
Has Anyone Ever Flipped Heads 76 Times in a Row? - tokenadult
http://blogs.scientificamerican.com/roots-of-unity/2014/01/27/rosencrantz-and-guildenstern-flip-coins/
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onion2k
_I am convinced that no one in the world has ever flipped heads 76 or 90 times
in a row on a fair coin_

Let's assume instead that it's 10 heads, 10 tails, 10 heads, 10 tails, 10
heads, 10 tails, 10 heads, and 6 tails. The probability of that coming up is
_exactly the same as 76 heads_.

Now, what at the chances of _any given permutation_ coming up? Still the same
as 76 heads.

So the author would, presumably, on balance of probability, be convinced that
no combination of any 76 coin tosses has ever come up. If 76 heads is unlikely
then any other permutation is equally unlikely. As someone who has flipped a
coin more than 76 times I can say for certain is wrong. At least 1 permutation
has definitely happened.

It is entirely illogical to be convinced that it wasn't heads all the way.

(But, for the record, it wasn't.)

~~~
fexl
Why the downvotes on onion's comment? I don't see anything factually incorrect
about it.

~~~
sp332
The odds are 1.3×10^-23 times the number of times anyone has attempted it, so
there's no reason to believe that it has ever happened.

~~~
maxerickson
Right, if you enumerate a million possible combinations the answer is still
that it is unlikely that any of them have ever come up.

If you enumerate all the possible combinations then of course one of them has
come up.

~~~
thisone
"a million-to-one chance succeeds nine times out of ten" \- Terry Pratchett

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simonsarris
It's much too fun not to try it ourselves:
[http://jsfiddle.net/simonsarris/as2Zu/](http://jsfiddle.net/simonsarris/as2Zu/)

So far I've "only" gotten 16 heads in a row after a few thousand flips

~~~
deletes
I wrote a short c program and ran it on 4 cores. Current best result is 36.

~~~
azth
pthreads?

~~~
deletes
threads.h, a C11 feature, almost no compilers support it unfortunately.

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Mc_Big_G
Heh, I was just playing with a quarter the other day and, with some practice,
I was able to learn how to get the rotation and timing right so it was heads
nearly every time. With practice, I'm sure someone could purposely get heads
76+ times in a row, but I imagine that wasn't the point of the article since I
only skimmed it.

~~~
sejje
I've heard the traditional (older style) American quarter is slightly biased
to tails, as the head makes the coin's weight distribution slightly lopsided.

~~~
arjie
You may find the following interesting:
[http://www.stat.berkeley.edu/~nolan/Papers/dice.pdf](http://www.stat.berkeley.edu/~nolan/Papers/dice.pdf)
They claim that a biased coin is impossible via weight distribution.

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gmuslera
[https://en.wikipedia.org/wiki/Gambler%27s_fallacy#Monte_Carl...](https://en.wikipedia.org/wiki/Gambler%27s_fallacy#Monte_Carlo_Casino)

But was only 26 times in a row, and wasn't coins. Still, is not impossible,
the rest of the article matters. And that it comes from literature remembers
me of the case of Teela Brown, author's hand are the ultimate superpower.

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Aaronneyer
Flipping 76 in a row is extremely improbable in the physical world, but
fortunately we have computers (Where it's still quite improbable).

    
    
        [10] pry(main)> choices, tries, current, current_max = [:heads, :tails], 0, 0, 0
        [10] pry(main)> loop do
        [10] pry(main)*   tries += 1
        [10] pry(main)*   flip = choices.sample
        [10] pry(main)*   if flip == :heads
        [10] pry(main)*     current += 1
        [10] pry(main)*   else
        [10] pry(main)*     current = 0
        [10] pry(main)*   end
        [10] pry(main)*   if current > current_max
        [10] pry(main)*     current_max = current
        [10] pry(main)*     puts "New max: #{current_max}, after #{tries} tries"
        [10] pry(main)*   end
        [10] pry(main)* end
    

Highest so far: "New max: 31, after 77576302 tries"

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jib
Fat Tony probably did.
[http://en.wikipedia.org/wiki/Ludic_fallacy](http://en.wikipedia.org/wiki/Ludic_fallacy)

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ronaldx
I feel like this question is quite paradoxical: the only reasonable way we
have of deciding whether a coin is fair is by flipping it repeatedly.

So has anyone ever flipped heads 76 times in a row on a fair coin? No. Because
we would judge that coin to be unfair.

In reality, an individual's the flipping method is likely to be more
deterministic than random and show bias - it's not the coin that is fair or
not, but the method of flipping it.

~~~
aristus
It's quite simple to implement a fair coin from a coin of unknown fairness. So
simple, I put it in a children's book.

[http://carlos.bueno.org/2011/10/fair-
coin.html](http://carlos.bueno.org/2011/10/fair-coin.html)

~~~
martijn_himself
Very nicely presented. How would you define 'simple'? While I can see the
heuristic process is simple (i.e. flip twice and choose the first result in
case of HT or TH) to follow, and you could arrive at the conclusion that this
gets rid of bias through experiment, I don't find this intuitively simple at
all.

EDIT: I've also noticed that if I choose 'Suppose Heads comes up 50% of the
time.' it says 'You'll need an average of 3.00 flips to get a fair coin.' If
heads comes up 50% of the time then I have a fair coin, so shouldn't that be
1.00 flip?

~~~
aristus
Re-deriving from scratch it is hard. No question about that. Magnetism doesn't
make a ton of sense either, but it's simple to demonstrate. Intuitive and
simple are not always the same thing.

If your coin happens to be absolutely fair, it will require on average 3 flips
to generate a fair flip via this method. The point is you don't _know_ a
priori whether a given coin is fair.

~~~
martijn_himself
Great reply, thanks, that makes a lot of sense. Very impressive work too on
the book.

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izzydata
I rolled snake eyes in a game of Risk 6 times in a row and I lost because of
it. That is about the extent of ridiculous luck I've run into.

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samatman
I've used this as an analogy (albeit a poor and leaky one) to explain the
difference between Bayesian and frequentist thinking.

A Bayesian who sees 76 heads in a row adjusted her priors early on and stopped
being surprised after awhile. 76 heads and a tail? That would be weird. 76
heads strongly suggests you were wrong about there being a tail side to that
coin.

The frequentist concludes that she's dealing with something anomalous: the
distribution is all off. The difference is in _how_ this is built into the
math: frequentist statistics can reveal, say, the difference between flip 4
being tails (and all the others heads) and flip 72 being tails (with all the
others heads), whereas in Bayesian terms it just 'falls out' of the math.

So here's a fun one. Given the 10h-10t-10h-10t-10h-10t-10h-6t: which model
does the best job of predicting (correctly imho) that we're more likely to see
four more tails than anything else?

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dazonic
The article quotes 500 flips to get 9 in a row. I'm not sure how many flips
this took but Derren Brown gets 10 in a row. Notable camera cut after the
intro but the 10 heads seems genuine.

[http://www.youtube.com/watch?v=X1uJD1O3L08](http://www.youtube.com/watch?v=X1uJD1O3L08)

~~~
sxp
It took him 9 hours:
[http://www.youtube.com/watch?&v=p8A-peQi220#t=407](http://www.youtube.com/watch?&v=p8A-peQi220#t=407)

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kens
The article says its a thousand times more likely to get a string of 76 heads
somewhere in 500 flips than the last 76 flips. This doesn't make sense to me -
seems like the odds improvement must be less than 500-76, not 1000. Is the
math wrong? (I'm on my phone so I can't check.)

~~~
tel
I agree with you unless we count 76 heads occurring anywhere within 500 flips,
not all contiguously.

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bladedtoys
It also raises a funny epistemic question: the likelihood of error in
observation or recording is higher than the likely outcome.

So the question probably ought to be "what are the odds of 76 heads and it
being detected correctly + the odds of not getting 76 heads but believing you
did". In the real world, the last part would obviously dominate and so we are
more likely to see false positives than real results.

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madaxe_again
No, but I have been stood at a roulette table with a friend who called and won
red/black 21 times in a row. He was unamused when I pointed out that had he
bet his entire stack every time, rather than the same £10 bet, he'd have
walked away having won ~£20M, rather than £210! He lost on the 22nd bet and
walked away.

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rikkus
Easy if you have a loaded coin.

enum Side { Heads, Tails }

void Main() { Func<Side> generator = () => { return Side.Heads; };

int heads = 0;

while (heads < 76) { if (generator() == Side.Heads) ++heads; else heads = 0; }

Console.WriteLine("Got {0} heads in row.", heads); }

~~~
rikkus
Note to self: Jokes and/or code not welcome on HN.

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Spooky23
It's highly unlikely, but unlikely things happen. There exists people who have
won the lottery and have been struck by lightning.

~~~
benched
But 'unlikely' is qualitative and not quantitative. As shown in the article,
you can measure how unlikely an occurrence is with a number.

~~~
Spooky23
So is the question at hand. "Has Anyone Ever Flipped Heads 76 Times in a Row?"

There's no quantitative way to assert whether or not someone at some point in
human history flipped a coin that landed heads 76 times in a row.

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timdiggerm
Of course, it only happens in the play because they're already dead.

