Impossible coin sequences?

[Cuddles]

No, you're not guaranteed that at all.

Because the question is actually one of predictability.

It may be impossible to predict, by looking at one keypress, which key will be pressed next, but still to be looking at a system which will never produce a single work of Shakespeare.

No. This is a very simple point that lies at the heart of your misunderstanding. As long as there is a non-zero chance for a particular outcome, whether it's a key being pressed, a coin landing up a certain way, or anything else, then that outcome is guaranteed to happen eventually given arbitrary time. This isn't up for debate, it's the very definition of non-zero probability. The only way a sequence can not be possible is if the system is set up so that at some point there is a probability of exactly zero involved.

The problem you seem to be having, as already noted several times, is that you're starting off with a system that is defined as always having a non-zero probability of every outcome, then arguing that at some point the probability magically changes to zero for no apparent reason. This argument simply doesn't make sense, especially since you've admitted to having absolutely no reason to think it is actually the case. It's a simple case of the null hypothesis and Occam's razor - there's no evidence it happens, so it's stupid to assume it does until such evidence is provided.

 

[Piggy]

As long as there is a non-zero chance for a particular outcome, whether it's a key being pressed, a coin landing up a certain way, or anything else, then that outcome is guaranteed to happen eventually given arbitrary time. This isn't up for debate, it's the very definition of non-zero probability.

That's right.

And in order for you to determine whether the very first phrase of your condition is accurate, you need to understand what the results-space of the physical system you're dealing with will be.

You cannot simply decide that a given system has a non-zero chance for any particular outcome. You have to have a reason to reach that conclusion.

 

[Piggy]

Which has been done over and over again in this thread. It really is simple Piggy: as long as there is some non-zero chance that each flip will come up heads, then a streak of all heads is possible.

No, I'm sorry, but explaining this principle is not the same thing as demonstrating that it applies in this case.

If you want to apply this logic, you have to demonstrate that there is a non-zero chance of this particular physical configuration producing a streak of 100 heads. And if you're talking about a human brain, arm, and hand, on Earth, in real time, then how in the world do you intend to demonstrate that?

 

[eeyore1954]

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/forums/showthread.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.

If it is impossible to get 100 heads in a row it is also impossible to get any other combination of 100 flips.

 

[Piggy]

There is a very big difference between biased and deterministic: I'm happy to accept the (rather far off) possibility that as streaks get longer people unconciously start affecting the flips in such a way that continuing the streak becomes less likely than predicted. That's very very different from saying that it becomes impossible. As I said, that requires 100% control of the flipping.

Rather far off?

Compared to the odds of flipping 100 heads in a row?

Not even close.

In any case, your definition of "impossible" has done a 180, it seems. When it came to outlandish streaks, a thing which we would not expect to happen in longer than the age of the universe had to be deemed "possible", but now something which is decidedly unlikely cannot be called possible?

And the ability to throw heads or tails at will is documented, so that's not out of the ballpark, either.

There's also no contradiction in undetectable limits on randomness. Rig every slot in Vegas to never let any "wheel" run a streak of 100, and the Gaming Commission would never detect it.

 

[Piggy]

urthermore, if this is your argument it seems that you concede that if, for instance, the human flipper were unaware of the outcome of the coin tosses (and thus any possible memory were taken out of the system) that all sequences would be possible, correct?

Well, that's an interesting system.

Physical fatigue might still loop the system back.

How would you know?

 

[Piggy]

No, because one is a conclusion based upon what we actually know about the world and the system in question, and another is just something dreamed up.

Would you care to apply that same logic to what we know about the results of coin tosses, versus what people have dreamed up about them?

 

[Piggy]

It's not at all hard for me to believe that the chances of getting 100 heads in a row are about 1 in 2¹⁰⁰. In fact, that's exactly what I believe. 1 / 2¹⁰⁰ is very small, to be sure, but it's not zero.

It's much harder for me to believe that the chances are precisely zero, because that would imply that the 100th flip is qualitatively different from the first 99: each of the first 99 might come up heads or tails, but if they all happen to come up heads, then somehow the 100th flip inexplicably must come up tails. What could possibly be special about that particular flip, compared to all the others that have ever taken place in the history of the world, which makes it certain to come up tails?

Regardless, I would still take my bet of my life against a Lotto jackpot that everyone on earth flipping coins for 10 years wouldn't come up with that streak.

1/2^100 is a hyper-astronomical number. To keep with the coin theme, if a coin were flipped every 10 seconds, I figure you'd have to flip it a little over 400 sextillion years before you'd made 2^100 flips. That's some 26 trillion times the age of the universe.

And each person on earth would be facing the same odds.

As for what stops the streak, I have no clue. I'm not saying any such thing exists. I do know you can easily design a system to do that and to have results indistinguishable from true randomness. So unless we can fully describe the system, then we don't know what the results-space looks like.

 

[Piggy]

It's been mentioned a few times, and I am baffled that the thread didn't stop dead...non-zero probability means possible. Why would not having perfect knowledge of a particular system mean anything, unless it somehow affected the probability of a given set of outcomes?

Is a given sequence possible? What's the probability of that? Oh, it's a real number between 0 and 1 that happens to not be zero? Then it is possible.

The question has been asked several times, in different forms, how that non-zero probability has been determined, and so far there's been no answer, merely assertions that it's non-zero.

Mind you, I'm not saying that it actually isn't.

 

[Piggy]

The only way your theory would work is if somehow the "human brain/arm/hand" idea reduced the heads possibility for a particular flip to zero.

That's right.

 

[AdMan]

Regardless, I would still take my bet of my life against a Lotto jackpot that everyone on earth flipping coins for 10 years wouldn't come up with that streak.

1/2^100 is a hyper-astronomical number. To keep with the coin theme, if a coin were flipped every 10 seconds, I figure you'd have to flip it a little over 400 sextillion years before you'd made 2^100 flips. That's some 26 trillion times the age of the universe.

And each person on earth would be facing the same odds.

So what? The odds are exactly the same for each unique combination of 100 throws. And yet, each time we throw a coin 100 times, we get one such unique, equally probable or improbable combination.

Why is it so hard for you to see that?

 

[Roboramma]

There is a very big difference between biased and deterministic: I'm happy to accept the (rather far off) possibility that as streaks get longer people unconciously start affecting the flips in such a way that continuing the streak becomes less likely than predicted. That's very very different from saying that it becomes impossible. As I said, that requires 100% control of the flipping.

Rather far off?

Compared to the odds of flipping 100 heads in a row?

Not even close.

Why are you comparing them? Neither I nor anyone else has suggested that flipping 100 heads in a row is likely. We all accept that it's phenomenally unlikely, so what's your point?
I simply said that your excuse for how it becomes impossible is less likely to be true than not, so if we are to sit here and try to figure out if it is actually impossible, even at this first step it's looking more likely to be possible than not.

But, as I said, even assuming that this unlikely thing is true, it still doesn't make streaks of 100 heads impossible.

In any case, your definition of "impossible" has done a 180, it seems. When it came to outlandish streaks, a thing which we would not expect to happen in longer than the age of the universe had to be deemed "possible", but now something which is decidedly unlikely cannot be called possible?

What are you talking about? What did I say "cannot be called possible"? I specifically said "If this unlikely thing is true..."

And the ability to throw heads or tails at will is documented, so that's not out of the ballpark, either.

Sure, but that's a different question. If you are saying "it's possible for a skilled coin tosser tossing coins forever to never get a streak of 100 heads, then I'll buy that as possible. But you are saying that people have 100% unconcious control of flipping without any prior training. And you have absolutely no evidence for that!

 

[Roboramma]

Well, that's an interesting system.

Physical fatigue might still loop the system back.

How would you know?

So, you are now suggesting that people getting tired makes coin flips come up tails 100% of the time?

 

[Roboramma]

That's right.

Any evidence of any possible mechanism that could cause that to happen?

 

[GlennB]

The question has been asked several times, in different forms, how that non-zero probability has been determined, and so far there's been no answer, merely assertions that it's non-zero.

Mind you, I'm not saying that it actually isn't.

That bolded part is just wrong. Saying that 1 in 2^100 is non-zero is not 'an assertion'. It's mathematical fact. Having to demonstrate it happening in real life in order to prove that it's true is an arbitrary and unreasonable condition for you to apply.

Sheesh. When I originally chipped in to this thread I thought you were being misunderstood.

 

[TubbaBlubba]

Well, that's an interesting system.

Physical fatigue might still loop the system back.

How would you know?

Depeds. Is it a dime or a shilling?

 

[alexi_drago]

100 heads is still a random sequence from a huge list of sequences, there's not enough ink on the planet, even if the oceans were all ink, to write down a list of all possible sequences of 100 tosses. To select a single sequence and ask if it's possible is like selecting any other of the possible sequences from the list and asking if they are possible.
Is there a better chance of a sequence occuring just because it looks more random to you?

EDIT: There are more sequences in that list that look more random than ordered so the chances are that a sequence with a more random than ordered appearance will come up.

 

[Mobyseven]

The question has been asked several times, in different forms, how that non-zero probability has been determined, and so far there's been no answer, merely assertions that it's non-zero.

Mind you, I'm not saying that it actually isn't.

That's not true -- I recall further up the thread someone explaining where it comes from. To wit: every time the coin is tossed there is a non-zero probability that it will come up heads. That, together with the fact that each coin toss is an independent event, gives you a non-zero probability that a run of 100 heads will occur.

 

[Ivor the Engineer]

That's not true -- I recall further up the thread someone explaining where it comes from. To wit: every time the coin is tossed there is a non-zero probability that it will come up heads. That, together with the fact that each coin toss is an independent event, gives you a non-zero probability that a run of 100 heads will occur.

Exactly. With a coin with at least one head on it, there's always a chance on every single flip that the coin will come up heads. Therefore a sequence of any length of heads is possible from any coin with a head on it.

 

[AvalonXQ]

Have we agreed on what "impossible" means yet, or is that what we're really arguing over?