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Has Anyone Ever Flipped Heads 76 Times in a Row?
- onion2k 13y agoI 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.)
- bdfh42 13y agoPossible confusion here. Given that there are a large number (possibly very large) of possible permutations that might be observed from a session of coin spinning it is not to hard to imagine that one might indeed be observed. The odds on a given permutation arising are very low.
- sp332 13y agoExactly, it's the odds of a given permutation coming up. Obviously the sum of the odds of all possible outcomes = 1. But each probability is extremely small. Edit to address the confusion directly: There's no extra reason to think it wasn't heads all the way, since it's exactly the same probability as any other sequence of 76. And at the same time, we can be pretty sure that no one has flipped most of the possible sequences! There are just so many, it would take forever to explore them all.
- hdctambien 13y ago"You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!" - Richard P. Feynman Six Easy Pieces: Essentials of Physics By Its Most Brilliant Teacher
- fexl 13y agoWhy the downvotes on onion's comment? I don't see anything factually incorrect about it.
- sp332 13y agoThe 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 13y agoRight, 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 13y ago"a million-to-one chance succeeds nine times out of ten" - Terry Pratchett
- cma 13y agoThe fact that if you don't chose what you are looking for, any sequence you come up with is rare, isn't news. Since they specified a sequence, all heads, you can say it has probably never happened, even while acknowledging that a minute fraction of the various possible (but individually just as rare) sequences have happened.
- benched 13y agoNo, the sense of the comment is completely wrong-headed with respect to probability. The probability that a sequence occurred is 1. The probability that the 10-10-10.... sequence mentioned has occurred is indeed as close to zero as the 76 heads.
- mistercow 13y agoThe factually incorrect part is the hidden premise that "convinced that X has never happened" is equivalent to "assigns P(x) = 0". In fact, it is equivalent to "assigns P(x) = epsilon", where the number of possible sequences is several orders of magnitude greater than 1/epsilon. It basically comes down to saying something like this: 1. 1/x ≈ 0 for very large x 2. x0 = 0 for all x 3. So x1/x ≈ 0 for very large x 4. But x/x = 1 Therefore 1 ≈ 0 This reasoning is correct, but the error tucked away in that last "≈" is exactly 1.
- tel 13y agoWhile most of the logic here is sound, I really disagree with the wording of the sentence So the author would, presumably, on balance of probability, be convinced that no combination of any 76 coin tosses has ever come up. It does not follow at all. The statement that "Sequence X_i has never been tossed" is independently probable for any long sequence X_i. The author is only making a single statement, and while it's true she has no particular reason to focus on the particular sequence of constant heads her statement is completely logical and very far from being refuted by observing any particular sequence of 76 coin flips unless it just so happens to be 76 heads. The illogical point only arises if we try to take many of these independent statements all at once. If we take some significant chunk of sequences and state they've each all together never been seen before then we eventually must stop feeling that statement is probable. One way to clarify the whole thing is to assign a bet to any given probabilistic statement. The author bets $10k that nobody has ever seen 76 heads. I can bet $10k that nobody has ever seen 76 tails. In each case our expected value on these bets is identical. Someone else could bet 10c on each possible permutation and be guaranteed to win, but obviously forced to distribute his bet. It's not at all illogical for me to feel very confident that your coin flipping sequence wasn't all tails. It's highly illogical for me to believe your coin sequence wasn't in the set "all possible coin flipping sequences of length 76".
- wisty 13y ago> 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. How much would you like to bet that this hasn't happened either?
- Jare 13y agoHow do you propose to find out?
- bhousel 13y agoLook at it another way: If you flip a coin 76 times, you generate a permutation, but 2^76 is such a large number that your permutation is likely unique. You can take any 76-coin sequence and say that it's mathematically likely that nobody in history has ever flipped it. Cards work similarly. Every properly shuffled deck of cards is likely a unique permutation that has never before been seen across the entire history of people shuffling cards.
- mistercow 13y agoRegarding cards, I've often wondered, if you factor in the birthday paradox, whether it is likely that any shuffled deck of cards has come out the same as a previous shuffled deck. I have not wondered hard enough about this to actually do the math, however.
- wisty 13y agoIt's still quite unlikely. You could look at the reasoning behind ZFS and git using SHA-256 hashes to de-dupe data. With 256 bits in the sample space, you it takes an unimaginable amount of effort to find any collisions (unless the hash has a weakness).
- izzydata 13y agoBut what about 76 different people all over the world flipping coins at about the same time all getting heads? Pretty much the same right?
- netrus 13y agoBut be careful - as we are talking here that the 10H - 10T - 10H ... sequence is equally unlikely. The likelihood that exactly 38 get head and 38 get tail is pretty significant ;)
- pessimizer 13y ago>So the author would, presumably, on balance of probability, be convinced that no combination of any 76 coin tosses has ever come up. Only if you presume that the author would make an error in basic reasoning for you to point out. Being convinced that it's highly unlikely that any particular combination of heads and tails 76 bits long has ever occurred with a fair coin != being convinced that no one has ever flipped a coin 76 times in a row. I am absolutely sure that if you asked the author "Do you ever think that somebody has had a run of coin flipping that consisted of, in this order, "10 heads, 10 tails, 10 heads, 10 tails, 10 heads, 10 tails, 10 heads, and 6 tails," you would have gotten exactly the same answer. Do you think that your described run is more likely to have occurred because it looks more representative? Or that since people have flipped coins more than 76 times in a row and had some result that all particular results can't still be improbable to have ever occurred or ever to occur? I don't understand your objection if it's anything other than post hoc reasoning (a particular arrangement happened, therefore its likelihood to occur must have been significant.)
- keithpeter 13y ago"So the author would, presumably, on balance of probability, be convinced that no combination of any 76 coin tosses has ever come up." Nope, the author would be convinced that any specified configuration of 76 tosses named in advance would not come up when you spun/tossed your coin 76 times. Any good?
- crystaln 13y agoAnd yet it's all correct. One can be convinced beyond any reasonable doubt that any given sequence has not been flipped, yet know that there is an infinitesimal chance of being wrong. We rely on this all the time in computer science. What are the chances of guessing the private key of a bitcoin address? Is it possible? Not really, but yes it's technically possible.
- gmuslera 13y agohttps://en.wikipedia.org/wiki/Gambler%27s_fallacy#Monte_Carlo_Casino https://en.wikipedia.org/wiki/Gambler%27s_fallacy#Monte_Carl... 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.
- jib 13y agoFat Tony probably did. http://en.wikipedia.org/wiki/Ludic_fallacy http://en.wikipedia.org/wiki/Ludic_fallacy
- Mc_Big_G 13y agoHeh, 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 13y agoI'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 13y agoYou 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.
- ulisesrmzroche 13y agoI was just about to come in and say that. I just flipped it 100 times heads for fun. I used to do more when I was a kid. I've been killin time with this trick since elementary when someone taught it to me, can't remember who.
- timdiggerm 13y agoOf course, it only happens in the play because they're already dead.
- kens 13y agoThe 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 13y agoI agree with you unless we count 76 heads occurring anywhere within 500 flips, not all contiguously.
- ronaldx 13y agoI 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 13y agoIt'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 13y agoVery 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 13y agoRe-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 13y agoGreat reply, thanks, that makes a lot of sense. Very impressive work too on the book.
- rikkus 13y agoEasy 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 13y agoNote to self: Jokes and/or code not welcome on HN.
- Spooky23 13y agoIt's highly unlikely, but unlikely things happen. There exists people who have won the lottery and have been struck by lightning.
- pessimizer 13y ago>There exists people who have won the lottery and have been struck by lightning. Neither of those things are unlikely. People probably also exist who accidentally shot themselves while cleaning a gun on April 22, 1981, or who slipped in the shower and died within an hour of telling someone "I could slip in the shower and die."
- benched 13y agoBut 'unlikely' is qualitative and not quantitative. As shown in the article, you can measure how unlikely an occurrence is with a number.
- Spooky23 13y agoSo 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.
- izzydata 13y agoI 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.
- dazonic 13y agoThe 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 13y agoIt took him 9 hours: http://www.youtube.com/watch?&v=p8A-peQi220#t=407 http://www.youtube.com/watch?&v=p8A-peQi220#t=407
- simonsarris 13y agoIt'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
- fphilipe 13y agoTry this in Julia for some extra speed: best = 0 i = 0 while true i += 1 count = 0 face = 1 while face == 1 face = rand(0:1) count += face end if count > best best = count println("new record: $best in iteration $i") end end
- deletes 13y agoI wrote a short c program and ran it on 4 cores. Current best result is 36.
- TempleOSV2 13y agoMiracles are common. 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
- madaxe_again 13y agoNo, 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.
- Aaronneyer 13y agoFlipping 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"
- samatman 13y agoI'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?
- bladedtoys 13y agoIt 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.