Impossible coin sequences?

[JJM 777]

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, ....

 

[GlennB]

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

 

[Alan]

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.

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.

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.

 

[Alan]

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.

 

[Furcifer]

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.

 

[This is The End]

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.

 

[ceptimus]

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

 

[Alan]

Does anybody who is saying it is unlikely think that they are arguing against me?

 

[bokonon]

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...

 

[CynicalSkeptic]

I prefer to start with 2^100 coins, flip them all then see aside all the tails.

Repeat with the remaining coins 99 times.

 

[Alan]

I am now volunteering to conduct that experiment. I just need people to donate the coins.

 

[ceptimus]

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!

 

[alex04]

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]

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..

 

[GlennB]

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.

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.

 

[alex04]

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.

 

[Alan]

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:

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.

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.

 

[GlennB]

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.

 

[Alan]

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.

 

[TubbaBlubba]

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.