No.13103956 Report

Quoted By: >>13104437

If you toss coin 6 times and it lands on heads all the time, then it is probably unfair.

Anonymous

Anonymous Sun 09 May 2021 15:08:00 No.13104146 Report

Quoted By: >>13105811

>>13103912
Gambler's fallacy applies when the probabilities of the events of the underlying stochastic process are indeed independent from trial to trial, but you evaluate or estimate future probabilities as if the underlying process's events were not independent. This is what we generally assume for all Bernoulli trials, and specifically for coin flips. For stochastic processes where the probabilities of events are not independent, such as the dealing of cards from a blackjack shoe, the probabilities indeed change from trial to trial, and thus in these cases it is not incorrect to assume that the likelihood of an event changes based on previous information. Bayes' Theorem tells us how to update our beliefs about a random process based on previous behavior of that process; our minds are efficient Bayesian inference engines, even for patterns that don't really exist. It does wonders for everyday life (e.g. people who cross the street too early get hit by cars => if I run out into the street then I will get hit by a car), but not so well for events that are truly independent. Coins have no memory and don't update their likelihood of coming up heads on the very next flip. Other processes might, but Bernoulli trials in general don't.

Furthermore, you're counting the 7 variations of 6 heads and 1 tails which include the one tails occurring in any order...

HHHHHHT
HHHHHTH
HHHHTHH
HHHTHHH
HHTHHHH
HTHHHHH
THHHHHH

...whereas the first situation you're describing only includes 1 sequence: HHHHHHT. You have to consider the order of the sequences you're analyzing.

P(7th coin heads given first 6 tails) = P(7th coin heads AND first 6 tails) / P(first 6 tails)
= (1/128)/(1/64)
= 1/2
= P(7th coin heads)

Anonymous

Anonymous Sun 09 May 2021 15:48:46 No.13104315 Report

Quoted By:

>>13103912
bump so OP reads and learns

Anonymous

Anonymous Sun 09 May 2021 15:50:52 No.13104329 Report

Quoted By:

>>13103912
house always wins
https://rumble.com/vgoga9-rekop-pirts.html

Anonymous

Anonymous Sun 09 May 2021 16:09:47 No.13104437 Report

Quoted By:

>>13103956
Guessing you've never actually gambled hey. 6 in a row is easily done.

Anonymous

Anonymous Sun 09 May 2021 16:21:37 No.13104488 Report

Quoted By: >>13105432 >>13105783

>>13103935
If the coin is fair, then it is much more unlikely to throw 7 heads than to throw
6 heads and one tails. Therefore, if you already threw 6 heads, it must be more
likely to throw tails next, by a wide margin. Otherwise you would be in a very
unlikely situation, much like walking on the street and getting hit by space debris.

Anonymous

Anonymous Sun 09 May 2021 16:52:40 No.13104610 Report

Quoted By:

>>13103912
it's
hhhhhhh
vs
hhhhhht
50/50

Anonymous

Anonymous Sun 09 May 2021 19:20:03 No.13105339 Report

Quoted By: >>13105380

No response from OP? Classic midwit

Anonymous

Anonymous Sun 09 May 2021 19:29:25 No.13105380 Report

Quoted By:

>>13105339
OP is busy with throwing his hamster against a wall, repeatedly.

Anonymous

Anonymous Sun 09 May 2021 19:38:17 No.13105432 Report

Quoted By:

>>13104488
>If the coin is fair, then it is much more unlikely to throw 7 heads than to throw 6 heads and one tails.
>Therefore, if you already threw 6 heads, it must be more likely to throw tails next, by a wide margin.
These contradict each other, and neither of them are true
What are you smoking bro

Anonymous

Anonymous Sun 09 May 2021 20:34:40 No.13105773 Report

Quoted By:

>>13103912
the universe doesn't have a set number of outcomes to give out. human beings are such little animals, always thinking about things as a resource that can be depleted and that's one of the reasons why they have such a hard fucking time with probability. assuming it's a fair coin and the outcome isn't conditional, it's always gonna be 50/50...

in the real world if this happens you're better off betting heads because there's likely something else going on with the coin or the tosser

Anonymous

Anonymous Sun 09 May 2021 20:36:26 No.13105783 Report

Quoted By: >>13105886

>>13104488
>if you already threw 6 heads
That's the key phrase here. Rethink your argument

Anonymous

Anonymous Sun 09 May 2021 20:41:31 No.13105811 Report

Quoted By:

>>13104146
also, gotta (you) this guy for the proof at the end.

QED motherfucker!

Anonymous

Anonymous Sun 09 May 2021 20:55:41 No.13105886 Report

Quoted By: >>13105976

>>13105783
Look, you are clearly not familiar with Bayesian statistics, so do not patronize.
The argument is not sensitive to any particular number of preceding throws
of heads. So suppose that $10^10$ throws of heads were made
beforehand, in succession. Then if the next throw were to also be heads,
you would be in a situation so unimaginable, that you might as well expect to be
hit by several pieces of space debris the moment you walk out the door.
It is just not going to happen, period. And everyone on /sci/ sees it as well.

Anonymous

Anonymous Sun 09 May 2021 21:08:31 No.13105976 Report

Quoted By: >>13112038

>>13105886
youre the one patronizing because you're missing the question. OP is trying to find the odds considering the series. You know it's possible to calculate the odds for throwing 7 heads in a row, OPs question therefore is tied to the previous throws because were keeping track of them

if you throw 6 heads in a row its more likely your next throw will be heads simply because there are less possible combinations.

now compute the odds from the beginning and watch as the discrepancy grows.

Anonymous

Anonymous Sun 09 May 2021 21:13:12 No.13106007 Report

Quoted By:

>>13103912
Because it's not a whatever % chance it will land on heads a sixth time. It's a 50% chance it will land on heads this time, six times in a row.

Anonymous

Anonymous Mon 10 May 2021 00:06:50 No.13106706 Report

Quoted By:

>>13103912
The number of trials does not change the data-generating process. You can have 10000 heads in a row (low probability event) but the 10001th toss still has a 50% chance of landing tails.

It's related to the "Wheaties curse", aka reversion to the mean.

Anonymous

Anonymous Mon 10 May 2021 15:05:18 No.13109640 Report

Quoted By:

So from OP's reasoning. I can toss a penny until it lands heads a bunch of times in a row and then get rich gambling.

Anonymous

Anonymous Mon 10 May 2021 16:46:29 No.13110007 Report

Quoted By:

People ITT are assuming the coin is fair. There's no reason to assume that. If I flip a coin 99 times, and it lands heads 99 times, what's the probability the next flip will also be heads? The answer isn't 50%, since the fact I got 99 heads in a row suggests the coin is biased. Similar principle applied with decks of cards where the shuffles may be unwittingly biased.

Anonymous

Anonymous Mon 10 May 2021 16:50:30 No.13110015 Report

Quoted By:

>>13103912
>You toss the coin 7 times and you know you'll get 6 heads, what are the odds that the last toss is heads?

Bayers theoryfags claim that it's not 50%

Anonymous

Anonymous Mon 10 May 2021 17:25:18 No.13110114 Report

Quoted By:

>>13103912
it depends what you're comparing it to
if you compare it to the chances it has to keep behaving as it did, obviously it's unlikely
if you compare it to one toss, the chance will always be 50%

so obviously the more coin you toss, the less likely it is to keep landing on heads
duh, are you 9?

Anonymous

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Anonymous Mon 10 May 2021 17:26:28 No.13110120 Report

Quoted By: >>13110751 >>13112772

I just simulated this scenario a million times and it landed on tails 83% of the time. wtf is going on

Anonymous

Anonymous Mon 10 May 2021 17:36:01 No.13110152 Report

Quoted By:

>>13103912
>Whats the fault in my judgement?
The coin has no memory. It doesn't know that it has landed on heads for six times.
>Is it not logical to think tails is likelier?
If you take in the whole sequence, it is actually more reasonable to expect that it'll land on heads again, since it might be weighted such.

Anonymous

Anonymous Mon 10 May 2021 17:58:32 No.13110222 Report

Quoted By: >>13110375

>frog
>twitter meme filename
What's going on is you're a faggot

Anonymous

Anonymous Mon 10 May 2021 18:42:39 No.13110375 Report

Quoted By:

>>13110222
Its a twitch file name. But nice try dimwit

Anonymous

Anonymous Mon 10 May 2021 19:54:26 No.13110684 Report

Quoted By: >>13110864

I assume the coin is fair.
>If I toss a coin 6 times and it lands on heads those 6 times, if I assume it's not likely to land on heads a 7th time I'm committing a gambler's fallacy
yes
>But if you consider all the possible variations of 7 coin tosses, only 1 of those contains all heads, while there are 7 variations of 6 heads and 1 Tails. Is it not logical to think tails is likelier?
literally what?
>Whats the fault in my judgement?
Gambler's fallacy, probably. HHHHHHH is just as likely as HHHHHHT. Each flip is completely and utterly independent of the previous flip if the coin is fair.

Anonymous

Anonymous Mon 10 May 2021 20:11:58 No.13110751 Report

Quoted By:

>>13110120
It means that you are in a simulation gone wrong.

Anonymous

Anonymous Mon 10 May 2021 20:36:28 No.13110864 Report

Quoted By: >>13110870 >>13114154

>>13110684
>I assume the coin is fair.
Why would you assume that? Would you still assume that if 85 out of 85 flips were heads?

Anonymous

Anonymous Mon 10 May 2021 20:37:20 No.13110870 Report

Quoted By: >>13111468

>>13110864
>Why would you assume that?
because that's the usual assumption when people pose epic coin-flipping hypotheticals
>Would you still assume that if 85 out of 85 flips were heads?
in real life? of course not

Anonymous

Anonymous Mon 10 May 2021 23:03:04 No.13111468 Report

Quoted By: >>13111683

>>13110870
That's my issue with these problems though. These hypotheticals are always posed as gamblers fallacies and applied to casinos... which is real life. These examples highlight certain aspects of probability, but few actually question the assumptions that go into this.

Anonymous

Anonymous Mon 10 May 2021 23:41:38 No.13111683 Report

Quoted By:

>>13111468
What? In the absence of weird bullshit going on, assuming a coin being fair is a very realistic assumption. Assuming a d6 to be fair is also a realistic assumption; of course it won't be perfectly fair in real life, but it will be very close to it.

Anonymous

Anonymous Mon 10 May 2021 23:44:50 No.13111706 Report

Quoted By:

>>13103912
there is only one variations of 6 heads followed by one tail.

Anonymous

Anonymous Tue 11 May 2021 00:14:12 No.13111822 Report

Quoted By:

>>13103912
The fault is that you're assuming that the overall behavior of the system must be reflected in the constituent parts of it. You're not evaluating the probability of x heads and y tails. You're evaluating the probability of heads vs tails on a specific coin toss.
But what you might do to screw with the math nerds is point out that you have no reason to believe it's a fair coin just because some hypothetical faggot told you it was.

Anonymous

Anonymous Tue 11 May 2021 01:09:14 No.13112038 Report

Quoted By:

>>13105976
>if you throw 6 heads in a row its more likely your next throw will be heads
No...

Anonymous

Anonymous Tue 11 May 2021 01:12:38 No.13112052 Report

Quoted By:

>ITT OP is retarded

Anonymous

Anonymous Tue 11 May 2021 04:20:12 No.13112772 Report

Quoted By:

>>13110120
I'm gonna be rich using this at the casino

Anonymous

Anonymous Tue 11 May 2021 12:36:33 No.13114107 Report

Quoted By: >>13114148

>>13103912
if you toss a fair coin, there is a 50% chance it will land on heads and a 50% chance it will land on tails. mind you, it's perfectly possible for a fair coin to get 6 heads in a row, so don't pull that "what if" argument.
/thread

Anonymous

Anonymous Tue 11 May 2021 12:43:57 No.13114130 Report

Quoted By:

>>13103912
The issue is the known data. List out all the possibilities of tossing a coin 7 times and the first 6 are heads. Then calculate the probability the next coin toss is heads

Anonymous

Anonymous Tue 11 May 2021 12:51:58 No.13114148 Report

Quoted By:

>>13114107
>it's perfectly possible for a fair coin to get 6 heads in a row
Yes, in an experiment. In real life, it would be naive to assume the coin is fair

Anonymous

Anonymous Tue 11 May 2021 12:53:01 No.13114154 Report

Quoted By:

>>13110864
>Why would you assume that?
because the problem stops being a math problem otherwise

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