[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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