[HN Gopher] Fair coins tend to land on the side they started (2023)
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       Fair coins tend to land on the side they started (2023)
        
       Author : seanhunter
       Score  : 388 points
       Date   : 2024-11-19 09:03 UTC (1 days ago)
        
 (HTM) web link (www.researchgate.net)
 (TXT) w3m dump (www.researchgate.net)
        
       | seanhunter wrote:
       | There's a nice presentation of the paper here
       | https://www.youtube.com/watch?v=-QjgvbvFoQA
       | 
       | In essence the effect comes from "precession" - the tendency of
       | the flip to not be purely vertical but to have some
       | wobble/angular momentum which causes it to flip in such a way as
       | to spend longer on one side than the other. Depending on the
       | technique this will have a greater or lesser effect on the
       | fairness of the coin toss, ranging from about p_same = 0.508 for
       | the best technique to one person in the study actually exhibiting
       | 0.6 over a large sample which is staggeringly unlikely if the
       | toss was purely fair. In the extreme, it shows in the video a
       | magician doing a trick toss using precession that looks as if
       | it's flipping but does not in fact change sides at all, purely
       | rotating in the plane of the coin and wobbling a bit.
       | 
       | The video is quite a nice one for setting out how hypothesis
       | testing works.
        
         | yread wrote:
         | link to the "wobble flip" trick
         | https://youtu.be/-QjgvbvFoQA?t=325
        
           | pinko wrote:
           | I think you accidentally linked to the same video as the
           | parent comment...
           | 
           | I bet this is the video you mean?
           | https://www.youtube.com/watch?v=A-L7KOjyDrE
        
             | swores wrote:
             | They linked to the same video, but to a specific timestamp
             | within it - by adding ' _?t=325_ ' to the URL, which tells
             | Youtube to play the video from 5m25s rather than from the
             | beginning.
        
         | Vecr wrote:
         | Ah man, please use Bayesian statistics there... Well, the
         | presenter says he doesn't know much about statistics.
        
           | drcwpl wrote:
           | This can be really relevant in various fields, statistics,
           | gambling, and decision-making. I like the fact that they
           | imply the importance of considering potential biases in
           | seemingly random events.
        
           | seanhunter wrote:
           | The paper does use Bayesian statistics. Presenter is a pure
           | maths PhD.
        
             | Vecr wrote:
             | I don't think I was clear, but I was only talking about the
             | presenter's attempted explanation of the statistics of this
             | problem.
        
       | ComplexSystems wrote:
       | I am curious how this changes if we condition on it flipping in
       | the air at least once. Can we think of this result as a mixture
       | distribution of a fair 50/50 chance of it flips at least once,
       | and a delta function that is 100% at the side it started on, if
       | not flipped at all?
        
         | vikingerik wrote:
         | Seems likely it would change. Here's another way to think about
         | it:
         | 
         | 0 rotations is more likely than 1 rotation, since there is a
         | wider range of rotation speeds that lead to exactly 0 rotations
         | than to exactly 1. Similarly, 2 flips is more likely than 3, 4
         | is more than 5, and so on. So you're always biased towards an
         | even number of flips and the starting side.
         | 
         | Take out the 0 case by your conditional, and you're left with 1
         | > 2, 3 > 4, 5 > 6, and so on, now biased towards an odd number
         | and the non-starting side.
        
         | joshuamorton wrote:
         | The paper requires that the coins flipped at least once to be
         | counted.
        
       | swayvil wrote:
       | This is clearly the law of _conservation of reality_ at work.
       | 
       | Likewise, when you hear a word for the first time suddenly you
       | hear it five times in a row. Or if you see somebody once you
       | suddenly start running into them all over the place.
       | 
       | It's because it's cheaper to repeat past realities than to create
       | new ones.
        
         | Vecr wrote:
         | I don't think that's true, isn't this tested in a way to
         | obviate that psychological effect? I've done coin-flipping in
         | computer simulations and that doesn't happen. (And yes it was a
         | bit more realistic vs a single element, multiple linked
         | elements flip more realistically. No air resistance simulation
         | though.)
        
           | swayvil wrote:
           | Oh sure, let's doubt the evidence of our senses in favor of
           | convention. That's good science.
        
             | Vecr wrote:
             | How good are you at Bayesian statistics,
             | conditionalization, and understanding various biases? The
             | simulation here should be good (it's better than mine).
        
               | swayvil wrote:
               | Next you'll cite Bible verse.
        
               | Vecr wrote:
               | I don't think Bible verses are related.
               | 
               | There are multiple ways to ground Bayesian statistics
               | without resorting to grounding in coin flips. The
               | simplest one isn't that robust, there's a mathematical
               | one but it's abstract and uses calculus, there's a
               | quantum one but I'm not even going there, and there's a
               | highly robust one that's too complex for me to
               | understand.
        
               | pugets wrote:
               | "We toss the coin, but it is the Lord who controls its
               | decision." - Proverbs 16:33 (TLB)
        
               | chrismorgan wrote:
               | The very verse I was about to post! (Though I was going
               | to quote it as more customarily and literally translated,
               | "The lot is cast into the lap, but its every decision is
               | from the LORD.")
               | 
               | To add interest: there are plenty of people who firmly
               | believe this, and make decisions by the drawing of lots,
               | in various possible forms. I'm one. It's taken me in
               | interesting and unexpected directions this year.
        
               | __MatrixMan__ wrote:
               | Aye, always at the ready with His noodly appendage.
        
         | grraaaaahhh wrote:
         | Or how when you look for something it always ends up in the
         | last place you look, if it weren't there would have been some
         | number of places you looked that were completely unnecessary.
        
           | brewdad wrote:
           | Personally, I like to keep looking for the thing long after
           | I've found it simply to prove the adage wrong. My keys
           | weren't in the last place I looked because I checked three
           | more places after I had them in my hand.
        
             | fluoridation wrote:
             | That's a dangerous game to play. What if you find the thing
             | a second time?
        
         | findthewords wrote:
         | Does this explain the rarity of antimatter?
        
         | __MatrixMan__ wrote:
         | So if computation in the enclosing universe got more expensive,
         | they'd enable more aggressive optimizations, and we'd see the
         | effect get stronger?
        
           | Vecr wrote:
           | I don't think this is a real, non-psychological effect in
           | general. For this coin flipping of this very particular
           | method, yes the physics simulations look right, but in
           | general it's not something I think exists, or would even
           | reduce the compute needed for the universe.
        
       | archermarks wrote:
       | Winner of the 2024 Ig Nobel prize in probability [1]. A nice read
       | as well!
       | 
       | [1] https://improbable.com/ig/winners/#ig2024
        
       | fedeb95 wrote:
       | you shouldn't bet on it though
        
         | Vecr wrote:
         | Probably not. A reasonable Kelly calculation would make the
         | attempt negative utility. Too much overhead. Also, depending on
         | who's betting against who, deviating from the very particular
         | protocol in the study would be highly incentivized.
        
       | outsidein wrote:
       | Flip it twice. Once to determine which side is up at second
       | throw. Reverse to counter bias at start of second throw. Then
       | flip again for final result.
        
         | two_handfuls wrote:
         | That only works for a fixed bias, it's gameable if the person
         | tossing the coin controls the bias.
        
           | outsidein wrote:
           | That is outside the preconditions of the paper: ,,if the
           | person tossing the coin controls the bias"
        
             | two_handfuls wrote:
             | Let me explain.
             | 
             | You said:
             | 
             | > Flip it twice. Once to determine which side is up at
             | second throw. Reverse to counter bias at start of second
             | throw. Then flip again for final result.
             | 
             | Suppose I'm throwing the coin using your technique and I
             | want to favor heads.
             | 
             | I hold tails up for the first throw, making tails more
             | likely.
             | 
             | Then as per your rule, I put heads up for the second throw.
             | Now, heads is more likely.
             | 
             | Choose the opposite starting face to make tails more
             | likely. So, your technique does no prevent the coin tosser
             | from being able to favor their desired outcome.
        
               | outsidein wrote:
               | The paper is discussion regular people (not malicious
               | people) tossing a coin, and under this precondition and
               | assuming a fair (unbiased) coin.
               | 
               | It is not about intentional favoring on result.
        
         | Aloisius wrote:
         | This won't fix the bias. It would be biased towards the obverse
         | of the starting side up of the first flip.
        
       | thih9 wrote:
       | This paper is also this year's Ig Nobel Prize winner:
       | 
       | > Probability: A team of 50 researchers, for performing 350,757
       | experiments to show that when a coin is flipped, it is slightly
       | more likely to land on the same side as it started.
       | 
       | source:
       | https://en.wikipedia.org/wiki/List_of_Ig_Nobel_Prize_winners...
        
         | damidekronik wrote:
         | From this year's Iq:
         | 
         | Botany: Jacob White and Felipe Yamashita, for finding that
         | certain plants imitate the leaf shape of nearby plastic plants
         | and concluding that "plant vision" is plausible.
         | 
         | This somehow doesn't fit the Iq award in my mind.
        
           | anigbrowl wrote:
           | They 'need' to fill slots not that the IN awards have become
           | an annual media event (presumably yielding some profit) so
           | they've taken to mocking perfectly legitimate research as
           | long as it is in some way scatalogical or counterintuitive. I
           | lost interest in the Ig Nobel prize as a result; they've gone
           | from an intermittent amusement to a celebration of ignorance.
           | 
           | Incidentally the plant mimicry thing seems to be a defense
           | against herbivorous mammals. It was previously theorized that
           | the shape information was transmitted by symbiotic bacteria;
           | the ability to imitate fake plants is a genuinely perplexing
           | result imo.
        
             | boomboomsubban wrote:
             | The Ig Nobel has always been for serious science that
             | sounds silly. Their website begins with
             | 
             | >The Ig Nobel Prizes honor achievements so surprising that
             | they make people LAUGH, then THINK. The prizes are intended
             | to celebrate the unusual, honor the imaginative -- and spur
             | people's interest in science, medicine, and technology.
             | 
             | There goal has never been to mock the award winners.
        
       | japoco wrote:
       | This is probably just because the coins aren't actually fair. If
       | the coin is slightly biased towards heads, the first throw is
       | more likely to heads, and so are all subsequent throws. Same for
       | tails.
        
         | Vecr wrote:
         | That's not the problem. You can test that by using a highly
         | secure random number generator, e.g. /dev/random in Linux, to
         | select the initial side. Keep track of that initial side,
         | record the side it lands on. This paper shows a same-side bias,
         | not a heads bias.
        
           | japoco wrote:
           | A same side bias is either a heads bias or a tails bias.
        
             | alt227 wrote:
             | Its not, its a bias towards which side the coin started on.
        
               | japoco wrote:
               | Which is either heads or tails.
        
               | glxxyz wrote:
               | A coin with a heads bias is more likely to land on heads
               | no matter how it's thrown.
               | 
               | A coin with a same side bias is more likely to land on
               | heads if it's thrown with heads facing up, and more
               | likely to land on tails if thrown with with tails facing
               | up.
        
               | toast0 wrote:
               | If you take a specific coin and find that when you
               | prepare it to be flipped showing heads up, that it is
               | more likely to land heads up, and that when you prepare
               | it to be flipped tails up, it is more likely to land
               | tails up, it seems confusing to call that coin 'heads or
               | tails biased'
        
             | Vecr wrote:
             | How? I described how to randomize the initial side. Boolean
             | true for heads, boolean false for tails, for example. Keep
             | pulling those from the Kernel's secure RNG.
        
         | onion2k wrote:
         | That's the opposite of what the paper says. If the coin was
         | biased you'd expect it to land on heads more often regardless
         | of what side it starts on. The coins land on the side they
         | start on more often.
        
           | japoco wrote:
           | No, first of all due to imperfections in the manufacture of
           | real coins, there are actually no fair coins. Also the bias
           | in the probability affects the first throw as well as all the
           | rest. If your dataset is composed of first throws/rest of the
           | throws, you're going to see they are correlated.
        
             | sigbottle wrote:
             | I think you're missing the fact that you don't have to
             | chain coin flips literally right after another.
             | 
             | As the other commenter said, in between coin flips, use a
             | highly secure PRNG to orient the coin randomly. This would
             | correct for your bias (if true).
        
             | zahlman wrote:
             | You're missing the point.
             | 
             | A coin that is biased towards heads is one that would more
             | often land on heads _regardless of how you hold it when you
             | start the flip_.
             | 
             | The study finding is that _every_ coin is more likely to
             | land on heads _if you start it with heads facing up_ , and
             | will _also_ be more likely to land on _tails, if_ you start
             | it that way instead. This bias, while small, is greater
             | than the typical observed bias due to imperfections in
             | manufacturing.
             | 
             | It's not about the "first throw" vs the "rest of the
             | throws". It's about _how you hold the coin_ when you go to
             | flip it. That 's what they mean by "started".
        
       | NameError wrote:
       | Easy way to get a fair result from an unfair coin toss: Flip the
       | coin twice in a row, in this case starting with the same side
       | facing up both times, so it's equally unfair for both tosses. If
       | you get heads-heads or tails-tails, discard and start over until
       | you get either heads-tails or tails-heads, which have equal
       | probabilities (so you can say something like HT = "heads" and TH
       | = "tails").
       | 
       | This works even if the coin lands heads 99% of the time, as long
       | as it's consistent (but you'll probably have to flip a bunch of
       | times in that case).
        
         | mankyd wrote:
         | Importantly - you don't have to know the odds of the coin ahead
         | of time, or which side is more likely. You only need to know
         | that it is consistent.
        
           | IncreasePosts wrote:
           | The odds are important to know because if someone gave you a
           | trick coin that always lands on heads, you will be flipping
           | coins until the end of the universe. And I'm sure you have
           | more important things to do than that.
        
             | Vecr wrote:
             | Nah, you can put in a rule to stop. It would be better to
             | know ahead of time, but you don't _need_ to.
        
             | magicalhippo wrote:
             | > you will be flipping coins until the end of the universe
             | 
             | Reminds me of one of my favorite movies, Rosencrantz &
             | Guildenstern Are Dead, which opens with just such a
             | scenario[1].
             | 
             | [1]: https://www.youtube.com/watch?v=RjOqaD5tWB0
        
         | legobmw99 wrote:
         | I've seen this attributed to John von Neumann, of all people
        
           | NameError wrote:
           | It seems like he did everything! I first heard of Von Neumann
           | in international relations & economics classes as the person
           | who established game theory, then later in CS classes as the
           | creator of mergesort, cellular automata, Von Neumann
           | architecture, etc.
        
             | vonneumannstan wrote:
             | Wait til you hear about what he did in Math and Physics...
             | 
             | Very easy to claim he was the most intelligent human to
             | ever live. Or perhaps he was never human...
             | 
             | https://en.wikipedia.org/wiki/The_Martians_(scientists)
        
               | EGreg wrote:
               | I consider LLMs to be the first successful non-von-
               | neumann architecture in many decades
        
         | ant6n wrote:
         | What if consecutive unfair coin flips are not independent?
        
           | FartyMcFarter wrote:
           | Then it's impossible to trust the coin in the general case.
           | 
           | Proof: Imagine the extreme case of the coin containing AI
           | that knows exactly how you use it and how to manipulate each
           | toss result. The coin itself can decide the outcome of your
           | procedure, so it's impossible to trust it to generate
           | randomness.
        
             | lisper wrote:
             | It's also impossible to prove that a given coin is not
             | being controlled by an AI. (Or a deity.)
        
               | FartyMcFarter wrote:
               | Yes, which is why you can only trust abstract coins that
               | exist in a formal system which assumes independent tosses
               | :)
               | 
               | If you require true randomness without any assumptions
               | this is not the universe for you.
        
               | jjk166 wrote:
               | Just perform the same coin toss in two universes.
        
         | simcop2387 wrote:
         | If anyone wants to look up why this might work, it's a
         | Whitening transform [0]. I can't find the name of the algorithm
         | itself being describe in the parent but there's more than just
         | that for accomplishing the same thing.
         | 
         | 0: https://en.wikipedia.org/wiki/Whitening_transformation
        
           | npsomaratna wrote:
           | Thank you. This was useful to learn.
        
           | aidenn0 wrote:
           | That's Von Neumann Whitening.
        
         | Aloisius wrote:
         | Each flip would need to start with the same side up though, if
         | this paper is correct.
        
       | cgag wrote:
       | I wouldn't be surprised if there is something to it, but I
       | suspected they didn't use legitimate coin flips (because it seems
       | like a large amount of people can't really flip a coin), and
       | looking at the videos confirms it, at least for the flips done by
       | Bartos:
       | 
       | https://osf.io/6a5hy/
       | 
       | They're very low RPM and very low time in the air. Nothing I
       | would accept for any decision worth flipping a coin for.
        
         | BiteCode_dev wrote:
         | That's not tossing a coin, that's barely throwing it in the
         | air.
         | 
         | To me this kills the credibility of the entire study and of the
         | authors.
         | 
         | Sure, there may be something to it, but people will have a very
         | different thing on their mind unless they check the video,
         | which I wouldn't have done without your prompting.
         | 
         | It's unlikely they don't understand how misleading it is.
         | 
         | And somehow I have the intuition a proper coin toss will not
         | exhibit the same properties.
        
           | thrw42A8N wrote:
           | Is it unlikely? If I didn't read your comment I wouldn't see
           | any problem there. I never saw anyone flipping a coin in a
           | different way. It's just not done much around me.
        
             | BiteCode_dev wrote:
             | If you claim to do a research on coin tossing, the minimum
             | is to be aware on how people toss coin.
             | 
             | The whole purpose of tossing a coin is randomness, so of
             | course you want high and fast.
             | 
             | If the result was that no matter how high and fast you
             | throw is you get this bias, it would have been interesting.
             | 
             | But now you just say "if you do things badly, things don't
             | work".
        
               | ummonk wrote:
               | No, the whole point of the paper (and the physics model
               | it is verifying) is to see what happens in normal human
               | coin tosses.
               | 
               | If you want to measure what happens specifically with
               | high and fast coin tosses, then that's an entirely
               | different study to be done.
        
               | philipov wrote:
               | I don't know what a normal human coin toss is. Does the
               | paper contain evidence/argument to justify their way of
               | flipping a coin as "normal"?
        
               | Vinnl wrote:
               | That still sound valuable if people generally tend to do
               | it badly? If only to provide an argument for doing it
               | properly.
        
           | hackernewds wrote:
           | a coin is likely to land on the same side. it was flipped
           | from if it was tossed by a machine at low RPM and height
           | consistently*
           | 
           | there's your paper
        
             | BiteCode_dev wrote:
             | I'm sure you will find similar behavior with dice if you
             | just gently let them fall from your hands instead of
             | throwing them across the table.
             | 
             | This is silly.
        
               | whythre wrote:
               | Somebody's grant money getting thrown down a hole...
        
           | nfw2 wrote:
           | I think it's still noteworthy that what many people consider
           | a "fair toss" is not in fact a fair toss. In other words it's
           | interesting from an applied psychology perspective even if
           | the physics of the phenomenon isn't particularly interesting.
        
         | TremendousJudge wrote:
         | This was my first objection as well. However, if most people
         | flip coins like that, then the measurements are valid -- the
         | conclusions are about what average people will do, not a
         | perfect mechanical coin flip. Otherwise you're falling in the
         | _no true coin flip_ fallacy.
        
           | Vecr wrote:
           | Yeah, if I'm actually forced to use a coin instead of a
           | computer system, I try to ping the thing off the ceiling and
           | at least one wall (not in that order). Hitting various other
           | things is a benefit, not a downside.
        
             | hammock wrote:
             | The guy in the grandparent YouTube video suggests shaking
             | the coin in a closed hand (or better, a box) to randomize
             | the starting side and then transferring it unseen to
             | someone else to flip it
             | 
             | Craps is also brought to mind where the dice have to bump
             | the back wall
        
               | roccomathijn wrote:
               | Let's abandon coin flipping in favour of coin shaking
               | then
        
               | dotancohen wrote:
               | It's a shake and then a flip. Put your hand on your hip
               | and bend your knees in tight.
        
             | layman51 wrote:
             | Your point about the coin hitting other things to be more
             | unpredictable reminded me of an interesting blog post[1]
             | about generating cryptographically secure random numbers.
             | The memorable part for me is the suggestion of using five
             | coins of different shapes and sizes so they get shaken a
             | consistent number of times in a large cup.
             | 
             | [1]: https://blog.sia.tech/generating-cryptographically-
             | secure-ra...
        
         | hackernewds wrote:
         | but they did?
         | 
         | here's the video
         | https://youtu.be/-QjgvbvFoQA?si=ZTT1LWWJC8T4LIQZ
        
           | strbean wrote:
           | That's the "the video", that's a video by a third party about
           | the study, and it doesn't include all footage or all
           | participants.
           | 
           | The comment you replied to links to footage of one of the
           | participants. You can see in that footage that the coin
           | hardly leaves his hand.
        
         | beefnugs wrote:
         | This makes me feel like, similar to everything else, even
         | science is actually a spectrum. Based on how much insanity to
         | put into the testing.
         | 
         | Even if the testing was as many flips as possible over years
         | and years of automated means, with a flipping machine that
         | varies flipping power and angle, and detecting sub-millimeter
         | wearing on the surface of a coin, and every single coin
         | style/size in existence, of every single wear level possible
         | from all positions and angles, through every different
         | combination of typical earth-based air percentages... What does
         | the result really mean? It doesn't actually come up with a
         | "conclusion", its just an accounting of an exact series of
         | events. You will still never use that into the future, you will
         | still describe the act as having a probability of outcome.
        
       | bgroat wrote:
       | This has been commonly known by magicians for decades. I doubt
       | that any single magician had conducted 350k flips, but I know I
       | personally did ~2,500 to test the effect when I was a kid.
       | 
       | And I'm sure if you got 30 magicians together to pool data we'd
       | have a meta-analysis of about this size but with experiments a
       | century ago
        
         | morning-coffee wrote:
         | Well, I suppose if you need fodder to fill your CV, this is one
         | way to do it.
        
           | CoastalCoder wrote:
           | Especially on LinkedIn!
           | 
           | A single person would write 17000 posts about their "amazing
           | journey" coin flip outcomes, and another 17001 "humbled by
           | success" coin flip outcomes
        
             | drcwpl wrote:
             | Exactly :-)
        
       | jgrant95 wrote:
       | anyone else thinking about Pokemon TCGP...
        
         | dev0p wrote:
         | Misty's flips are not fair, that's for sure
        
       | d--b wrote:
       | And a toast covered in jam lands 100% of the time on the jam
       | side.
        
         | Uehreka wrote:
         | And cats always land on their feet. In combination, these facts
         | can be exploited to achieve perpetual motion:
         | https://youtu.be/Z8yW5cyXXRc
        
       | helboi4 wrote:
       | I think I figured this out when I was about 6 years old. It
       | pretty much is always true.
        
       | metalman wrote:
       | statistics be dammed,I'll flip you for it.....heads I win tails
       | you loose
        
       | steeeeeve wrote:
       | I learned a trick with flipping coins from a barber at my
       | grandpas shop when I was probably 6 or 7. Since then I've always
       | been able to flip a coin and determine what the outcome is. It's
       | really just being consistent with the flip and the catch.
        
         | FartyMcFarter wrote:
         | If this is done with a quick toss and the coin is flipping
         | rapidly in the air, that's pretty impressive.
        
           | burningChrome wrote:
           | This is anecdotal evidence but Dennis Rodman (the pro
           | basketball player) was the greatest rebounder of all time.
           | One of his teammates related to how he would watch guys shoot
           | (usually during warmups) and count the rotation of the ball.
           | Based on how many times the ball would rotate, he knew if it
           | was going in or not and then would position himself to get
           | the rebound.
           | 
           | I would imagine OP did something similar. Watch the coin as
           | its rotating and then grabbing it and then flipping to the
           | side he predicted.
        
             | searealist wrote:
             | Sandy Miller is widely considered to be the best volleyball
             | player of all time. He would famously wear the same
             | unwashed shorts every game for good luck. Maybe this was
             | his trick.
        
           | snowwrestler wrote:
           | I knew someone else who could do this pretty reliably. He
           | said it was a "feel the timing" thing. Best analogy he had
           | was maybe like landing an ice skating triple jump, or a
           | complex dive. It happens too fast to be consciously
           | controlled. Instead the trick is to train the body to get a
           | feel for success and then just let the body do it.
        
           | lupire wrote:
           | It's easy. All you need to do is rotate (yaw) your hand when
           | flipping so that the coin spins but never actually flips, or
           | a little slower so it flips only once. A watchful eye can
           | detect it happening, though.
           | 
           | You can preview the effect by spinning a coin slowly on a
           | table.
           | 
           | This is a common problem in intro Physics Mechanics class.
        
       | aquafox wrote:
       | FWIW, there is also a 2007 paper [1] that offers a physical
       | explanation.
       | 
       | [1]
       | https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_co...
        
         | hackernewds wrote:
         | as long as a machine is used for consistency*
        
         | seanhunter wrote:
         | That is referenced in both the paper and the video in fact.
         | Apparently Diaconis presented a model which predicted about 51%
         | preference for "Same side" and also did 2500 flips and said
         | that about 250k flips would be needed to get 3 sigma of
         | significance. So this paper decided to test it empirically and
         | got to about exactly that number after 350k flips from a team
         | of researchers.
        
       | whatever1 wrote:
       | In other news, probabilities again used to prove whatever
       | conclusions we were planning to present anyway.
       | 
       | It is time to stop the show, probabilities cannot prove
       | specifics. Aka they cannot prove that the coin I hold is fair or
       | not. We can only get trends for big populations.
       | 
       | There is only one way to prove if a coin is fair. Measure the
       | actual thing that matters. In this case mass distribution. And if
       | the measurement is inaccurate, then count atoms. One by one.
        
         | mirekrusin wrote:
         | Also, there is fair _coin_ and fair coin _flip_, two different
         | things.
        
       | noman-land wrote:
       | Haven't read the paper yet but this is so weird because when I
       | was a kid I noticed this phenomenon myself. I noticed I could
       | reliably flip a coin such that when it landed it would land on
       | the same side as it was flipped from. I was getting like 80%
       | accuracy and I didn't even know what I was doing to achieve it. I
       | could just usually feel when I flipped it that I "did it right".
       | I used it a couple times to win coin toss decisions but then
       | sorta forgot about it and relegated it to a statistical fluke. It
       | would be amazing of there was some merit to it.
        
         | cbsmith wrote:
         | There's a "fair coin", and then there's a "fair flip". It's
         | actually pretty difficult to do a truly "fair flip".
        
           | lupire wrote:
           | A fair coin is just a coin. There is no such thing as an
           | unfair coin, unless its third side is so huge that it can't
           | be reasonably called a coin.
        
             | cbsmith wrote:
             | You're going to have a lot of fans amongst con men. ;-)
             | 
             | Unfair coins very much do exist:
             | https://izbicki.me/blog/how-to-create-an-unfair-coin-and-
             | pro...
        
         | Frummy wrote:
         | Maybe you were like one with the coin and always pushed it the
         | optimal way for like the same type of movement and direction
         | and rotation for the same amount of rotations in air etc like
         | perfected an initial condition and kept it stable like it
         | rotated 6 times and landed the same way
        
           | Tetraslam wrote:
           | the Force is with them
        
         | aqfamnzc wrote:
         | Sounds like maybe you were doing something like this?
         | https://news.ycombinator.com/item?id=42184069
        
       | yapyap wrote:
       | what if they got evidence from 350.758 flips, would this impact
       | anything
        
       | acyou wrote:
       | The paper looks like it has a large sample size, but it actually
       | has a sample size of only 48 testers/flippers. Some of the videos
       | of those testers show very low, low-rpm coin tosses, we're
       | talking only 1-2 flips. Where they also flipped thousands of
       | times, presumably in the same way. So there is actually a very
       | small sample size in the study (N = 48), where testers that don't
       | flip properly (low rpm, low height, few coin rotations) can
       | affect the results disproportionately.
       | 
       | Doesn't look like the study author backgrounds are particularly
       | focused on statistics. I would presume with 48 authors (all but 3
       | of which flipped coins for the study), the role of some might
       | have been more test subject than author. And isn't being the
       | subject in your own study going to introduce some bias? Surely if
       | you're trying to prove to yourself that the coins land on one
       | side or another given some factor, you will learn the technique
       | to do it, especially if you are doing a low-rpm, low flip. Based
       | on the study results, some of the flippers appear to have learned
       | this quite well.
       | 
       | If the flippers (authors) had been convinced of the opposite
       | (fair coins tend to land on the opposite side from which they
       | started) and done the same study, I bet they could have collected
       | data and written a paper with the results proving that outcome.
        
         | salt4034 wrote:
         | > testers that don't flip properly
         | 
         | I think that's the point. It shows that people don't usually
         | flip properly, leading to biased results.
        
           | fluoridation wrote:
           | But _is_ that the case? The only way I 've ever seen people
           | flip a coin is by flicking it in the air with their thumb and
           | either catching it or letting it hit a surface. I've never
           | seen someone flip a coin like it was a die.
        
           | lcnPylGDnU4H9OF wrote:
           | There is a [video presentation of the
           | paper](https://www.youtube.com/watch?v=-QjgvbvFoQA) which
           | does a good job of explaining the inspiration for the study
           | within the first few minutes.
           | 
           | It sounds like what they were intending to study is the
           | actual variance that is introduced, on average, by
           | imperfections in throws conducted by humans. Unless that's
           | mistaken, it's a fair point to consider the n=48 here. Did
           | they discover an average that can be generalized to humans or
           | just to those 48?
        
             | chongli wrote:
             | Yes and what immediately jumps out to me as a source of
             | bias is that they asked this small group of 48 coin
             | flippers to flip thousands of times each. I would've
             | thought it would be obvious that when you ask people to do
             | something thousands of times they might do it in a
             | different (and biased) way than someone doing that thing
             | only once.
             | 
             | Get a hundred thousand people to flip a coin once each and
             | then see what happens!
        
               | fluoridation wrote:
               | What's more, from the numbers cited it sounds like they
               | had 48 people do nothing but flip coins for 8 hours (avg.
               | 15 flips/min). Whether continuous or with breaks, there's
               | no way you won't become seriously consistent. 7000 flips
               | is many more flips most people will perform in their
               | entire lives.
        
               | dylan604 wrote:
               | In some circles, they'd make a post about how their "AI"
               | flipped a coin 8000 times.
               | 
               | Waiting for the HNer that likes electronics hacking to
               | Show HN: My coin flipping robot I built over a weekend
               | for consistent flips.
        
               | dfxm12 wrote:
               | _Get a hundred thousand people to flip a coin once each
               | and then see what happens!_
               | 
               | Of all the stats we collect in sports, I wonder if
               | someone has info on coin tosses in sports like American
               | Football, Tennis, etc. I wonder if there are even rules
               | regulating how a coin should be tossed in different
               | sports...
        
               | skykooler wrote:
               | Having stats on the outcome of coin tosses in sports
               | wouldn't help, because it's unlikely that the state of
               | the coin _before_ flipping was recorded.
        
           | arandomusername wrote:
           | Except that flipping a coin hundreds/thousands of time in a
           | row is not a representive of how people will flip a coin a
           | single time/few times.
        
         | saalweachter wrote:
         | If you are doing anything with human subjects, even something
         | dumb like having them flip coins for an hour while recording
         | the results, you need approval from your local ethics board.
         | 
         | If you are doing self-experimentation, you do not.
         | 
         | 48 "authors" is a bit extreme, but it's the norm to do some
         | light human research with a half dozen authors as the subjects.
        
         | KwisatzHaderack wrote:
         | > only 48 testers/flippers
         | 
         | I assumed they did these coin flips were done using a machine.
         | But I guess they wanted to test if human flippers because they
         | wanted to make claims about the human coin flip phenomenon.
        
           | kybernetikos wrote:
           | But if you get someone to flip a coin thousands of times for
           | a boring reason, I would lose confidence that they are
           | flipping in the same way a normal human would.
        
           | halgir wrote:
           | If you programmed a machine to flip a coin in the same exact
           | way every time, would you not expect the coin to land the
           | same way every single time? If you program some randomness
           | into the machine to simulate human flipping, then you'd
           | simply move scrutiny from the coin to the machine's
           | programming.
           | 
           | I think the result could be better described as "humans tend
           | to flip fair coins to land on the side they started".
        
             | saagarjha wrote:
             | One would expect chaos effects to come into play.
        
               | oefnak wrote:
               | One might, but that would be wrong.
        
         | binarymax wrote:
         | 1-2 flips should just invalidate the toss. Anyone in a real
         | scenario upon seeing this would call shenanigans.
         | 
         | We need some minimum flippage for the toss to count.
        
         | its-summertime wrote:
         | > the role of some might have been more test subject than
         | author
         | 
         | The reason is because it was used as incentive:
         | 
         | > Intrigued? Join us and earn a co-authorship
         | 
         | Per the linked youtube video.
        
         | tomrod wrote:
         | Actually, I think it's more sound to approach this with
         | clustered standard errors. Basic intuition is similar, but the
         | sample size is what it is per person, and your observations
         | aren't independent across draws but are across people.
         | 
         | https://en.m.wikipedia.org/wiki/Clustered_standard_errors
        
         | bambax wrote:
         | The real lesson is probably that if you're skilled enough,
         | and/or train for long enough, you can influence the odds
         | significantly without anyone ever noticing anything.
        
           | lupire wrote:
           | That has been known for decades. It's not the lesson of this
           | paper.
        
         | anigbrowl wrote:
         | _testers that don 't flip properly_
         | 
         | Clearly the coin flips at the beginning of sports fixtures need
         | to be assessed by a panel of highly skilled judges who can
         | pronounce on their validity. We'll also need local, regional,
         | national, and international organizations to train, select, and
         | maintain the quality of coin flipping judges and to maintain
         | the integrity of the discipline while moving forward as new
         | coins are minted and different sorts of flipping styles are
         | proposed by. Membership of such organizations should be limited
         | to those afilliated with the Ancient Order of Coin Flippers.
        
           | askvictor wrote:
           | I was more thinking we'll need a Department of Randomness (or
           | Ministry of Randomness for Westminster countries)
        
             | pc86 wrote:
             | Perhaps whether it's a Department or a Ministry could be
             | decided randomly.
        
               | Green-Man wrote:
               | Randomly how? By a coin toss? Who will toss then? How
               | many times? How skilled the participants should be? All
               | these important questions must be decided by some
               | authority. Sort of a Department of Equal Distribution. Or
               | a Ministry of Fair Tosses. Wait a second...
        
               | moi2388 wrote:
               | The obvious solution is to hand it off to the Department
               | of Catch 22. Or the Ministry of infinite recursion.
               | Wait..
        
         | jdlshore wrote:
         | The paper is an experimental validation of a previous paper
         | that presented a statistical model. The experiment found the
         | exact results predicted by the model. The reason for the non
         | 50/50 result is precession of the coin.
        
       | vkaku wrote:
       | I guess our world has been run with unfair flips, LOL.
        
       | dudeinjapan wrote:
       | Yes... but the choice of which side they start is a random one!
        
       | pkkkzip wrote:
       | I noticed phenomenon in poker as well. Someone who runs well
       | ahead of the crowd continues to do so seemingly even playing
       | randomly with no thought into traditional poker theory.
       | 
       | For example, if a strong pair starts off with a bad beat then it
       | tends to continue that trend. The word trend doesn't mean its
       | going to happen but that its likely to continue the past.
       | 
       | When someone continues exploiting this trend they have seemingly
       | "broken" the game, it no longer functions like a calculated game
       | of odds and when somebody plays like a maniac (like in the first
       | scenario i mentioned) there is seemingly no other defense than to
       | wait until the trend breaks but no matter how seasoned a player
       | is they cannot shake the past and its perceived likelihood of
       | continuing.
       | 
       | This effect is rampant in stock market as well when there is
       | seemingly less "random" reinforcements and belief in the crowd
       | which without fail has given rise to black swans/massive
       | collective drawdowns of the world war causing variety.
        
       | matwood wrote:
       | When I was a kid we played quarters (dating myself) a lot. I felt
       | this was the case, but nice to see it studied.
        
       | tarkin2 wrote:
       | What I've learnt from this thread is that the problem with fair
       | coin flips is not if they're fair it's whether we count them as a
       | proper coin flips. And so who gets to decide?
       | 
       | And if most people aren't flipping like that then should we
       | design a machine that flips the coins? And we try to control
       | other factors as well? Or is a human--their imperfections
       | included--flipping the coins inherently important to the idea of
       | coin flipping, statistics and randomness?
        
       | amoss wrote:
       | My heart goes out the cryptographers. All that code, written over
       | decades, that assumes coin flips are 50:50. So much updating and
       | rewriting to do. Quite a few algorithms that will need a rethink
       | to remain fair.
        
         | TheRealPomax wrote:
         | If your cryptographer's code is based on coin flips, you
         | probably want to find a new cryptographer.
        
       | calibas wrote:
       | I think I can explain it:
       | 
       | Other side: 1/2 flip, 1 1/2 flips, 2 1/2 flips...
       | 
       | Same side: 1 flip, 2 flips, 3 flips...
       | 
       | It seems like there's equal chances, but my theory is that the
       | 1/2 flip is the least likely thing to occur. When you take that
       | into account, there's a slightly increased chance that it's going
       | to land on the same side.
        
       | sans_souse wrote:
       | thought experiment: if we design a mechanical arm to enable coin
       | flipping utilizing advanced tech to establish fine-grained
       | adjustments and calibrations to effectively reproduce results
       | with any given coin to and work out formulas to arrive at these
       | results; are we currently or will we ever be able to say with
       | absolute certainty what any given coin toss's result will be?
        
       | fbartos wrote:
       | Hi, I'm the first author of the manuscript, so I thought I could
       | answer some of the questions and clarify some issues (all details
       | are in the manuscript, but who has the time to read it ;)
       | 
       | Low RPM tosses: Most of the recordings are on crapy webcams with
       | ~ 30FPS. The coin spin usually much faster than the sensor can
       | record which results in often non-spinning-looking flips. Why did
       | we take the videos in the first place? To check that everyone
       | collected the data and to audit the results.
       | 
       | Building a flipping matching: The study is concerned with human
       | coin flips. Diaconis, Holmes, and Montgomery's (DHM, 2007) paper
       | theorize that the imperfection of human flips causes the same-
       | side bias. Building a machine completely defeats the purpose of
       | the experiment.
       | 
       | Many authors and wasted public funding: We did the experiment in
       | our free time and we had no funding for the study = no money was
       | wasted. Also, I don't understand why are so many people angry
       | that students who contributed their free time and spent the whole
       | day flipping coins with us were rewarded with co-authorship. The
       | experiment would be impossible to do without them.
       | 
       | Improper tosses: Not everyone flips coin perfectly and some
       | people are much worse at flipping than others. We instructed
       | everyone to flip the coin as if they were to settle a bet and
       | that the coin has to flip at least once (at least one flip would
       | create bias for the opposite side). We find that for most people,
       | the bias decreased over time which suggests that people might get
       | better at flipping by practice = decrease the bias and it also
       | discredits the theory that they learned how to be biased on
       | purpose. From my own experience - I flipped coins more than
       | 20,000 times and I have no clue how to bias it. Also, we did a
       | couple of sensitivity analyses excluding outliers - the effect
       | decreased a bit but we still found plentiful evidence for DHM.
       | 
       | If you doubt my stats background, you are more than welcome to
       | re-analyze the data on your own. They are available on OSF:
       | https://osf.io/mhvp7/ (including cleaning scripts etc).
       | 
       | Frantisek Bartos
        
         | ineptech wrote:
         | Hi, thanks for replying. I have no complaints about your
         | analysis, and agree that your results strongly support the
         | D-H-M model (that there is a slight bias in coin-flipping over
         | all and that it is caused by precession). However, it looks
         | like about a third of your volunteers had little or no bias,
         | presumably due to flipping end-over-end with no precession, and
         | about a third had a lot of precession and a lot of bias.
         | 
         | Your paper draws the conclusion that coin-flipping inherently
         | has a small-but-significant bias, but looking at table 2 it
         | seems like an equally valid conclusion would be that some
         | people flip a coin with no bias and others don't. Did you
         | investigate this at all? In particular, I'd expect that if you
         | took the biggest outliers, explained what precession is and
         | asked them to intentionally minimize it, that the bias would
         | shrink or disappear.
        
           | fbartos wrote:
           | Yes, there is indeed a lot of heterogeneity in the bias
           | between flippers and we are going to put more emphasis on it
           | in an upcoming revision. However, it's hard to tell whether
           | there are two groups or a continuous scale of increasing
           | bias. From our examination of the data, and continuum seem to
           | be the more likely case, but we would need many many more
           | people flipping a lot of coins to test this properly.
           | 
           | Yes, training the most wobbly flippers sounds like a very
           | interesting idea. It might indeed answer additional questions
           | but it's not really something I wanna run more studies on :)
        
             | ineptech wrote:
             | Understandable, but I guess it's hard to put much weight on
             | this data given how easy it is to introduce the effect
             | being studied intentionally. Were the subjects aware of
             | D-H-M beforehand? I wasn't before today, but I've been able
             | to fake a coin flip with precession for many years (a very
             | useful skill for parents of two small children) and if I
             | was participating in a study like this I would be pretty
             | hyper-aware of how much "sideways" I was giving it.
        
         | emmelaich wrote:
         | The first thing I looked for was how high was the flip and did
         | it land on a hard or soft surface. Neither seemed to be
         | mentioned in the paper.
         | 
         | From the one video I looked at, the flip seems to be a few feet
         | high at most, and land back in the hand.
        
           | fbartos wrote:
           | > In each sequence, people randomly (or according to an
           | algorithm) selected a starting position (heads-up or tails-
           | up) of the first coin flip, flipped the coin, caught it in
           | their hand, recorded the landing position of the coin (heads-
           | up or tails-up), and proceeded with flipping the coin
           | starting from the same side it landed in the previous trial
           | (we decided for this "autocorrelated" procedure as it
           | simplified recording of the outcomes). (p.3)
           | 
           | Wrt to the height, that naturaly varied among people and
           | flips and we did not measure it.
        
         | sandworm101 wrote:
         | The NFL still flips coins professionally. I wonder if they have
         | better-than-webcam footage of each flip. Somewhere out there a
         | bookie might be very interested in any potential bias.
        
           | miki123211 wrote:
           | That makes me wonder whether any bookmakers or sports betting
           | arbitration shops have ever internally ran a study like this.
           | 
           | With how much money there is in sports betting, it could
           | potentially be somewhat lucrative, though I wouldn't be
           | surprised if the bias doesn't actually end up mattering that
           | much in practice.
        
           | aidenn0 wrote:
           | IIRC, past studies have suggested that letting the coin land,
           | rather than catching it, reduces or eliminates the bias.
        
           | LVB wrote:
           | Some hi-res footage of an NFL toss:
           | https://youtu.be/-sjAyQcv0oM
        
         | hardmath123 wrote:
         | Re: Low FPS webcam - here's an approach that attempts to
         | analyze coin tossing data from the _sound_ rather than the
         | _video_, since sound is typically recorded at a much higher
         | sampling rate (high enough to "hear" the spinning of the coin).
         | https://cs.stanford.edu/~kach/can-one-hear-the-fate-of-a-coi...
        
         | PittleyDunkin wrote:
         | How do you control against the prospect of your coin flippers
         | being biased in terms of the videos people choose to upload?
        
           | fbartos wrote:
           | We did not. However, we find it highly unlikely since
           | everyone was incentivised to upload as much as possible, and
           | the number of coin flips determined the order of the
           | manuscript. Also, we did some basic analyses to check
           | irregularities in the uploaded sequences, and we did not find
           | any issues.
        
         | M95D wrote:
         | I have a question about the ethics of this study.
         | 
         | Were you not concerned that a study that shows a bias in coin
         | flipping would undermine the trust people have in this simple
         | method settling arguments, leading to even more arguments
         | between people, possibly fights and injuries, in situations
         | where a coin flip would have settled an existing argument?
         | 
         | Thank you.
         | 
         | PS: This isn't supposed to to be a serious question, if anyone
         | has doubts. :)
        
         | QuantumGood wrote:
         | Couldn't a bit of a Benford's Law curve be at work with the
         | lesser flippers? Assuming a minimum full flip, results begin
         | with:
         | 
         | 1.0 flip, lands on side it started
         | 
         | 1.5 flips, lands on opposite side
         | 
         | 2.0 flips, lands on side it started
         | 
         | etc
        
       | mihaic wrote:
       | Here's a little through experiment I use to come to this
       | conclusion:
       | 
       | Let's say you start a counter from the number 0, and keep on
       | incrementing it. The moment you stop it to look at the counter,
       | is it going to be odd or even?
       | 
       | At any given moment in time, either the number of observed odd
       | numbers is the same as the number of even numbers, or the number
       | of even numbers is larger by 1 (such as going from 0 to 1 to 2).
       | So in the end there's always a slightly larger chance at stopping
       | on an even number.
       | 
       | I know it's more complicated, I use it just as an intuitive
       | explanation.
        
       | Animats wrote:
       | Useful. This demonstrates that coin flipping merely amplifies
       | noise in human manipulation.
       | 
       | A classic example in the old PSSC high school physics curriculum
       | was a little catapult-like device which tossed a coin, spinning
       | it a few times in mid-air, and repeatably landing it on the same
       | side. It's a demonstration that Newtonian physics is repeatable.
        
         | mrbungie wrote:
         | Yes, that's because a coin toss is not intrinsically random,
         | but just pseudo-random due to its chaotic behaviour which is
         | especially notable at relatively "extreme" starting conditions.
         | 
         | But if the tosser were to control, manipulate or just don't
         | care enough about adding entropy to the toss, those random
         | generation qualities of the object would start to fall apart.
         | 
         | PS: As I read before, dice/coins are not entropy generators but
         | rather, entropy sinks+processors.
        
           | lupire wrote:
           | What in the Universe is an entropy generator?
        
       | sorenKaram wrote:
       | not enough flips
        
       | stevage wrote:
       | Not totally relevant, but I once discovered it's pretty easy to
       | cheat a coin toss, at least with an Australian 20c coin. Flip the
       | coin, catch in your hand, and in the process of transferring it
       | to the back of your other hand, feel which way up it is, and
       | optionally flip it.
       | 
       | With our coins, the head (the Queen's face at the time) is pretty
       | distinct with a large smooth area, compared to the rough feel of
       | the platypus and water.
       | 
       | So if ever you're flipping for anything that matters, make sure
       | the coin lands directly on the ground.
        
       | harry8 wrote:
       | Pr(same side)=0.508, 95% credible interval (CI) [0.506,0.509]
       | 
       | Toss it 100 times, overstating the effect you'd expect it to land
       | on the same side it started 51 times, opposite side 49.
       | 
       | This seems to have been lost in much of the discussion. Employing
       | this in professional NBA basketball you /might/ get one extra
       | toss win per season out of your 100 games compared to any other
       | way of selecting without taking into account the starting side.
       | 
       | Good luck using this!
        
       | quantadev wrote:
       | I'm not sure I believe this coin flip bias, but I would if lots
       | of other researchers can reproduce it.
       | 
       | If indeed it's happening, the only explanation can be something
       | to do with very deep Quantum Mechanics including multiverse
       | theory, where we're simply "more likely" to be in a universe
       | where the coin ends where it starts. (But honestly it seems like
       | it would take trillions of flips to detect, just as a hunch) So
       | that would make this experiment, believe it or not, akin to the
       | infamous Slit-Experiment in Particle Physics, where multiverses
       | are one way that's theorized as an explanation. That is, we're
       | sort of in "all universes" as s superposition until something
       | interacts in a way forcing us into ONE universe. (i.e. wave
       | collapse)
       | 
       | Along the same multiverse theme, I also have this other wild
       | conjecture (feel free to ridicule it!) which is that AI LLM
       | (Large Language Models) are "tending towards intelligence" during
       | training because at each quantum collapse (of which Model
       | Training has astronomically high numbers, with powerful computer
       | data centers running for months) we're nudged just slightly more
       | probabilistically into a universe where LLMs are "smart" as
       | compared to "dumb", and so when you multiply it all up over
       | months of churning, that puts us into a universe with
       | dramatically smarter AI, because of the sheer number of
       | computations, adding all the probabilities. I realize the
       | training of AI is "deterministic" but nonetheless only quantum
       | probabilities "determine" which universe we collapse into at each
       | QM decoherence. So you can ask WHY is there this 'nudge' towards
       | universes with smart LLMs? Probably because in all future
       | universes we only exist because LLMs save us, or help us in some
       | way, so other timelines/universes are "less" likely.
        
         | left-struck wrote:
         | >If indeed it's happening, the only explanation can be
         | something to do with very deep Quantum Mechanics including
         | multiverse theory
         | 
         | Why would that be the only explanation? that seems like very
         | low down on a long list of possible explanations.
         | 
         | I didn't read the paper but the author was discussing how some
         | people impart precession onto the coin which is a likely
         | explanation for causing a bias.
        
           | teaearlgraycold wrote:
           | Any relatively new field of physics gets the same treatment
           | as religion.
        
             | quantadev wrote:
             | Now that so many physicists and legitimate experts (non-
             | quacks) believe in Simulation Theory, we've sort of
             | "merged" physics and Religion. The general agreed upon
             | definition of God is "whatever thing is simulating the
             | universe". Of course all the Religious dogma and mythology
             | stories are things that most of them don't believe.
        
           | quantadev wrote:
           | The fact that some people cause it and some people don't (the
           | coin flip bias) can have an explanation something like having
           | to do with their impact on the causality chain if our
           | universe/timeline. It could be anything from which one of
           | them is older, to which one of them has a future offspring
           | that does something big that has a big impact on the universe
           | (in terms of Butterfly Effect kind of knock-on effects).
           | 
           | But I just don't see a person being able to flip accurately
           | enough cause this. No way. But I'm just playing along here. I
           | don't truly believe this experiment is anything but either a
           | hoax, or mistake.
        
       | upmind wrote:
       | Curious if this is true for dice, whenever me and my family play
       | monopoly, my dad likes to look at the dice (as he's shaking it)
       | and he usually gets a high number if he can see a low one and
       | vice versa.
        
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