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Gambler's Fallacy?

over 9 years

The gambler's fallacy is the idea that if you take a coin and flip it two times that it is more likely to end up with a heads on the second try if the first try landed on heads.

It's true that the individual instance of flipping the coin is always 50/50, until you introduce the possibility of a group of coin flips. For example.

Flipping a coin two times and ending up in a situation where you get heads twice, is only likely to happen in 1/4 Instances.

Heads - Heads. - 1/4 Heads - Tails. - 1/4 Tails - Tails. - 1/4 Tails - Heads. - 1/4

The actual chance you have of landing heads after the first flip is not 50/50.

Because first you had to land heads in order for the possibility of two heads in a row ever occurring.

This has the implication of being a meta-tool for people who want to up their chances of guessing correctly who is Mafia and who isn't, based on what they were in previous games. Because there is a different chance of being Mafia twice in a row than there is being Mafia in one game.

Enough of a chance that people would bet money on it.

Sort of related: https://epicmafia.com/topic/69634

Are the odds of landing heads on the second flip 1/2 or 1/4?
25
1/2
3
1/4
over 9 years
Is this Petri and is s/he trolling?
over 9 years
Wow I wish I had read this thread years ago maybe I would have been better at mafia
over 9 years
1) This is why you should use something like http://justflipacoin.com/

2) Time is everything.
over 9 years
LOL!!! Women and maths
over 9 years
You're as obstinate as a mule.
over 9 years
As a consequence of HTHT or THTH being a better likelihood, this gave birth to the system wherein people would double their bets on the opposite coin turning up. Because they are -always- betting in their favour.

And it works! I even posted examples of it on the first page.

http://i.imgur.com/4hHhKDo.png

The condition for not losing your money is, have more money! The more bets you can make that you do not make a streak, the higher your odds are that you will not lose all of your cash.

For this reason the breakpoint for the gambler would always be on the jackpot that was just before the one that could've bust them. If they win that bet, they simply stop playing and take away their earnings.
over 9 years

Zhuorb says

Don't you think the probability of it flipping heads would be 1/2 for him?


It wouldn't be, and this is usually demonstrated in a graphing artefact whenever probability is measured.

In a probability distribution graph, a curve is made where the centre of the graph is, that goes up. It can be done with other graphs, but the point that matters is this.

If the coin was truly random, you would expect that a curve would not exist, and that you'd see more often that a combination of HHHHHH Turns up, assuming all of those were flips. But HHTTHH Is more likely, and it has always been reported from testing methods that this is true. I showed those graphs earlier, with samples of 666, and 1000. Those are nice sample sizes to determine that the curve is happening.

At the start of a person's flips, you usually see that the graph slants more toward one side than the other, but gradually it approaches the true weight number (0, between -1 and +1).

Conventional wisdom would tell us that if the coins are not acted upon, this curve would not show up with the consistency that it does.

And, as expected, the instances where the unlikely events happen in comparison to the amount of tries is small in comparison to permutations that include HTHTHT, or TTHTHHT.

Because of this, if we simply added this new person's coin to the pile of previous events, and if we were on a streak of eight heads, then yes, this person is included into the first group, and they have a very good chance of landing tails.

It is because these events are not separate that this is the case. To say that these events are separate would imply that one of them could not exist. Which by consequence, would be a claim that the impossible exists.

The only way in which this person's chances could be 50/50 is if his flip was the first one that had ever occurred in existence, see?
over 9 years
I'm going to base my mafia games on numbers. I will town read everyone until someone claims a role. Before that the odds of them being town are roughly 3/4
over 9 years
Why are we feeding the troll?
over 9 years
As for your case about a coin flip being dependent on the previous one, what would you say to a person who hasn't noticed the previous flips, and says the next one will show a head? Don't you think the probability of it flipping heads would be 1/2 for him?
over 9 years
You need to learn basic probabilities before trying to understand this, VictoriaEldor
over 9 years
It's only 1/4 when you consider flipping a head twice over a sample space of four.

Since you don't have a defined sample space over here(it increases continually), you take into account the individual probabilities. Each coin flip is a mutually exclusive event, i.e you have a 1/2 chance of getting a head again.
over 9 years

Edark says


VictoriaEldor says

The basic concepts of math support my point though. Which is that a fair coin flips randomly, although we are not flipping a fair coin by definition of the coin being 1/2.

Because the coin can no longer land in absolutely any random direction with consistency, otherwise it would not be giving the results of a coin which is supposed to be giving 1/2!


"The basic concepts of math support my point though. "

No it doesnt but since your twisted idiotic mind cant understand how it really works I can understand why you would think this way and why you fail to understand the most simplistic explanations to why you're wrong.

You should really talk to a mathteacher


In this case I am the math teacher.
over 9 years

VictoriaEldor says

The basic concepts of math support my point though. Which is that a fair coin flips randomly, although we are not flipping a fair coin by definition of the coin being 1/2.

Because the coin can no longer land in absolutely any random direction with consistency, otherwise it would not be giving the results of a coin which is supposed to be giving 1/2!


"The basic concepts of math support my point though. "

No it doesnt but since your twisted idiotic mind cant understand how it really works I can understand why you would think this way and why you fail to understand the most simplistic explanations to why you're wrong.

You should really talk to a mathteacher
over 9 years
The basic concepts of math support my point though. Which is that a fair coin flips randomly, although we are not flipping a fair coin by definition of the coin being 1/2.

Because the coin can no longer land in absolutely any random direction with consistency, otherwise it would not be giving the results of a coin which is supposed to be giving 1/2!
over 9 years
If you need to change the basic concepts of math to prove your point, you're doing it WRONG
over 9 years
"Question. Why do human beings have the ability to arbitrarily decide which events are grouped and which ones are not? Who are you to say that you are the observer of previous events in this case?"

By using very simple logic
over 9 years
Question. Why do human beings have the ability to arbitrarily decide which events are grouped and which ones are not? Who are you to say that you are the observer of previous events in this case?

What is to stop someone from saying that gravity is a universal constant after having seen it repetitively affect the universe in which we exist? The answer is simple, there is no separate group, and the observers of the weighted chance are only adjusting to see the outcome of the primary group's chances (everything).
over 9 years
Your utter lack of understanding of basic maths is mindboogling
over 9 years
And if I were to say that the chance of a role means that someone will end up in one of the boxes on the top or bottom, this demonstrates that there is a weight towards this being true as well: http://gyazo.com/78cd55252e1b448e69052819e4fd4f7a
over 9 years
"It is hard to distinguish between a chain of events and a single event, because a single event always exists, and therefore the next single event, assuming it was 50%, would always be previously affected by the last chance of a 50% ever happening."

NO THEY WONT WTF
over 9 years

Edark says

Is it hard to seperate CHAIN OF EVENTS and a SINGLE EVENT?


It is hard to distinguish between a chain of events and a single event, because a single event always exists, and therefore the next single event, assuming it was 50%, would always be previously affected by the last chance of a 50% ever happening.

At first, probability exercises usually demonstrate a brief period of unreliability in the beginning. It's likely that this happens because the chain of events is getting adjusted to the weights it has been given.

For example. So I flip a coin twice, why are my odds 25% Of landing on double heads, if someone else somewhere landed on heads in that instant?

Also, I did the trials for people; so they don't have to: http://i.gyazo.com/4dc24a2497e9cd1cf3126c7d2c5e564e.png
over 9 years
you cant say that a SINGLE chain have a BIGGER chance of happening, for example if you flip maf 2 times, the next flip you will have a bigger chance of flipping town.

NO YOU WONT, every freaking chain of 3 coinflips, regardless of the premise(the previous coinflips) have 12,5% chance of happening and EVERY SINGLE INSTANCE OF A COINFLIP DOESNT AFFECT THE OTHER

You cant just break a chain and say that it had a bigger chance of happening without LOOKING at the OTHER possiblites and THEIR chance of happening, which is what GROUP PROBABILITY IS.
over 9 years
every single chain of 2 coinflips have a probability of 25% chance of happening

every single chain of 3 coinflip have a probability of 12,5% chance of happening

every single instance of a coinflip is a 50/50

dont mix these 2 up you moron
over 9 years
Is it hard to seperate CHAIN OF EVENTS and a SINGLE EVENT?