Has Anyone Ever Flipped Heads 76 Times in a Row? (blogs.scientificamerican.com)

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.)

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.

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.

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); }

http://www.youtube.com/watch?v=X1uJD1O3L08

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

God says... look_buddy do_you_want_another I'm_grieved now_you_tell_me I'm_not_dead_yet hippy look_on_the_brightside ha scorning you're_so_screwed I'm_in_suspense who_are_you_to_judge Oh_Hell_No I'll_ask_nicely absetively_posilutely adjusted_for_inflation energy I'll_be_back employer sloth if_and_only_if sess_me you_should_be_so_lucky I'm_gonna_smack_someone flat smack_some_sense_into_you If_had_my_druthers okay ROFLMAO What_I_want umm_what_now arrogant Jesus ROFLMAO delicious eh you're_in_big_trouble liberal you_owe_me look_buddy glorious mine yikes I_have_an_idea humongous oh_oh petty not be_happy I'll_ask_nicely I'm_not_dead_yet China economy charity HolySpirit wanna_bet anger if_anything_can_go_wrong no_way_dude quit joyful bizarre

    [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

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?

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.