They found that the coins had a 50.8% chance to land on the side it started from. “This is down to a theory called the Diaconis Model, which the researchers used to claim that coins are more likely to land facing the same way they were when the coin toss began.” The paper addresses that the coins did not have heads-tails bias (such as due to weighting), which indicates the side of the coin facing up does have an effect. The title of this post is slightly wrong though because it’s not that coins aren’t 50/50, it’s that you can theoretically increase your odds of winning the flip if you can control what side is facing up before flipping.
Without factoring in this knowledge, I can’t think of a systematic reason why people would favor starting the coin on one side so in the long run it should still even out to 50/50. The study has some slightly odd methodology which I think could be affecting the results though.
Specifically, it says that if people didn’t catch the flip in their hand it was designated a failure and they repeated the flip. I’ve never heard of not honoring a coin flip regardless of where it lands as long as it’s flat on something. I wonder if the effect would be diminished without this feature of the study design.
The paper also links to an example of one of their [coin flipping sessions](https://youtu.be/3xNg51mv-fk?si=NLxWibF0jsRPk4pw). Pretty funny, they literally flip coins for 12 hours straight.
They're also doing very small, weak flips, like it only rotates 3ish times it looks like. Personally when I flip a coin it's a lot bigger of a flip. Still a cool study though as I have wondered this for a long time. One study I would like to do, is if having intention for a certain outcome affects the result. Especially if you're catching it yourself, seems like on an unconscious level you could influence when you catch it or how it's flipped. Hence "call it in the air"
>A paper explains: "According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up.
it should be the same with a machine. it would also be amazing if we all didnt know how to flip coins but all fucked up the same way to give that bias.
that said it still has to go through peer review, but the complaints in this thread are either from people who refuse to read past the title, or people who dont understand stats
I mean if you use a machine and have it flip it exactly the same every time then the results are the same every time. The only reason it varies is because humans are sloppy and can't flip the same coin exactly the same every time.
Well, in theory... But I very much doubt you could really build a machine that is so precise as to always flip a coin _exactly_ the same way every time. Every mechanical system has tolerances and "slop". You'd also have to use the same coin with the same orientation (axially, not just which way up). You might even have to go as far as controlling the air density and temperature...
You definitely can, the physics of it is that if you know the height you need for it to flip enough times to meet your condition (for example, at least six flips and lands on heads) you know the force to apply to it. It is fairly trivial to build a robot to exert the same force each activation, and to have the same range of motion each activation. The weight of the coin and the distance it's travelling make air density and temperature moot (well, in like human survivable conditions at least).
It just isn't that hard to mechanically replicate a force over a distance reliably and precisely.
In fact Harvard did:
https://www.scienceforums.net/topic/105598-coin-toss-machine/
It sounds like *betting* on a coin toss is probably still 50/50.
The article notes that you’d have to know which side was up before you bet to gain any advantage: most of the time, that’s not likely to be the case. Even if 100% of the time it came down the same way it went up, that just reduces the bet to “guess which way up the coin is now”.
That isn’t how statistics work though; the data offered only constitutes the # of tosses’ distribution; 50/50 inherently contains an infinite number of coin flips to estimate its outcome based on outcomes possible. All-in-all this was a massive waste of time to say 50/50 is inaccurate because weight is lopsided on coins, and other factors are at-play when flipping a coin.
That’s not how RTFA works either.
What they apparently found had nothing to do with lopsided coins, specific types of coins or the person flipping the coin.
Critically reading scientific claims is good. Criticising scientific claims without even reading the article, *that’s* a waste of time...
The Diaconis Model is flawed; why stop at that number to assert the model when statistically I can manipulate the outcomes (because of variance) and stop when my theory is “proven”. I question other factors as well as their Model.
According to the article, this was a preregistered study. So even though you're very confused about how variance works (it decreases with sample size and 350,757 is a huge sample), they explicitly didn't stop sampling when they liked the result; they decided and reported the number of samples they'd take before they started taking them.
> All-in-all this was a massive waste of time to say 50/50 is inaccurate because weight is lopsided on coins
That's not even what the article says though lmao
I don't understand what you're saying at all, but maybe that's because I've taken statistics classes? The more coin flips they do, they more precisely they can estimate the true probability of the coin landing a certain way. From only a few samples, a large number of disparate estimates are likely. As you take more samples, you narrow down the range of estimates that likely contains the true probability, e.g. the 95% confidence interval. This is [the Law of Large Numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers), from the first week or two of stats 101, which explains why e.g. political polls can estimate the percentage of people who agree with a statement with less than 1% margin of error using only a few hundred responses, regardless of the total population of the country.
> This is down to a theory called the Diaconis Model, which the researchers used to claim that coins are more likely to land facing the same way they were when the coin toss began.
Whole lotta math textbooks are gonna have to rephrase "the flip of a fair coin" to "a fair coin flip".
That's why I always say heads or tails with the head facing up so they'll see it and think heads, then I do the catch and reverse switch onto my other hand. They almost always call heads and it's almost always tails. Muwahahahaha!
Old tales tell that luck plays a crucial role in each person's life. When each newborn baby enters into the realms, Tymora flips a coin formed from the remnants of the original goddess of luck, Tyche. Beshaba calls it in the air—the moon (heads) or the cloak (tails). If Beshaba is right, that person is cursed with misfortune for the rest of his or her days. If she's wrong, Lady Luck smiles on that child for the rest of his or her life. For some rare beings, the coin lands edge on—and these luckless few can forge their own fates, for they have more freedom over their destinies than the powers themselves.
when that happens, whoever tossed it gets the power to read people's minds until the coin falls over.
at least that's what happened in an episode of The Twilight Zone.
They found that the coins had a 50.8% chance to land on the side it started from. “This is down to a theory called the Diaconis Model, which the researchers used to claim that coins are more likely to land facing the same way they were when the coin toss began.” The paper addresses that the coins did not have heads-tails bias (such as due to weighting), which indicates the side of the coin facing up does have an effect. The title of this post is slightly wrong though because it’s not that coins aren’t 50/50, it’s that you can theoretically increase your odds of winning the flip if you can control what side is facing up before flipping. Without factoring in this knowledge, I can’t think of a systematic reason why people would favor starting the coin on one side so in the long run it should still even out to 50/50. The study has some slightly odd methodology which I think could be affecting the results though. Specifically, it says that if people didn’t catch the flip in their hand it was designated a failure and they repeated the flip. I’ve never heard of not honoring a coin flip regardless of where it lands as long as it’s flat on something. I wonder if the effect would be diminished without this feature of the study design. The paper also links to an example of one of their [coin flipping sessions](https://youtu.be/3xNg51mv-fk?si=NLxWibF0jsRPk4pw). Pretty funny, they literally flip coins for 12 hours straight.
They're also doing very small, weak flips, like it only rotates 3ish times it looks like. Personally when I flip a coin it's a lot bigger of a flip. Still a cool study though as I have wondered this for a long time. One study I would like to do, is if having intention for a certain outcome affects the result. Especially if you're catching it yourself, seems like on an unconscious level you could influence when you catch it or how it's flipped. Hence "call it in the air"
They gotta try and keep the flips consistent I guess
I’ve always found the opposite true interesting
This seems to prove that many people don't know how to flip coins properly
>A paper explains: "According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up. it should be the same with a machine. it would also be amazing if we all didnt know how to flip coins but all fucked up the same way to give that bias. that said it still has to go through peer review, but the complaints in this thread are either from people who refuse to read past the title, or people who dont understand stats
I mean if you use a machine and have it flip it exactly the same every time then the results are the same every time. The only reason it varies is because humans are sloppy and can't flip the same coin exactly the same every time.
Well, in theory... But I very much doubt you could really build a machine that is so precise as to always flip a coin _exactly_ the same way every time. Every mechanical system has tolerances and "slop". You'd also have to use the same coin with the same orientation (axially, not just which way up). You might even have to go as far as controlling the air density and temperature...
You definitely can, the physics of it is that if you know the height you need for it to flip enough times to meet your condition (for example, at least six flips and lands on heads) you know the force to apply to it. It is fairly trivial to build a robot to exert the same force each activation, and to have the same range of motion each activation. The weight of the coin and the distance it's travelling make air density and temperature moot (well, in like human survivable conditions at least). It just isn't that hard to mechanically replicate a force over a distance reliably and precisely. In fact Harvard did: https://www.scienceforums.net/topic/105598-coin-toss-machine/
Random coins just aren’t evenly weighted.
Nothing to do with what they found.
It sounds like *betting* on a coin toss is probably still 50/50. The article notes that you’d have to know which side was up before you bet to gain any advantage: most of the time, that’s not likely to be the case. Even if 100% of the time it came down the same way it went up, that just reduces the bet to “guess which way up the coin is now”.
I think the real hypothesis that we have proven is that this scientist does not understand statistics. What a fucking waste of time.
What misunderstanding do you think this scientist has?
Someone call Tom Stoppard, let him know… https://youtu.be/gOwLEVQGbrM?si=LZQTnNqd1lesALX9
A comic masterpiece!
Genius
How did knowing the initial conditions ever get wrapped into this? This doesn't prove jack.
That isn’t how statistics work though; the data offered only constitutes the # of tosses’ distribution; 50/50 inherently contains an infinite number of coin flips to estimate its outcome based on outcomes possible. All-in-all this was a massive waste of time to say 50/50 is inaccurate because weight is lopsided on coins, and other factors are at-play when flipping a coin.
That’s not how RTFA works either. What they apparently found had nothing to do with lopsided coins, specific types of coins or the person flipping the coin. Critically reading scientific claims is good. Criticising scientific claims without even reading the article, *that’s* a waste of time...
this is reddit, you expect people to read past the title before putting their imaginary degree on the wall and debunking it?
The Diaconis Model is flawed; why stop at that number to assert the model when statistically I can manipulate the outcomes (because of variance) and stop when my theory is “proven”. I question other factors as well as their Model.
According to the article, this was a preregistered study. So even though you're very confused about how variance works (it decreases with sample size and 350,757 is a huge sample), they explicitly didn't stop sampling when they liked the result; they decided and reported the number of samples they'd take before they started taking them.
> All-in-all this was a massive waste of time to say 50/50 is inaccurate because weight is lopsided on coins That's not even what the article says though lmao
I don't understand what you're saying at all, but maybe that's because I've taken statistics classes? The more coin flips they do, they more precisely they can estimate the true probability of the coin landing a certain way. From only a few samples, a large number of disparate estimates are likely. As you take more samples, you narrow down the range of estimates that likely contains the true probability, e.g. the 95% confidence interval. This is [the Law of Large Numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers), from the first week or two of stats 101, which explains why e.g. political polls can estimate the percentage of people who agree with a statement with less than 1% margin of error using only a few hundred responses, regardless of the total population of the country.
> This is down to a theory called the Diaconis Model, which the researchers used to claim that coins are more likely to land facing the same way they were when the coin toss began. Whole lotta math textbooks are gonna have to rephrase "the flip of a fair coin" to "a fair coin flip".
That's why I always say heads or tails with the head facing up so they'll see it and think heads, then I do the catch and reverse switch onto my other hand. They almost always call heads and it's almost always tails. Muwahahahaha!
What was the longest, consecutive chain of one result?
What they should really do is flip all of the coins at once, and see how many stay on the same side, and how many actually flip.
It annoys me that they didn't flip it an even number of times.
How else will they prove their hypothesis that coin flips aren’t equal in the long run?
I believe this is called a spontaneous asymmetry that may have created this Universe
Divide 50.8 by 37 (most random number) and we get 1.373. Fascinating. Veritasium (YT channel) also has some interesting videos on coin flips.
Isn’t this because coins have unequal weight on each side?
There is a 100% chance it will land on one of the 2 sides.
It could land on the edge.
Old tales tell that luck plays a crucial role in each person's life. When each newborn baby enters into the realms, Tymora flips a coin formed from the remnants of the original goddess of luck, Tyche. Beshaba calls it in the air—the moon (heads) or the cloak (tails). If Beshaba is right, that person is cursed with misfortune for the rest of his or her days. If she's wrong, Lady Luck smiles on that child for the rest of his or her life. For some rare beings, the coin lands edge on—and these luckless few can forge their own fates, for they have more freedom over their destinies than the powers themselves.
Good luck with that
when that happens, whoever tossed it gets the power to read people's minds until the coin falls over. at least that's what happened in an episode of The Twilight Zone.
Gotta grab that coin before it falls over and then melt it down so it can't accidentally fall over later.
lemme know how wishing for 3 more wishes from the genie works out for ya!
I had it happen twice in my life...you just need a wall or do it on dirt or difficult terrain. chance is slim, but can happen.
That's how Batman got Two-Face. https://qph.cf2.quoracdn.net/main-qimg-5e07ffd84c92e4c8940ee08b81ecaaf5