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.
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.
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.
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?
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.
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.
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.)
How good are you at Bayesian statistics, conditionalization, and understanding various biases? The simulation here should be good (it's better than mine).
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.
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.
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.
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.
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.
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.
> 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.
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.
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.
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.
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.
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.
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.
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.
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'
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.
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.
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.
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".
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).
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.
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.
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.
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.
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:
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.
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.
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.
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.
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.
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
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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?
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!
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.
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...
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.
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.
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.
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".
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.
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.
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.
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...
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.
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.
192 comments
[ 3.6 ms ] story [ 264 ms ] threadIn 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.
I bet this is the video you mean? https://www.youtube.com/watch?v=A-L7KOjyDrE
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.
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.
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.
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.
[1] https://improbable.com/ig/winners/#ig2024
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.
It is not about intentional favoring on result.
> 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...
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.
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.
>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.
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.
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).
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".
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).
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
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)
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.
If you require true randomness without any assumptions this is not the universe for you.
0: https://en.wikipedia.org/wiki/Whitening_transformation
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.
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.
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".
If you want to measure what happens specifically with high and fast coin tosses, then that’s an entirely different study to be done.
there's your paper
This is silly.
Craps is also brought to mind where the dice have to bump the back wall
[1]: https://blog.sia.tech/generating-cryptographically-secure-ra...
here's the video https://youtu.be/-QjgvbvFoQA?si=ZTT1LWWJC8T4LIQZ
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.
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.
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
A single person would write 17000 posts about their "amazing journey" coin flip outcomes, and another 17001 "humbled by success" coin flip outcomes
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.
You can preview the effect by spinning a coin slowly on a table.
This is a common problem in intro Physics Mechanics class.
[1] https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_co...
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.
Unfair coins very much do exist: https://izbicki.me/blog/how-to-create-an-unfair-coin-and-pro...
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.
I think that's the point. It shows that people don't usually flip properly, leading to biased results.
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?
Get a hundred thousand people to flip a coin once each and then see what happens!
Waiting for the HNer that likes electronics hacking to Show HN: My coin flipping robot I built over a weekend for consistent flips.
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...
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.
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.
I think the result could be better described as "humans tend to flip fair coins to land on the side they started".
We need some minimum flippage for the toss to count.
The reason is because it was used as incentive:
> Intrigued? Join us and earn a co-authorship
Per the linked youtube video.
https://en.m.wikipedia.org/wiki/Clustered_standard_errors
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.
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.