IS Forum
Forum Index Register Members List Events Search Today's Posts Mark Forums Read Help

Go Back   International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology
 


Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today.
Tags probability

Reply
Old 18th February 2011, 06:54 PM   #1
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
Impossible coin sequences?

Is a sequence of 100 heads in a row literally impossible to get without cheating?

This was discussed in another thread but a mutual decision has been made to start a new thread about it.
http://www.internationalskeptics.com...d.php?t=200394

My position is that it is entirely possible to get that sequence without cheating.

Each flip is approximately 50/50, regardless of what came before. All heads is as likely as any other single sequence.

Last edited by Alan; 18th February 2011 at 06:56 PM.
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 06:58 PM   #2
sol invictus
Philosopher
 
sol invictus's Avatar
 
Join Date: Oct 2007
Posts: 8,613
A sequence of posts I'm hoping Piggy will respond to:

Originally Posted by sol invictus View Post
suppose we play the following game. I make a table with 100 entries. Each entry is either F or NF. Let's say there are 50 Fs and 50 NFs in some more or less random order. Now, here's the game - I flip a coin 100 times. Before each flip I consult the corresponding entry in my table. If it says F, I flip the coin over after catching it, before uncovering it and reading it. If it says NF, I don't flip it before uncovering it.

Do you stil believe that a sequence of 100 heads is impossible, given that setup? Note that if 100 heads is impossible, then whatever sequence you'd get by starting with 100 heads and turning all the Fs into tails is also impossible, since that's what I would have gotten had I not flipped the Fs. But since my table of Fs and NFs was arbitrary, that means all sequences are impossible, which is obvious nonsense.

Therefore, 100 head sequences are possible.
Originally Posted by Piggy View Post
Try that with the example of the cup and stairs and you should see the error you're making.
Originally Posted by sol invictus View Post
I read your example, but no, I don't see the "error I'm making". Can you tell me what it is?

While you're at it, can you answer the question I asked you? Is a sequence of 100 heads still impossible if I flip/don't flip the coin after catching it according to a pre-determined plan?
sol invictus is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 07:17 PM   #3
Fnord
Metasyntactic Variable
 
Join Date: Oct 2006
Posts: 6,623
Originally Posted by Alan View Post
Is a sequence of 100 heads in a row literally impossible to get without cheating?

<snip>

My position is that it is entirely possible to get that sequence without cheating.

Each flip is approximately 50/50, regardless of what came before. All heads is as likely as any other single sequence.
Agreed.

To believe otherwise is to fall for the Gambler's Fallacy; "... the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process then these deviations are likely to be evened out by opposite deviations in the future."WP
__________________
Belief is the subjective acceptance of a (valid or invalid) concept, opinion, or theory;
Faith is the unreasoned belief in improvable things;
and Knowledge is the reasoned belief in provable things.
Belief itself proves nothing.
Fnord is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 07:40 PM   #4
Safe-Keeper
Penultimate Amazing
 
Safe-Keeper's Avatar
 
Join Date: Jun 2007
Location: Norway
Posts: 10,415
Given that you have, for example, 10 coin tosses, and the results are either H or T, the sequence HHHHHHHHHH is no more unlikely than any other, such as HTHHTHHTTH. It is us humans who attribute certain results a special meaning, even though statistically they're no less likely to happen. So yes, it's perfectly possible to get a sequence of a hundred heads. It's just as possible as it is to get any other result, in fact.
__________________
"He's like a drunk being given a sobriety test by the police after being pulled over. Just as a drunk can't walk a straight line, Trump can't think in a straight line. He's all over the place."--Stacyhs
"If you are still hung up on that whole words-have-meaning thing, then 2020 is going to be a long year for you." --Ladewig
Safe-Keeper is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 07:50 PM   #5
AdMan
Penultimate Amazing
 
AdMan's Avatar
 
Join Date: Feb 2010
Posts: 10,293
Originally Posted by Alan View Post
Is a sequence of 100 heads in a row literally impossible to get without cheating?

This was discussed in another thread but a mutual decision has been made to start a new thread about it.
http://www.internationalskeptics.com...d.php?t=200394

My position is that it is entirely possible to get that sequence without cheating.

Each flip is approximately 50/50, regardless of what came before. All heads is as likely as any other single sequence.

That sequence is just as possible as any other unique sequence of 100 coin flips.

And yes, each flip is 50/50, regardless of what came before.
__________________
As long as people believe in absurdities they will continue to commit atrocities.
- Voltaire.
AdMan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 07:50 PM   #6
Vorpal
Extrapolate!
 
Join Date: Jan 2005
Posts: 1,104
The first quote in post #2 really clinches the matter in an intuitive and obvious fashion: all sequences are possible because we can relabel them in an arbitrarily predetermined way, and there is no reason for the universe to care about our labels. I don't understand Piggy's reasons for rejecting this.

---
Throughout that thread, I couldn't make sense of Piggy's argument. Perhaps it's because I live in mathland, but at times he seems to invade that land as well:
Originally Posted by Piggy View Post
It's hardly bizarre to note that long strings of coin flips generate a rugged result space, and that smooth result spaces at great extension are typical of rigged setups.
Originally Posted by Piggy View Post
Do you have any evidence that the statistical model proposed in this case is effective all the way out to the edges, where the long stretches of heads/tails live?
This is suggestive of some sort of "space of sequences", with the special sequences of runs "live" on the edge. So presumably they're special because they're... hard to reach, being on or near the edge?

But for any sequence, there's exactly one possible way to obtain it: the coin has to sequentially go through the exact prescription of the sequence. So they're all "on the edge". If one insists on thinking of the space in terms of reachability, then it looks like a tree:
Code:
      *      * = flip
   T/   \H
   *     *   <- 1-sequences: (T),(H)
  / \   / \
 *   * *   * <- 2-sequences: (TT),(TH),(HT),(HH)
    etc.
With exactly one way to reach every possible sequence, and the "edge" being just the final level under consideration. The only way to change that is to introduce some sort of absolute rule that prunes that tree, e.g., "if you have 99 heads, you can only get a tail." So what's the reason for the universe to suddenly start caring? I think that was one of Sol's arguments as well; I just re-motivated it in terms of some space-with-edges that Piggy seems to have a conceptualization of.
__________________
For every philosopher, there exists an equal and opposite philosopher. They're both wrong.
Vorpal is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 07:59 PM   #7
Illustronic
Thinker
 
Illustronic's Avatar
 
Join Date: Jul 2008
Posts: 174
It's also entirely possible to bowl a 300 game, though very much less likely than any other bowling score.
Illustronic is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 07:59 PM   #8
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
It is a very clever argument but I'd say it's a bit difficult to understand.

I love the part that states that if one of them is impossible, then all of them are impossible.
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 08:00 PM   #9
icerat
Philosopher
 
icerat's Avatar
 
Join Date: Apr 2008
Location: sweden
Posts: 5,764
Originally Posted by AdMan View Post
That sequence is just as possible as any other unique sequence of 100 coin flips.
which would be 1:2^100, but only before you start tossing the coins, and it's the same for *any* sequence of a 100 coin flips. And clearly it's not impossible to get a sequence of 100 coin flips.

where people get confused is not understanding that the probability of throwing a head, after having thrown 99 heads in a row, is 1:2
__________________
Benford's law of controversy - Passion is inversely proportional to the amount of real information available

Last edited by icerat; 18th February 2011 at 08:01 PM.
icerat is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 08:03 PM   #10
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
Originally Posted by Illustronic View Post
It's also entirely possible to bowl a 300 game, though very much less likely than any other bowling score.
Are you suggesting that this is also the case with coins?

You would be wrong. Each flip is 50/50. Each flip has an equal chance of being anything. This is not the case in ten pin bowling.

Last edited by Alan; 18th February 2011 at 08:05 PM.
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 08:08 PM   #11
AdMan
Penultimate Amazing
 
AdMan's Avatar
 
Join Date: Feb 2010
Posts: 10,293
Originally Posted by Illustronic View Post
It's also entirely possible to bowl a 300 game, though very much less likely than any other bowling score.

Yes, bowling a 300 game is much less likely than any other score, because it's not random. It involves skill.

With tossing a coin 100 times, getting 100 heads in a row is no less likely than getting another similarly unique sequence, even if it looks like a random mix of heads and tails.
__________________
As long as people believe in absurdities they will continue to commit atrocities.
- Voltaire.

Last edited by AdMan; 18th February 2011 at 08:30 PM.
AdMan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 09:12 PM   #12
Myriad
The Clarity Is Devastating
 
Myriad's Avatar
 
Join Date: Nov 2006
Location: Betwixt
Posts: 20,891
Here's another way to clarify the issue:

As explained already, any specific sequence of 100 flips is equally possible, so of course they're all possible.

What is not possible is to predict the sequence that will occur, with any practically significant degree of confidence.

So, it's absolutely not possible to confidently predict HHHHHHHHHHHH.... Nor, of course, HTTTHTTHHHTH... or any other specific sequence.

But the only absolute impossibility is of confidently predicting. That impossibility does not rub off onto the possibility of any specific sequence occurring. And thus, it does not preclude the possibility of the sequence you predict occurring; or in other words, the possibility of correctly predicting. Those are merely astronomically unlikely.

Respectfully,
Myriad
__________________
"*Except Myriad. Even Cthulhu would give him a pat on the head and an ice cream and send him to the movies while he ended the rest of the world." - Foster Zygote
Myriad is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 09:37 PM   #13
TubbaBlubba
Knave of the Dudes
 
Join Date: Jul 2010
Posts: 12,936
It's discussion like these that sometimes make me question the sanity of some of the most brilliant posters here.
__________________
"The president’s voracious sexual appetite is the elephant that the president rides around on each and every day while pretending that it doesn’t exist." - Bill O'Reilly et al., Killing Kennedy
TubbaBlubba is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 09:48 PM   #14
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
What is your position?
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 10:00 PM   #15
Piggy
Unlicensed street skeptic
 
Piggy's Avatar
 
Join Date: Mar 2006
Posts: 15,905
Thanks, Alan, for starting the thread.

It's nearly midnight here, way past my bedtime, and I have appointments in the big city tomorrow, so I have to do a drive-by (sorry, Sol) but I now have this thread on my subscription list.

First I'll say that I have no objections to the stats regarding the range of possible outcomes of a system which produces all mathematically possible configurations of T/H for a given series length.

As far as the gambler's fallacy, just to give a kind of preamble to my way of thinking, let's rephrase it this way....

Suppose you're betting on a run of 100,000 fair coin tosses that has already occurred. At random, the result of 50,000 of those tosses are revealed.

As it turns out, 75% of the revealed results are heads, and only 25% are tails.

What odds are you willing to take that the remaining 50,000 will be evenly split among heads and tails? Would you accept even money on a bet that 25,000 (+/- 2,500) of the unrevealed flips ended up heads? Or would you be inclined to bet that the majority of the unrevealed flips were tails?

In other words, would you bet that the one-off event (the revealing of a random selection of results) was the abberation, or would you bet that the extended series of events resulted in a significant abberation?
__________________
.
How can you expect to be rescued if you don’t put first things first and act proper?
Piggy is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 10:03 PM   #16
nimzov
Guest
 
Join Date: Apr 2004
Posts: 954
Originally Posted by Safe-Keeper View Post
Given that you have, for example, 10 coin tosses, and the results are either H or T, the sequence HHHHHHHHHH is no more unlikely than any other, such as HTHHTHHTTH.
In theory. But in practice the first sequence would indicate a higher probability of an unfair coin than the second sequence.
nimzov is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 10:22 PM   #17
Piggy
Unlicensed street skeptic
 
Piggy's Avatar
 
Join Date: Mar 2006
Posts: 15,905
Originally Posted by nimzov View Post
In theory. But in practice the first sequence would indicate a higher probability of an unfair coin than the second sequence.
I'll elaborate more later, but my position is that the statement you're responding to is inherently flawed.

The real question we need to be dealing with is this: Given a supposedly fair toss, is a completely smooth results-space more or less likely to indicate cheating than is a non-smooth results-space (regardless of the exact configuration of the non-smooth space)?

By analogy, let us consider the task of determining whether we are in the ocean or a swimming pool by means of examining the behavior of the water within a nearby radius.

If we detect low turbulence and no tidal effect, then we are either in a swimming pool, or in an unusually stable sector of ocean.

Suppose that the circumstances do not change over the course of 2 hours.

Assuming that we know we are somewhere in the real world, do we conclude that we might be in the middle of an unprecedented anomaly, or that we're in a swimming pool?

If we listen to the logic of the post you're responding to, we simply count the "extremly unlikely" low-turbulence/no-tide scenario as one of a large number of equally unlikely possible configurations.

But if we use our faculties of reason, we will realize that there are a large number of configurations that conform to "we are in the ocean" and a much smaller number of configurations that conform to "we're in a pool".

So this business of claiming that a run of 100 heads is equally un/likely as any particular scenario of mixed tails and heads is a red herring.

The important feature to recognize is that a vast number of mixed heads/tails configurations will be typical of the results-space of a long series of fair coin tosses, while a long series of only heads or tails is typical only of a rigged system.

The appeal to the supposed equal likelihood of any one particular configuration is a misapplication of statistics to the actual situation on the ground.
__________________
.
How can you expect to be rescued if you don’t put first things first and act proper?
Piggy is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 10:24 PM   #18
sol invictus
Philosopher
 
sol invictus's Avatar
 
Join Date: Oct 2007
Posts: 8,613
Originally Posted by Piggy View Post
As far as the gambler's fallacy, just to give a kind of preamble to my way of thinking, let's rephrase it this way....

Suppose you're betting on a run of 100,000 fair coin tosses that has already occurred. At random, the result of 50,000 of those tosses are revealed.

As it turns out, 75% of the revealed results are heads, and only 25% are tails.

What odds are you willing to take that the remaining 50,000 will be evenly split among heads and tails? Would you accept even money on a bet that 25,000 (+/- 2,500) of the unrevealed flips ended up heads? Or would you be inclined to bet that the majority of the unrevealed flips were tails?
That question is impossible to answer (at least for me) until you tell us more precisely what the circumstances are. Specifically, exactly how do we know that the coin is "fair"?
sol invictus is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 10:27 PM   #19
Vorpal
Extrapolate!
 
Join Date: Jan 2005
Posts: 1,104
Originally Posted by Piggy View Post
In other words, would you bet that the one-off event (the revealing of a random selection of results) was the abberation, or would you bet that the extended series of events resulted in a significant abberation?
It's not a particularly relevant question, because as in the other thread, multiple people have tried to make you see the explicit distinction between
(1) whether for a fair coin, all sequences are equiprobable, and that a particular high-run sequence is just as likely as any other particular sequence when you're predicting before the fact, and
(2) whether in observing a coin that gives a very high run of heads, it is reasonable to conclude that the coin is not fair (which is actually simpler than the situation you've just posited).

You seem to be rhetorically arguing that the answer to (2) is a resounding 'yes'. I don't think anyone has said otherwise. Moreover, that answer is perfectly consistent with answering 'yes' to (1).

For a fair coin, no high-run sequence is any way more special than any other sequence. What can be considered special is the event of getting some (nonspecified) high-run sequence, i.e., the set of high-run sequences is much less numerous than the set of sequences without high runs.

You clearly recognize this:
Originally Posted by Piggy View Post
Ah, but that's an improper comparison. ... The proper comparison would be TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TTTTTTTTTTTTTTTTTTTT..... versus everything else, not versus a single alternative chosen at random.
And then Sol followed up in #123:
Originally Posted by sol invictus View Post
There are two questions that need to be separated here.

Q1) Is a sequence of 100 heads on a fair coin possible?
A1) Yes. The claim that it isn't can be immediately disposed of by noting that said sequence is no more unlikely than any other, and some sequence must always result.

Q2) Is a sequence of 100 heads on a supposedly fair coin more likely to be the result of a truly random fair sequence or of cheating?
A2) Cheating, almost certainly.
No one disputes your claim about concluding unfairness, at least in that particular case. The dispute is entirely based on you not admitting that (1) is a completely correct statement in its own right that's also consistent with (2).
__________________
For every philosopher, there exists an equal and opposite philosopher. They're both wrong.

Last edited by Vorpal; 18th February 2011 at 10:29 PM.
Vorpal is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2011, 10:33 PM   #20
Little 10 Toes
Master Poster
 
Little 10 Toes's Avatar
 
Join Date: Nov 2006
Location: Directly above the center of the Earth
Posts: 2,697
The problem with your ocean vs pool analogy is that I could be in a lake. Is that a pool or the ocean. I could be standing in a puddle and fit every other criteria. The other problem is that you're trying to use an analogy when one isn't really needed.

If I flip a fair coin, and the first two results are HH, what likelihood is the third flip to be H? It's the same chance that it will come up to be T.
Little 10 Toes is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 12:19 AM   #21
JJM 777
Suspended
 
Join Date: Jun 2004
Posts: 4,060
Originally Posted by Alan View Post
Is a sequence of 100 heads in a row literally impossible to get without cheating?
It´s not impossible. It´s just 50% less probable than a sequence of 99 heads, and 75% less probable than a sequence of 98 heads, ....
JJM 777 is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 01:41 AM   #22
GlennB
Loggerheaded, earth-vexing fustilarian
 
GlennB's Avatar
 
Join Date: Sep 2006
Location: Wales
Posts: 31,398
Originally Posted by Alan View Post
Is a sequence of 100 heads in a row literally impossible to get without cheating?
As has been stated many times already, any specific sequence of 100 flips is just as likely as any other.

But if you were aiming to come up with a specific sequence you'd have to target something like 100 straight H's just because of the difficulty of manipulating a genuine coin the way you want to. You'd choose a double-headed coin and go for the 100 H's.

Has a sequence of 100 H's ever happened? In the other thread sol said:

"2^100 is about 10^30, which is about how many viruses there are on earth at any given moment. So if there's some improbable event that applies to viruses and has probability equal to flipping tails 100 times on a fair coin, it happens to one every day (or however long viruses live)."

Consider every coin flip that's ever happened (whether observed or not, such as the way a given coin lands when you put coins on a table or into a machine). Put a figure on the average number of coins in existence per day, the number of flips experienced per day and the number of days humans have been using coins :

Average number of coins : 10^10
Average flips per coin per day : 10^2
Total days coins used : 10^6

These are probably wildly inaccurate numbers, but it doesn't really matter. Clearly we've had nowhere near enough trials to even remotely expect to find a 100H sequence has actually happened. In fact I'd guess the Earth isn't going to survive long enough to see it, but breakfast calls too loud for me to bother with rough calculations.

Piggy's original stance seemd to be that if you saw a 100-flip trial under way and beginning with 15 H's then you're watching a biased trial. I would agree to the extent that I'd love, at that point, to get some money on the sequence continuing to 100 H's, assuming the odds were attractive. Evens would be plenty attractive enough for me
GlennB is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 01:57 AM   #23
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
That is not the topic of this thread. What Piggy was arguing was that it is literally, truly impossible to get 100 heads in a row.

Originally Posted by GlennB
These are probably wildly inaccurate numbers, but it doesn't really matter. Clearly we've had nowhere near enough trials to even remotely expect to find a 100H sequence has actually happened. In fact I'd guess the Earth isn't going to survive long enough to see it, but breakfast calls too loud for me to bother with rough calculations.
Then we have not seen enough trials to expect any one combination to have happened.

We have been seeing sequences with an equal chance of happening every time there are 100 coin flips, and sequences less likely to occur every time there are 101 coin flips.

Quote:
Piggy's original stance seemd to be that if you saw a 100-flip trial under way and beginning with 15 H's then you're watching a biased trial.
Not necessarily.

Last edited by Alan; 19th February 2011 at 02:01 AM.
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 01:58 AM   #24
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
And I feel like I have to clarify because it is embarrassing me that some people responding might have misunderstood: I am not advocating for the point of view that it is impossible.
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 02:34 AM   #25
Furcifer
Guest
 
Join Date: Apr 2007
Posts: 13,797
Originally Posted by Alan View Post
And I feel like I have to clarify because it is embarrassing me that some people responding might have misunderstood: I am not advocating for the point of view that it is impossible.
Assuming it takes 3 seconds to complete a trial and you did it 8 hours every day your adult life, you'd get about 250 million attempts. It's not literally impossible, but statistically it's virtually impossible.
Furcifer is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 02:37 AM   #26
This is The End
 
This is The End's Avatar
 
Join Date: Sep 2007
Posts: 10,924
I literally do not understand Piggy's stance at all. Not one bit.

He must realize that saying one specific outcome of 100 flips is impossible is the exact same thing as saying that each and every other possible outcome of 100 flips is impossible.
__________________
________________________
This is The End is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 02:42 AM   #27
ceptimus
puzzler
 
Join Date: May 2003
Posts: 6,464
The chance of getting one head in a row is one half, two heads a quarter and so on.

The chance of getting 100 heads in a row is one in 2^100 (that's 2 x 2 x 2 ... with 100 twos)

That's a big number - it's approximately 126765 followed by twenty five zeros.

The number of atoms in a coin is only about 5 followed by 22 zeros.

Now lets assume that every time you flipped a coin you caused one atom to be worn away from it. Let's also assume that once 20% of the coin has worn away, you can no longer tell heads from tails, so you have to swap to a new coin.

If the coins were nickles, you'd (on average) have to wear out about six million dollars worth for each run of 100 heads to occur.

Now you can already see that it's practically impossible to get a run of 100 heads. And, of course, the assumption about only wearing one atom away per flip was ludicrous. No matter how careful you are, you would cause much more wear than that so you'd actually need a whole lot more than $6 million, and a correspondingly longer amount of time spent flipping
ceptimus is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:08 AM   #28
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
Does anybody who is saying it is unlikely think that they are arguing against me?
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:10 AM   #29
bokonon
Illuminator
 
bokonon's Avatar
 
Join Date: Aug 2007
Posts: 4,438
Originally Posted by ceptimus View Post
If the coins were nickles, you'd (on average) have to wear out about six million dollars worth for each run of 100 heads to occur.

Now you can already see that it's practically impossible to get a run of 100 heads. And, of course, the assumption about only wearing one atom away per flip was ludicrous. No matter how careful you are, you would cause much more wear than that so you'd actually need a whole lot more than $6 million, and a correspondingly longer amount of time spent flipping
On average, yes. However, since the sequence in question is just as likely to occur at the beginning of the experiment as in the middle or at the end, it is not practically impossible, only (as I believe everyone but Piggy has been saying) as unlikely as any other 100-trial sequence.

Every time you flip a fair coin 100 times, something truly unique and practically miraculous just happened. You'll never see another run quite like that again.

Makes me shiver just to think of it...
__________________
Laugh while you can, monkey boy.
bokonon is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:12 AM   #30
CynicalSkeptic
Master Poster
 
CynicalSkeptic's Avatar
 
Join Date: Oct 2006
Posts: 2,608
I prefer to start with 2^100 coins, flip them all then see aside all the tails.

Repeat with the remaining coins 99 times.
CynicalSkeptic is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:18 AM   #31
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
I am now volunteering to conduct that experiment. I just need people to donate the coins.
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:23 AM   #32
ceptimus
puzzler
 
Join Date: May 2003
Posts: 6,464
Originally Posted by CynicalSkeptic View Post
I prefer to start with 2^100 coins, flip them all then see aside all the tails.

Repeat with the remaining coins 99 times.
Not guaranteed to work though. For example they might all come up tails on the first flip!

Or you might get to, say the 98th flip with, say, three heads left, and then all those come up tails!
ceptimus is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:25 AM   #33
alex04
Critical Thinker
 
Join Date: Jun 2007
Posts: 483
Originally Posted by Piggy View Post
So this business of claiming that a run of 100 heads is equally un/likely as any particular scenario of mixed tails and heads is a red herring.
If you compare the likelihood of 100 heads versus anything other than 100 heads, then yes it is extremely unlikely.

If you compare the likelihood of 100 heads to any other single combination, it is equally as likely/unlikely. And renders the selection of any combination of heads or tails (yes, even if 'all' are heads) an arbitrary one.

Assuming I'm wrong here; what makes the selection of 100 heads so special that it's mathematical likelihood is reduced? I could arbitrarily pick any single combination, and very likely not see that combination reproduced ever again.
alex04 is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:26 AM   #34
alex04
Critical Thinker
 
Join Date: Jun 2007
Posts: 483
Originally Posted by Alan View Post
I am now volunteering to conduct that experiment. I just need people to donate the coins.
haha, I knew there was something behind all this..
alex04 is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:28 AM   #35
GlennB
Loggerheaded, earth-vexing fustilarian
 
GlennB's Avatar
 
Join Date: Sep 2006
Location: Wales
Posts: 31,398
Originally Posted by Alan View Post
That is not the topic of this thread. What Piggy was arguing was that it is literally, truly impossible to get 100 heads in a row.
Originally Posted by Piggy View Post

If you've got a fair coin and a fair set-up -- normal atmosphere, a human hand doing the flipping, etc. -- then the actual randomization of the world we live in sees to it that 100 heads in a row never actually happens. Yes, it's possible on paper, but not in our actual universe.
From what I've read, Piggy is distinguishing between everyday life (it is impossible) and probability-theory-world (it is possible). Elsewhere I've noticed people calculating that it would take many universe ages of coin-flip trials to reach the point where H(100) could be expected to be witnessed in a certain time frame. I believe this is Piggy's point.

Different folks are using the word "impossible" in different ways.
GlennB is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:38 AM   #36
alex04
Critical Thinker
 
Join Date: Jun 2007
Posts: 483
Originally Posted by GlennB View Post
From what I've read, Piggy is distinguishing between everyday life (it is impossible) and probability-theory-world (it is possible). Elsewhere I've noticed people calculating that it would take many universe ages of coin-flip trials to reach the point where H(100) could be expected to be witnessed in a certain time frame. I believe this is Piggy's point.

Different folks are using the word "impossible" in different ways.
Piggy's point is quite clear. The fallacy, is saying that there's something special about H(100).

And with that; where do you draw the line at impossible? H(90)? H(70)? H(40)? H(20)? H(10)?

My understanding, is that putting a limit anywhere is simply incorrect, and meaningless.
alex04 is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:50 AM   #37
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
Originally Posted by GlennB View Post
From what I've read, Piggy is distinguishing between everyday life (it is impossible) and probability-theory-world (it is possible). Elsewhere I've noticed people calculating that it would take many universe ages of coin-flip trials to reach the point where H(100) could be expected to be witnessed in a certain time frame. I believe this is Piggy's point.

Different folks are using the word "impossible" in different ways.
I asked him this:
Originally Posted by Alan
Could we perhaps agree that it is just very, very, very unlikely to happen any particular time instead of literally, truly, 100% impossible?
He did not agree.
Originally Posted by Piggy
I think, with respect to the wishes of the OP, if anyone wants to pursue this topic any further, a new thread should be started.

In fact, this issue has cropped up in several different forms over the years here on JREF.

Can we say that leprechauns do not exist, or must we be content to simply call them "extremely unlikely"? Is "strong atheism" unjustifiable? Is it really true that it's possible that a statue might wave its hand, or that a mixture of gasses might coincidentally segregate? Are we really obliged to concede that Sagan's dragon is merely "unproven" and not "false"?

My stance has consistently been that it is incorrect to hedge on these issues. And I have as yet seen no provable arguments to the contrary.

But this thread is not the place to hash that out.

If anyone's interested, please, let's move it outside.
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 03:58 AM   #38
GlennB
Loggerheaded, earth-vexing fustilarian
 
GlennB's Avatar
 
Join Date: Sep 2006
Location: Wales
Posts: 31,398
Originally Posted by Alan View Post
I asked him this:

He did not agree.
And I sympathise with his response there, and find it consistent with his general approach in this debate. It's massively irritating to have to hedge everyday language, within a finite universe, to take into account the extremes of probability theory.
GlennB is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 04:11 AM   #39
Alan
Illuminator
 
Alan's Avatar
 
Join Date: Oct 2009
Posts: 3,714
Originally Posted by GlennB View Post
And I sympathise with his response there, and find it consistent with his general approach in this debate. It's massively irritating to have to hedge everyday language, within a finite universe, to take into account the extremes of probability theory.
I sometimes call things impossible in 'everyday' conversations. But this is not that. It was a discussion about the extremes of probability theory! If somebody doesn't take the extremes of probability theory into account when talking about just that very topic then it's like somebody not taking chemicals into account in a discussion about chemistry.

Even if you are correct and the possible/impossible question was a misunderstanding, Piggy wrote some very strange statistical claims about its likelihood that we could discuss anyway.

Last edited by Alan; 19th February 2011 at 05:04 AM. Reason: major rewrite
Alan is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th February 2011, 04:18 AM   #40
TubbaBlubba
Knave of the Dudes
 
Join Date: Jul 2010
Posts: 12,936
Originally Posted by Alan View Post
What is your position?
That predicting a sequence of 100 coin tosses beforehand, even with many repeats, is rather ludicrously unlikely. So is, of course, any state of the world that derives from a series of essentially random earlier events.
__________________
"The president’s voracious sexual appetite is the elephant that the president rides around on each and every day while pretending that it doesn’t exist." - Bill O'Reilly et al., Killing Kennedy
TubbaBlubba is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Reply

International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -7. The time now is 09:19 PM.
Powered by vBulletin. Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.

This forum began as part of the James Randi Education Foundation (JREF). However, the forum now exists as
an independent entity with no affiliation with or endorsement by the JREF, including the section in reference to "JREF" topics.

Disclaimer: Messages posted in the Forum are solely the opinion of their authors.