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.
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.
link to the "wobble flip" trick https://youtu.be/-QjgvbvFoQA?t=325
Ah man, please use Bayesian statistics there... Well, the presenter says he doesn't know much about statistics.
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.
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.
[delayed]
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
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:
They're very low RPM and very low time in the air. Nothing I would accept for any decision worth flipping a coin for.
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.
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".
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.
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
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.
Somebody’s grant money getting thrown down a hole…
but they did?
here's the video https://youtu.be/-QjgvbvFoQA?si=ZTT1LWWJC8T4LIQZ
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
Let's abandon coin flipping in favour of coin shaking then
FWIW, there is also a 2007 paper [1] that offers a physical explanation.
[1] https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_co...
as long as a machine is used for consistency*
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...
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.
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
Well, I suppose if you need fodder to fill your CV, this is one way to do it.
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
Exactly :-)
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.
If this is done with a quick toss and the coin is flipping rapidly in the air, that's pretty impressive.
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.
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.
what if they got evidence from 350.758 flips, would this impact anything
Winner of the 2024 Ig Nobel prize in probability [1]. A nice read as well!
I think I figured this out when I was about 6 years old. It pretty much is always true.
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.
Also, there is fair _coin_ and fair coin _flip_, two different things.
you shouldn't bet on it though
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.
statistics be dammed,I'll flip you for it.....heads I win tails you loose
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.
That only works for a fixed bias, it's gameable if the person tossing the coin controls the bias.
That is outside the preconditions of the paper: „if the person tossing the coin controls the bias“
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.
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.
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.
So if computation in the enclosing universe got more expensive, they'd enable more aggressive optimizations, and we'd see the effect get stronger?
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.
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 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.)
Oh sure, let's doubt the evidence of our senses in favor of convention. That's good science.
How good are you at Bayesian statistics, conditionalization, and understanding various biases? The simulation here should be good (it's better than mine).
Next you'll cite Bible verse.
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.
“We toss the coin, but it is the Lord who controls its decision.” - Proverbs 16:33 (TLB)
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.
Does this explain the rarity of antimatter?
And a toast covered in jam lands 100% of the time on the jam side.
And cats always land on their feet. In combination, these facts can be exploited to achieve perpetual motion: https://youtu.be/Z8yW5cyXXRc
anyone else thinking about Pokemon TCGP...
Misty's flips are not fair, that's for sure
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).
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.
Thank you. This was useful to learn.
I’ve seen this attributed to John von Neumann, of all people
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.
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...
I consider LLMs to be the first successful non-von-neumann architecture in many decades
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.
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.
> 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].
Nah, you can put in a rule to stop. It would be better to know ahead of time, but you don't need to.
What if consecutive unfair coin flips are not independent?
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.
It's also impossible to prove that a given coin is not being controlled by an AI. (Or a deity.)
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.
Just perform the same coin toss in two universes.
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 same side bias is either a heads bias or a tails bias.
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.
Its not, its a bias towards which side the coin started on.
Which is either heads or tails.
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'
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.
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).
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".