Impossible coin sequences?

[sol invictus]

It was whether or not you'd ever actually encounter a run of 100 heads or tails in a fair coin-flipping system, or a human one, on earth.

If was? Because that's not what you said, and it's not what everyone here is responding to.

The odds that you'd ever actually encounter a run of 100 heads or tails in a fair coin-flipping system are exactly the same as the odds of encountering any other unique string of 100 heads and tails. That's true by definition of "fair". That is what everyone is trying to explain to you.

Yes, those odds are very very tiny - but it's quite literally nonsense to assert they are zero, as has now be explained ad nauseum.

 

[AdMan]

The issue was never whether a series of 100 values of "T" or "H" was impossible for any system you could imagine.

It was whether or not you'd ever actually encounter a run of 100 heads or tails in a fair coin-flipping system, or a human one, on earth.

Ah, you're right, I never meant that it was possible to throw 100 heads in a row on earth, I always thought you were talking about doing it on Mars.

On earth (where physics and probability may work differently from the rest of the universe..?), maybe it's not possible.

Huh??

 

[Roboramma]

I'm talking about the physical system. After all, what other system is there? When we're talking about coin flips, we're necessarily talking about some physical system, whether it's a machine or my right hand.

If you want to say that any particular system has a particular results-space, and not some other, you're going to have to show why that is.

It's not enough to demonstrate what all the possible combinations are. You also have to demonstrate that the system will achieve them all.

Sure, and to do that you look at the actual properties of the system, our understanding of the physical laws of the universe, and deduce the implications of that.

So, for instance, in the case of coins, as sol pointed out there are no fair coins, but we can figure out the probabilities of coming up heads vs. tails. We can then deduce (from the fact that neither is impossible and that subsequent flips are in no way influenced by past flips) that all combinations are possible. If we use the abstraction of a fair coin, that's fine, and in that case we find that all combinations are equally probable.
It really is that simple, and it really is based on the actual physical system involved.

 

[Roboramma]

Piggy's viewpoint here seems to me to be increadibly unscientific, from two perspectives.

The first, and most important, is the view that we can't know anything if we haven't done that specific experiment. It comes down to something like this: we've measured the speed of light to come out to approximately 3x10⁸ m/s. There are some valid questions about whether or not that value has changed with time or is different in different parts of the universe. But Piggy's view is like asserting that we don't know that speed of light is on sunny wednesday afternoons when the temperature is exactly 10.005^oC and the finance minister of Kenya has just given a live speech for French television, because we haven't done that experiment.

When asked how those things could possibly affect the speed of light he'll reply that he doesn't know, but you can't possibly know either.

Now, that may be true in a way, but I'm confident that if we do measure it in those circumstances it will come out to be the same as it was that last time we made the measurement. And if we refuse to make those sorts of assumptions, science becomes basically useless, because we can no longer put confidence in any conclusions. The point of science is to make useful predictions, but they are predictions about a universe that is different than it was at any time when previous experiments were made.

The second problem I have is that Piggy actually goes further than this: he accepts the abstraction of a fair coin, from which the conclusion that any possible combination is equally likely necessarily follows, and then goes on to suggest that the messiness of the world will make the coin not fair (not in so many words, but that's what his argument amounts to) but doesn't realise that he has just changed the scenario by doing so.

Either we can discuss fair coins (in which case what colour underwear Tom Cruise is wearing today doesn't affect the results of our coin tosses), or we can't. But it's silly to talk about fair coins and then suggest that there are outside forces that affect their results - if those outside forces exist the coin isn't fair.

 

[69dodge]

The Diaconis machine remembers 100%.

I don't think that's right. The machine doesn't remember the results of previous flips and change future flips based on them. It has no mechanism by which to do that. Flips are independent. It's just that the machine can be set up so that, on each flip, the probability of getting heads is 100%.

 

[Myriad]

...a computerized switch that excludes runs of, say, over 25, but randomizes the results otherwise, and nobody in our world will be able to detect that it's not truly random.

Here's one way a fair random binary bit generator (equivalent to a fair coin flipper) that was rigged not to permit any runs longer than 25 might be detected, in the real world.

You own a chain of 10 casinos. Each casino has 500 one-dollar slot machines in it of a certain type, each of which gets 2000 plays per day. That type of machine pays (among the rest of its payout schedule) a jackpot of 5 million dollars, with the odds of winning the jackpot on a one-dollar bet set at 1 in 67.109 million.

The odds of generating 26 1's in a row (i.e. all "heads") from a fair random binary bit generator are 1 in 67.109 million, so the Gaming Control Board okays a machine design based on using one of those as a randomizer and scoring a jackpot win whenever 26 1's come out. They do not know that the particular circuit you use in the machines has been rigged to prevent any runs of more than 25 1's. After all, it's impossible (or so you think) to tell the difference.

And yet, after only two weeks, when no jackpot has been won despite 140 million plays, the authorities start to get suspicious. After four more weeks, they launch a full investigation. Shortly thereafter, you go to jail, unless you've already fled the country with the money.

Respectfully,
Myriad

 

[Roboramma]

True, but it doesn't stop it from being indistinguishable from randomness from the perspective of the people using it.

Set up a Diaconis device with a computerized switch that excludes runs of, say, over 25, but randomizes the results otherwise, and nobody in our world will be able to detect that it's not truly random.

Sure, but you seem to be suggesting that the we should assume the existence of such a switch when there is no known mechanism that could cause it and no evidence that it exists.

 

[MetalPig]

It was whether or not you'd ever actually encounter a run of 100 heads or tails in a fair coin-flipping system, or a human one, on earth.

Unlikely. Only about 1 in 2^100 runs will show 100 heads, so divide the number of runs you 'encounter' by that number and you get an idea of the likelihood that you encounter a run of 100 heads.

Now perform 100 fair flips and note the sequence. That sequence had the exact same likelihood of appearing as 100 heads. Yet, it happened, so it can't be impossible.

 

[This is The End]

It was whether or not you'd ever actually encounter a run of 100 heads or tails in a fair coin-flipping system, or a human one, on earth.

I'm not understanding why you keep bringing up whether or not the "coin-flipping system" is "fair".

As Sol pointed out many posts ago, even if it was weighted 90% tails to 10% heads, a run of 100 heads would still be entirely possible.

 

[Cuddles]

How on God's green earth should I know?

Here's the important point. You made a claim - that a run of 100 heads is not possible. You have no evidence to support that claim, since the only evidence that you haven't seen one also supports the null hypothesis. You also have now made it clear that you have no theory to suggest how it could possibly be the case. That's pretty much a textbook definition of blind faith.

Edit:

I'm not understanding why you keep bringing up whether or not the "coin-flipping system" is "fair".

As Sol pointed out many posts ago, even if it was weighted 90% tails to 10% heads, a run of 100 heads would still be entirely possible.

This is the point I was making with the monkeys as well. As long as there is a finite chance for any key to be pressed each time, you are guaranteed to eventually get the works of Shakespeare. It's exactly the same situation. As long as the scenario isn't artificially constrained, such as the biased generator above preventing runs of more than 25, changing the weightings only changes the exact probability, not the qualitative result.

 

[Piggy]

It was whether or not you'd ever actually encounter a run of 100 heads or tails in a fair coin-flipping system, or a human one, on earth.

It was? Because that's not what you said, and it's not what everyone here is responding to.

Well, the OP isn't mine, btw. And there's more than one train of conversation going on, as usual.

Originally, I was talking about whether you'd ever get a series of 100 heads or tails by flipping a coin (with your hand) here on Earth -- even assuming that the task of flipping might have to be handed on from person to person.

Then I got into a conversation with Ivor about the possibility of designing a fair coin-tossing system (which a human may or may not be) that could be fair and limit streaks.

And by that time there were other posters discussing other things.

Anyway, by now I've had to turn tail on the "can't get to 100" idea. That didn't pan out too well.

But there's still no way to know whether human coin-flipping actually is fair or actually does allow non-bounded runs. And I'm certain that it's possible to create a system which is indistinguishable by humans from a random system, but which excludes streaks beyond a finite boundary.

 

[Piggy]

Ah, you're right, I never meant that it was possible to throw 100 heads in a row on earth, I always thought you were talking about doing it on Mars.

On earth (where physics and probability may work differently from the rest of the universe..?), maybe it's not possible.

Huh??

Are you going to argue that coin-flipping on Earth and on Mars must be identical physical systems?

 

[Piggy]

So, for instance, in the case of coins, as sol pointed out there are no fair coins, but we can figure out the probabilities of coming up heads vs. tails. We can then deduce (from the fact that neither is impossible and that subsequent flips are in no way influenced by past flips) that all combinations are possible.

You're talking about a human brain operating a human hand.

You have no grounds for stating that a given flip is uninfluenced by past flips.

 

[AdMan]

Are you going to argue that coin-flipping on Earth and on Mars must be identical physical systems?

Of course not. The point is that the same probability and the same laws of physics apply on Mars as on Earth.

You can get 100 heads in a row on Mars, and you can on Earth as well.

 

[Roboramma]

But there's still no way to know whether human coin-flipping actually is fair or actually does allow non-bounded runs.

Actually, there is:

So, for instance, in the case of coins, as sol pointed out there are no fair coins, but we can figure out the probabilities of coming up heads vs. tails. We can then deduce (from the fact that neither is impossible and that subsequent flips are in no way influenced by past flips) that all combinations are possible.

And I'm certain that it's possible to create a system which is indistinguishable by humans from a random system, but which excludes streaks beyond a finite boundary.

Sure, but we have no more reason to believe that human coin flippers are such a system than that the earth will suddenly pause in it's orbit tomorrow. You can invest in nails are rope if you like, but I'm taking my chances.

 

[ponderingturtle]

It's also entirely possible to bowl a 300 game, though very much less likely than any other bowling score.

Not even 576.279?

 

[Piggy]

Piggy's viewpoint here seems to me to be increadibly unscientific, from two perspectives.

The first, and most important, is the view that we can't know anything if we haven't done that specific experiment. It comes down to something like this: we've measured the speed of light to come out to approximately 3x10⁸ m/s. There are some valid questions about whether or not that value has changed with time or is different in different parts of the universe. But Piggy's view is like asserting that we don't know that speed of light is on sunny wednesday afternoons when the temperature is exactly 10.005^oC and the finance minister of Kenya has just given a live speech for French television, because we haven't done that experiment.

My understanding is that if you're dealing with the results space of a random system, it's literally impossible to know what it will be until the calculations are actually performed.

The speed of light in a vacuum isn't comparable, because it is a constant (as far as we know).

On the other hand, very different sorts of real-world values, such as the price of oil, do indeed depend on weather, politics, and media.

So if we're dealing with a brain controlling a hand, what sort of system are we looking at, precisely? What will its results space look like when it comes to coin-tossing? Is there anything in that system that will limit streaks, such as unconscious sabotage, for example? Is it truly random, or is there actually a very few number of states that don't vary perfectly randomly?

I don't believe answers to those questions are yet available.

When asked how those things could possibly affect the speed of light he'll reply that he doesn't know, but you can't possibly know either.

I'd never suggest that for the speed of light in a vacuum, but for a brain and a hand, you bet.

Now, that may be true in a way, but I'm confident that if we do measure it in those circumstances it will come out to be the same as it was that last time we made the measurement.

What measurement? You've never made any measurements of people flipping coins that would allow us to draw conclusions about whether it actually does run through all possible combinations or not. Neither has anyone else.

And if we refuse to make those sorts of assumptions, science becomes basically useless, because we can no longer put confidence in any conclusions. The point of science is to make useful predictions, but they are predictions about a universe that is different than it was at any time when previous experiments were made.

No, it's actually good science not to overgeneralize or overstate.

Look at the decelerating universe or the ever-expanding black hole.

We don't know enough about people flipping coins to say if it's true that all mathematically describable combinations will actually be demonstrated, given enough time.

Why is that so difficult to accept?

The second problem I have is that Piggy actually goes further than this: he accepts the abstraction of a fair coin, from which the conclusion that any possible combination is equally likely necessarily follows, and then goes on to suggest that the messiness of the world will make the coin not fair (not in so many words, but that's what his argument amounts to) but doesn't realise that he has just changed the scenario by doing so.

Either we can discuss fair coins (in which case what colour underwear Tom Cruise is wearing today doesn't affect the results of our coin tosses), or we can't. But it's silly to talk about fair coins and then suggest that there are outside forces that affect their results - if those outside forces exist the coin isn't fair.

Actually, this was the point I concede to Ivor. You can't have a fair coin that limits streaks. The two are incompatible by definition.

But you can certainly have a coin that is "locally fair" in that its behavior is literally indistinguishable from the behavior of a fair coin by the people using it, even though it limits streaks.

 

[Piggy]

I don't think that's right. The machine doesn't remember the results of previous flips and change future flips based on them. It has no mechanism by which to do that. Flips are independent. It's just that the machine can be set up so that, on each flip, the probability of getting heads is 100%.

The machine has a perfect memory, because its construction gives it one. Feed coins into it in the same configuration -- heads or tails up -- as long as you like, you'll see how well the Diaconis machine remembers.

 

[Piggy]

Here's one way a fair random binary bit generator (equivalent to a fair coin flipper) that was rigged not to permit any runs longer than 25 might be detected, in the real world.

You own a chain of 10 casinos. Each casino has 500 one-dollar slot machines in it of a certain type, each of which gets 2000 plays per day. That type of machine pays (among the rest of its payout schedule) a jackpot of 5 million dollars, with the odds of winning the jackpot on a one-dollar bet set at 1 in 67.109 million.

The odds of generating 26 1's in a row (i.e. all "heads") from a fair random binary bit generator are 1 in 67.109 million, so the Gaming Control Board okays a machine design based on using one of those as a randomizer and scoring a jackpot win whenever 26 1's come out. They do not know that the particular circuit you use in the machines has been rigged to prevent any runs of more than 25 1's. After all, it's impossible (or so you think) to tell the difference.

And yet, after only two weeks, when no jackpot has been won despite 140 million plays, the authorities start to get suspicious. After four more weeks, they launch a full investigation. Shortly thereafter, you go to jail, unless you've already fled the country with the money.

Respectfully,
Myriad

Oh, no doubt. Which means that the machine was badly rigged.

But that doesn't change the fact that no human being is going to get suspicious in any real-world coin-flipping situation, when 25 consecutive heads or tails fails to come up.

 

[ponderingturtle]

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.

My position is that it is imposible to deal out a randomized deck of cards because 1 chance in 8.06581751709439E+67. Clearly impossible.