So, you flip a coin 9 times

[TE-23]

Him and One Punch Jarv are doing a job for UEM.

[diaspora]

So Rosencrantz and his mate are not dead...but didn't we win a game on the toss of a coin once but only after it landed on its side in the mud first...think it was against Cologne

[Original202]

I hope most people on this thread don't ever try and make money from gambling.

 

2/1 is not evens.

 

You'd have 3 goes:

 

Outcome A comes in twice and outcome B comes in once - hence 2/1.

 

Evens is 1/1....

 

Anyway, we're still missing some key facts here. Does one side of the coin have buttered spread onto it for example? Edit: Flyingpig already asked. But it needs asking twice.

[Dirk]

From Wiki

 

The ludic fallacy is a term coined by Nassim Nicholas Taleb in his 2007 book The Black Swan. 'Ludic' is from the Latin ludus, meaning 'play'. It is summarized as "the misuse of games to model real-life situations".[1] Taleb characterizes the fallacy as mistaking the map (model) for the reality (see map-territory relation), an inductive side-effect of human cognition.

 

It is a central argument in the book and a rebuttal of the predictive mathematical models used to predict the future --as well as an attack on the idea of applying naive and simplified statistical models in complex domains. According to Taleb, statistics only work in some domains like casinos in which the odds are visible and defined. Nassim’s argument centres on the idea that predictive models are based on platonified forms, gravitating towards mathematical purity and failing to take some key ideas into account:

 

* It is impossible to be in possession of all the information.

* Very small unknown variations in the data could have a huge impact (the Butterfly effect).

* Theories/models based on empirical data are flawed, as events that have not taken place before cannot be accounted for.

 

Example 1: Suspicious coin

 

One example given in the book is the following thought experiment. There are two people:

 

* Dr John, who is regarded as a man of science and logical thinking.

* Fat Tony, who is regarded as a man who lives by his wits.

 

A third party shows them a coin and explains that there is a 50/50 chance of the coin coming up heads or tails when it is flipped.

 

* The coin is then tossed 99 times and it comes up heads every time.

* The two people are both asked to give the odds of the coin coming up heads a 100th time.

* Dr John says that the odds are not affected by the previous outcomes so the odds must still be 50/50.

* Fat Tony says that the odds of the coin coming up heads 99 times in a row are so low (less than 1 in 633 billion billion billion) that the initial assumption that the coin had a 50/50 chance of coming up heads is most likely incorrect.

 

The ludic fallacy here is to assume that in real life the rules from the purely hypothetical model (where Dr John is correct) apply. Would a reasonable person bet on black on a roulette table that has come up red 99 times in a row (especially as the reward for a correct guess are so low when compared with the probable odds that the game is fixed)?

 

In classical terms, highly statistically significant (unlikely) events should make one question one's model assumptions. In Bayesian statistics, this can be modeled by using a prior distribution for one's assumptions on the fairness of the coin, then Bayesian inference to update this distribution.

 

Ludic fallacy - Wikipedia, the free encyclopedia

Edited March 26, 2009 by Dirk

[Ezekiel 25:17]

The ludic fallacy is a term coined by Nassim Nicholas Taleb in his 2007 book The Black Swan. 'Ludic' is from the Latin ludus, meaning 'play'. It is summarized as "the misuse of games to model real-life situations".[1] Taleb characterizes the fallacy as mistaking the map (model) for the reality (see map-territory relation), an inductive side-effect of human cognition.

 

It is a central argument in the book and a rebuttal of the predictive mathematical models used to predict the future --as well as an attack on the idea of applying naive and simplified statistical models in complex domains. According to Taleb, statistics only work in some domains like casinos in which the odds are visible and defined. Nassim’s argument centres on the idea that predictive models are based on platonified forms, gravitating towards mathematical purity and failing to take some key ideas into account:

 

* It is impossible to be in possession of all the information.

* Very small unknown variations in the data could have a huge impact (the Butterfly effect).

* Theories/models based on empirical data are flawed, as events that have not taken place before cannot be accounted for.

 

Example 1: Suspicious coin

 

One example given in the book is the following thought experiment. There are two people:

 

* Dr John, who is regarded as a man of science and logical thinking.

* Fat Tony, who is regarded as a man who lives by his wits.

 

A third party shows them a coin and explains that there is a 50/50 chance of the coin coming up heads or tails when it is flipped.

 

* The coin is then tossed 99 times and it comes up heads every time.

* The two people are both asked to give the odds of the coin coming up heads a 100th time.

* Dr John says that the odds are not affected by the previous outcomes so the odds must still be 50/50.

* Fat Tony says that the odds of the coin coming up heads 99 times in a row are so low (less than 1 in 633 billion billion billion) that the initial assumption that the coin had a 50/50 chance of coming up heads is most likely incorrect.

 

The ludic fallacy here is to assume that in real life the rules from the purely hypothetical model (where Dr John is correct) apply. Would a reasonable person bet on black on a roulette table that has come up red 99 times in a row (especially as the reward for a correct guess are so low when compared with the probable odds that the game is fixed)?

 

In classical terms, highly statistically significant (unlikely) events should make one question one's model assumptions. In Bayesian statistics, this can be modeled by using a prior distribution for one's assumptions on the fairness of the coin, then Bayesian inference to update this distribution.

 

Ludic fallacy - Wikipedia, the free encyclopedia

 

 

Pretty much sums up how I feel about the situation.

[Crazyhorse7778]

 

:whistle:

[Guest TK-421]

the correct answer is very slightly less than 50/50 as it could land on its edge

 

If it's a fifty or a twenty it could land on heads, tails or one of seven edges. I suppose there's even a remote chance it could land on one of the corners where two edges meet, depending on the surface it's landing on.

[Dirk]

Pretty much sums up how I feel about the situation.

 

Taleb suggests in the book that there is some "unknown" cause working on the coin.

[Nick Leeson]

That's very interezzzzzz

[mars]

The ludic fallacy is a term coined by Nassim Nicholas Taleb in his 2007 book The Black Swan. 'Ludic' is from the Latin ludus, meaning 'play'. It is summarized as "the misuse of games to model real-life situations".[1] Taleb characterizes the fallacy as mistaking the map (model) for the reality (see map-territory relation), an inductive side-effect of human cognition.

 

It is a central argument in the book and a rebuttal of the predictive mathematical models used to predict the future --as well as an attack on the idea of applying naive and simplified statistical models in complex domains. According to Taleb, statistics only work in some domains like casinos in which the odds are visible and defined. Nassim’s argument centres on the idea that predictive models are based on platonified forms, gravitating towards mathematical purity and failing to take some key ideas into account:

 

* It is impossible to be in possession of all the information.

* Very small unknown variations in the data could have a huge impact (the Butterfly effect).

* Theories/models based on empirical data are flawed, as events that have not taken place before cannot be accounted for.

 

Example 1: Suspicious coin

 

One example given in the book is the following thought experiment. There are two people:

 

* Dr John, who is regarded as a man of science and logical thinking.

* Fat Tony, who is regarded as a man who lives by his wits.

 

A third party shows them a coin and explains that there is a 50/50 chance of the coin coming up heads or tails when it is flipped.

 

* The coin is then tossed 99 times and it comes up heads every time.

* The two people are both asked to give the odds of the coin coming up heads a 100th time.

* Dr John says that the odds are not affected by the previous outcomes so the odds must still be 50/50.

* Fat Tony says that the odds of the coin coming up heads 99 times in a row are so low (less than 1 in 633 billion billion billion) that the initial assumption that the coin had a 50/50 chance of coming up heads is most likely incorrect.

 

The ludic fallacy here is to assume that in real life the rules from the purely hypothetical model (where Dr John is correct) apply. Would a reasonable person bet on black on a roulette table that has come up red 99 times in a row (especially as the reward for a correct guess are so low when compared with the probable odds that the game is fixed)?

 

In classical terms, highly statistically significant (unlikely) events should make one question one's model assumptions. In Bayesian statistics, this can be modeled by using a prior distribution for one's assumptions on the fairness of the coin, then Bayesian inference to update this distribution.

 

Ludic fallacy - Wikipedia, the free encyclopedia

 

 

So what are the odds on the initial assumption being incorrect?

[sir roger]

I always remember our maths teacher giving us a probability question about 2 black balls and 2 white balls being in a bag & asked us the probability of the first 2 balls being the same colour. The answer given in his book was 2/1 & he kept muttering that it was wrong. We had to explain to him that the first ball's colour was irrelevant & that this left 3 balls in the bag & a 2/1 chance of the same colour coming out. He still wouldn't accept it though & it was at that stage that I realised I would need to do some private study of my own if I wanted an O Level in maths.

[lukem]

I always remember our maths teacher giving us a probability question about 2 black balls and 2 white balls being in a bag & asked us the probability of the first 2 balls being the same colour. The answer given in his book was 2/1 & he kept muttering that it was wrong. We had to explain to him that the first ball's colour was irrelevant & that this left 3 balls in the bag & a 2/1 chance of the same colour coming out. He still wouldn't accept it though & it was at that stage that I realised I would need to do some private study of my own if I wanted an O Level in maths.

 

I am most probably wrong with this but..

 

If it leaves 3 balls left in the bag, then the chance of getting the same colour as the previous ball is now 1/3, reducing the overall odds?

 

I think I'm with your teacher on this one.

 

EDIT - No I'm not, I read your post as 1/2 not 2/1.

[kelster]

1/2^10 = 1/1024.

 

Derren brown proved it was possible on one of his programmes, but it took him hours of flipping a coin to get the sequence. The odds aren't staked on the possibility of a single event occurring but of a sequence.

 

What was he trying to prove? Any outcome based on probability will occur eventually given enough time. It is possible that you could flip a thousand heads given enough time, it would take about 2.5 * 10^283 times the age of the universe, but eventually it would happen. Why doesn't Derren Brown try that? That'll keep the cunt occupied and off TV.

[mars]

It might not take longer than the age of the universe to flip 1000 heads in a row - I have a sneaky feeling it will happen next time I try it.

 

Casinos make there money from people who have problems accepting the Gambler's Fallacy - the notion that dice, cards, etc can remember what happened in the past and will act to "average things out". For some reason it seems to be human nature to fall for this - I wouldn't pick lottery numbers that came up last week, but logically I know they have just the same chance of turning up as any other combination.

[briefs]

The question is very ambiguous.

 

If you're betting on what the coin will do on the 10th flip, whether it's after 9 or 90 other flips, and you're making that the 'single event', then the probability of getting a head is 1/2.

 

But, if you're betting on 10 heads coming out in a row and you're identifiying the whole 10 flips as the 'single event', then the probability of that happening is 1/1024.

[mars]

If you have already flipped nine heads hasn't the probability of a 10 head sequence risen to 0.5?