I spent weeks in middle school practicing flipping a coin to make it look like it was flipping when it reality it was just spinning while remaining with the same face up. It worked about 60% of the time. Won a lot of bets.
Interesting! I did a bit of another thing at about the same age. I have found, that with the right size of the coin (15-20 mm in diameter) and training you can just capture the coin at the right time from the air to get the desired result. Somehow I managed to make ~80 percent same-side captures and ~60 percent other-side captures (in comparison with initial orientation).
Know what I do is, when I catch the coin out of the air I try to catch it while swiping my hand towards my face so I have a split second to glimpse how it is resting on my palm. Then you can either open your hand and reveal the coin as is or open your hand sort of tilted down so that the coin flips onto your fingers. Works nearly every time @@man0fstraw
is that 60% of the time getting the result you wanted, or 60% of the time getting the technique right with a 40% chance for it to be an honest coin flip?
Good question. Its a fine line because if you want the coin to look like it's flipping you have to toe the line between a spin and real, fair flip. So I would say that it was more that 60% of the time the technique worked well enough that it looked like a convincing coin flip while still being reliably on the side I wanted. The other 40 percent was split evenly between it either not look convincing enough or it flipping so that I couldn't tell which side it would land on. @@catkook543
Me, I used a half dollar. Since the heads side is smoother than the tails side, I would flip the coin, often as high and as rapidly spinning as possible, telling my mark to "call it in the air." I make a show of catching the coin, then I open my hand to reveal that the person guessing got it wrong. Of course, when I catch it, I can tell which side is facing my fingers. I practiced making the motion of opening my hand almost perfectly identical, but I could control which side came up. Making them figure out how I did the trick was the most fun for me, especially as after the second or third go, almost every guy will wind up suckered into having to try to win.
No. First you need an ACTUAL fair coin (that is not slightly heavier on one side or that has a bias in air resistance). Then you need to flip it in a fair way. And even then, there is likely to be a very small bias. But this bias is small even in the case of an unbalanced coin - generally within the margin that cannot easily disprove the null hypothesis. Spinning a coin is even more unfair, as it magnifies the weight effect.
I recall reading many years ago that most coins do have a bias because heads/tails are not perfectly symmetrical, with 1 side slightly heavier. However, this bias appears at the 1 part in 10k-100k level, so is completely drowned out by the same side bias.
@@mlthornton1 Doesn't matter what you think, this is not a matter of opinion. Statistically, it's compelling enough to matter and consider when flipping a coin.
I'm a soccer referee and this will actually change the way I do the coin flip. I kind of knew that there was a face up bias, but I never thought through my mechanics to hide the coin before the flip. Now it'll be a little more fair. 2% more.
your changes actually make it less fair for the disadvantaged teams because without your changes, their disadvantage would have been an advantage instead
You could even shake it around in your hands where no one can see it and then flip the coin from cover so it's only revealed for an instant, making it extremely difficult to spot.
@@itskittyme A coin toss is intended to randomly select from between two options. "Fair" in a coin toss means it has an equal chance of landing heads or tails. The closer you can approach to exactly even chances the more fair it is, by definition. Losing an unintended advantage is not "less fair," it's more fair.
A note on coin flip strategy - some people routinely flip the coin upside down (usually catching the coin and then slapping it face down on the back of their other hand) - in that case you should bet on the opposite side instead
That is a George Castanza. When everything do do always comes out wrong, do the opposite of what you usually do and your winning streak will be😅 endless.
As a magician in my youth, I spend a lot of time learning how to make a cointoss look fair when in fact I controlled the result. It was this exact wobble effect..
You can make the coin toss a little more complicated to ensure that it's fair: Flip the coin two times. If it shows heads-tails, you win. If it shows tails-heads, your opponent wins. If it shows the same side twice in a row, repeat the process. That way, whatever the probability p of heads is, your chance of winning is p*(1-p), while your opponent's chance is (1-p)*p.
this does'nt work. lets assume heads is up and I win with heads-tails you win with heads-tails. i am gonna assume that the 51% figure shown here is correct i have 0.51*0.49 chanse to win you have 0.49*0.49 chanse to win In the case of a reroll i am also more likely to have adventge in the next flip the chanse for head-heads is 0.51*0.51 the chanse of tails-tails is 0.49*0.51
@@נירמנחמי No, if you have the same side up in the re-roll as initial side up, then it is the same for both! Say, we begin with "Heads" up. I win if it is HT and you win if it is TH Now, if you keep heads up in the re-roll too, then my chances of winning are : 0.51 * 0.49 (according to the video's probability) And your chances of winning are : 0.49 * 0.51 So our chances are equal! Fair. P(HT) = 0.49*0.51 = P(TH) P(HH) = (0.51)² P(TT) = (0.49)²
@@dhruvgupta6389 you are assuming independent probability. You ignore the fact that the result of the second flip is effected by the result of the first
@@נירמנחמי The key is you don't just re-roll the Duplicate, you chuck them BOTH out and start from scratch. EG. if you roll Heads, then roll Heads again, then roll Tails, Heads tails don't win, since you chucked out the heads. It's now Tails-head with the advantage. If it comes up Tails again, then it's back to no advantage to either side. And you always flip with heads up.
You can get a lot closer to 50:50 by flipping two coins, one starting on heads and the other on tails, and calling whether they will both land the same way up as each or not. The chances of them landing the same way up are 2*(0.51*0.49)=0.4998.
feinman's coin flip says to flip twice and if outcomes are same - reflip otherwise choose first (or last) of the two that ensures 50:50 no matter the bias (still has trouble with correlations)
@@NoNameAtAll2No, that only works for unfair flips where p(heads) =/= p(tails). It doesn't work with p(same side) =/= 50٪. If the coin starts heads, heads tails has p(same) * p(different) odds, or .51*.49. If the coin starts heads, tails heads has p(different) * p(different) odds, or .49*.49, which is a lower chance.
@@autumn4442 It still works then, you can just redeclare heads to be when the coin landed on the same side it was initially and tails as when it changes sides when you flip it.
@@flameofthephoenix8395 Yeah, I realized that later in a different comment I made to someone making the same observation as the person I was responding to. Someone else also suggested always starting the next flip with heads up, that way you deal with p(tails|heads start) and p(heads|heads start). Since you always start with heads up regardless of the previous flip result, it returns to the same problem/solution as simple unfair coins between heads and tails
I remember when this paper first came out. All the paper did was convince me that the researchers didnt know how to flip a coin. As long as you can actually flip the coin wobble will be totally irrelevant. If you have a decent coin, you can clearly hear when you've flipped it properly and when you've screwed it up. The height of your catching hand vs. the peak height of the coin and the rotational (flipping) speed are going to be the determining factors. They are NOT going to be controlled or predictable in real life. They are the random action. The coin is just a means of measuring it.
But doesn't the fact that more people much smarter than you support the paper prove that you're just ranting online? And also, you can OPENLY look up people who are experts in coin flips and dice throws to get EXACTLY the outcome they want, and they use "wobble" to their advantage, and YES, they CAN predict when and where to put their catching hands to get what they want or throw how hard with how much "spin" or "wobble"
@@acmhfmggru my question was how do you plan to check. do you plan to ask someone to perform 5 before allowing them to do one that decides something? is the deciding flip not valid if it doesnt make a ringing sound?
I agree. The whole premise of the argument is that in the flip you introduce radial spin that provides a slight gyroscopic element that makes the coin less likely to flip over. If you flip it properly, flicking the edge so that the coin does indeed rotate heads over tails I still believe that's going to be random as the coin will spin heads over tails multiple times in flight. The slight radial spin is just not going to matter.
Something else to throw in here. The physics result of unintentional bias is for a defined axis of rotation through the face of the coin. However, there's another form of intentional bias that results from the rotational speed of the flip using an axis across the coin, not through its center. With a little practice, you can deliberately determine the flip result with a nearly 100% accuracy. I used to do this with my students all the time. Show them the coin, including its face. Ask them to call the toss before the toss, then control the toss's flip speed to affect the outcome - always coming up opposite of what they called. (I think I lost a handful of times over a decade)
Tradionally in soccer, the coin is flipped caught in the hand and then placed on the back of the other hand for the reveal. Which means the the 51% bias up face, becomes the down face. ❤ Surely this bias depends on the height the coin is flipped and how far it drops. In American football the coin is tossed and lands on the ground, so there are probably more time for turns there.
Back when I was younger, I was able to make a coin almost always land on the same side by flicking it in such a way where it would wobble without actually flipping (it would look like it was flipping to the naked eye, but it wasn't). It’s been many years, but I believe I recall it involving flicking such that your thumb skims the edge of the coin in a somewhat outwards motion. There is most definitely an amount of precision required for it.
That's really cool! I am able to make a fully spinning coin land on one side most of the time, (practiced doing one rotation, up to five which is believable), but can only do it with quarters since different sized coins are too tricky. Yours seems way more versatile
i think you were trying to rotate the coin vertically while it is in a slanted position (not perfectly flat). As it rotates, it looked like it wobbled. Kinda like those beyblade toys that wobble when slowing down.
@@mlthornton1 i guess technically but due to the connotation of those words more detail and context is added (or implied) as a result of them being used. Strictly speaking denotatively, you are right.
I liked your suggestion about dealing with unfair coins from your other coin-flipping video where you flip it twice (with the same side starting up based on this research). If you get heads followed by tails, it's Heads. If you get tails followed by heads, it's Tails. If you get two of the same, then the bias kicked in, and you should throw out that result. I always like thinking of this as the first flip being "provisional", and the second flip confirming the validity of the provisional flip by returning the opposite.
Not bad. There will still be a bias as (.495)^2 + (.505)^2 i not equal to 0.5. But that is pedantry in practice, it is much much closer: 50.005% instead of 51%
@@hippophile I think you got your math wrong there; what you calculated is the odds of flipping a coin twice and getting either HH or TT, but that doesn't matter for this scenario. They're talking about this process: 1) Flip a coin twice 2) Check if the results are different 2a) If they're different, take the first value 2b) If they're the same, ignore this result and go back to step 1 For a coin whose flipping has probability p of returning heads and probability (1-p) of returning tails, the chance of getting heads followed by tails is (p(1-p)) = p-p^2, and the chance of getting tails followed by heads is ((1-p)p) = p-p^2. That means that no matter the actual value of p, if you flip the coin twice then the odds that you got "heads and then tails" is equal to the odds that you got "tails and then heads". And the odds that you got "heads and then heads" or "tails and then tails" doesn't matter for the fairness of the result, because if you get either of those then you just flip the coin two more times instead.
Unfortunately, that method doesn't work for this type of unfairness. To fix it, you have to know the starting orientation, then one person calls same as initial position & different from previous flip, and the other calls different from initial flip, but same as the previous flip. If the coin starts heads, one person calls heads tails, while the other person calls tails tails.
@@autumn4442 The Von Neumann doesn't work for serially correlated data at all. It's a debiaser for uncorrelated data. This is explained in the original paper, but the improved version (The Yuval Peres debiaser) is a lot more explicit and the paper is easier to find. Take SCC=-1 data "0101010101010101" the output is 00000000. It failed to debias it because it's serially correlated. So the Von Neumann debiaser is not a good algorithm to use for this kind of statistical property.
You can always bias it in your favor if you're flipping, because you can either catch it, or catch it and then flip it on the back of your other hand, making the other person's choice meaningless.
I'm SO happy a paper was finally written on this subject. I had a friendly, but extended debate with my teacher in high school about this part of this subject: My argument: Flipping a coin cannot possibly be a true 50/50 chance. The reason we believe or assume so, is because calculating or counting the number of spins a coin makes before hitting the ground is incomprehensibly complex for us to do in such a short period of time. We just agree it's 50/50. The counter argument is that "flipping a coin" in the abstract sense is always 50/50, as that's what the example is there to demonstrate. The conclusion is that they don't contradict each other: It's just that inconclusively stating something as fact, even observed from the perspective of something as "pure" as math, is extremely difficult. Which is why I'm so happy someone did a paper on this! Having geniuses define and describe the very thing my high school brain was trying to comprehend is incredibly cathartic!
"It's too complex, therefore it can't be X" is not a solid argument... You were right but, ironically, you could just as accurately have arrived to that conclusion by flipping a coin 😅
@@BillyViBritannia The argument isn't that the action "is too complex" - it's that our perception of it is. For example, if I were to flip a pineapple pizza instead of a coin - would you say there an equally likely chance of the throw being fair? Probably not, for reasons that should be intuitive. Those reasons are why we agree a coin is "random" - because we perceive it as "too complex" - while reality is different. Whereas flipping a pizza isn't "random" but it depends on the person throwing the pizza.
@@nivyan the fact that reality is or isn't complex says nothing about the probability of a random (for all intents and purposes) event being 50\50. The mechanism may be complex and non deterministic like the spin of a particle or it can be simple like a person flipping a switch. In either case the probability of either outcome could very well be 50% Where I disagree with you is that regardless of whether the coin flip, the pizza or anything is or isn't easy enough to calculate, that alone is no reason to reject the 50% hypothesis. And in fact when you are not sure it's the best guess.
@@BillyViBritannia We don't disagree about the points you're making. My point is about how we perceive something. My point is that, in reality, it's impossible to replicate a perfectly 50/50 coin. Because you'll eventually flip the coin in a way where it lands on its side - standing up. It's extremely improbable, but that one throw makes the 50/50 impossible. This has been demonstrated on video on many occasions (mostly in uncontrolled environments, because why would you test that?). That's the "reality" of flipping a coin - that we perceive it as a perfect 50/50 throw and or consider it to perfectly overlap with theoretical probability - but it just doesn't. Alternative example for clarity: Even if you were to program a piece of software that spits out a random number - it's still not random. It's determined by whatever the algorithm does to spit out that number. The reason we PERCEIVE it as random, is because that algorithm is too complex for a normal human to understand.
With practice you can actually flip a coin consistently so it spins the same number of times before catching. It only spins at like 5 revolutions per second so you need to catch it with an accuracy of 100ms. Very doable.
With practice you can do a terrible, fake flip, yes. Or you can properly flip a coin and have it flipping several dozen times per second and ringing like a bell.
I DO remember a paper about 10 years ago or so predicting this going over the physics and calculations and said that it would need flips above 250,000 to be able to detect and prove. Never realized there was a team that ACTUALLY DID IT. edit: Just saw the video description, I guess it was more than 10 years ago. I went back and saw that it was referenced in text in the video. wish it was mentioned in the voiceover too
Technically, it's not a bias, it's serial correlation. The bias is 50/50 over a large number of tosses. But there is bias conditioned on the previous toss which is what binary serial correlation is.
No. The bias is towards the face that's up just before the toss not towards the previous flips outcome. He only says that bit at the beginning because he assumes that you when you pick the coin up after a toss, you put it the same side up. You can then say that the coin is biased towards the previous outcome which is not strictly true
@@feliksporeba5851A single flip doesn't have a measurable bias. Over a large number of flips, the bias would approach 0.5 but the serial correlation could be easily computed.
@@Trizzer89 Serial correlation is exactly what the paper described. The tendency for the next result to be the same as the previous (positive SCC) or different to the previous (negative SCC). SCC tests measure that tendency and gives it a number from -1 to +1 with 0 being no SCC (serial correlation coefficient). See Knuth's books for a full definition, or my book on the topic (Random Number Generators - Principles and Practices). If the coin on your thumb is 50/50 uniformly randomly placed then the outcome is also 50/50 because you don't know the starting state. If you do know the starting state then you can predict the next with slightly higher chances of being right. Over many coin flips, where the landing state is also the starting state of the next flip, the average outcome over time will be 50/50, but with small positive SCC (which is what the paper describes) you would expect to see the distribution of runs (sequences of the same value) be skewed towards longer sequences. If you know the starting state of a single flip, you would be able to predict the next one so you could call that bias, but over many flips where you don't control the starting state, the average will be 50/50 while the predicability of the next flip will remain 49/51 when you know the starting states.
This must have been inspired by one of the recent top Hacker News articles. One of the comments said that a way to negate this is to do flips in groups of two. When you eventually get to a group of two that is not the same (heads-tails, or tails-heads) then you take the first flip of that group as the result.
Although I can see that a manual coin flip is an inexact operation, and so may not give a 50% chance of the coin landing the other way up, the actual deviation from 50% surely depends on the coin-flipping technique: Coins more accurately flipped will give a probability of either face closer to 50%. It depends on how close the initial spin axis of the coin is to one of its principal axes of rotation; if your flip is closer to throwing the coin like a Frisbee you will get a higher probability of same-side results. All this really shows is that the chance of a same-side result is at least 50%. So I put the same amount of trust in that 51% figure as I do in results from people who have demonstrated that bread really does fall butter-side down, but whose results are only valid for a certain range of table heights.
In science something isn't statistically significant until there's a 5% difference. So it being merely 50.8% means it doesn't come close to being statistically significant. That and like you said, it's an inexact operation. Many people will flip it in many different ways at many different speeds. And skilled ones can actually manipulate the result in their own favor.
@@thenonexistinghero That's now how statistical significance works, at all. Something is considered statistically significant if there is a 5% chance or less that the difference between two groups is due to chance alone. Or in other words, a 95% chance that the difference between two groups is due to an actual, existing difference. You calculate a p value to determine this. p < 0.05 is considered significant. 50.8% vs 49.2% over a sample of 300k trials is MASSIVELY statistically significant. I bet their p value was < 0.001 - less than a 1 in a thousand chance that the results were due to chance alone.
This actually gives me more questions than it answers. First of all, how were the coins flipped? Just so that they land on the flooror so that they're caught in the air and then turned around on the other hand? How strongly did they snap the coin at the start? This influences how many turns it will make in the air. How high did they throw the coin? And so on, and so forth. I think it would be more telling if there mere more different testers, than if few testers make a lot of throws but always with the same method.
@@djcortex8635 No need to read the paper, it's a sham. First of all, a statistical difference of 0.8% is nothing and falls well within the margin of error (something is not statistically significant until there's a difference of about 5%). Second, coins are tossed in many different ways by many different people and at many different speeds. And 3rd, if you're really good you can actually achieve the result you're aiming for a lot of the time by tossing the coin in almost exactly the same way with the same force every time (and yes, there's also research that proves people can do this. Even ones that aren't that skilled can still get their preferred result over 2/3rds of the time). Statistically in perfect testing conditions the chance of getting a result that's the same side as the one you toss might be 50.8%, but in reality that's not the case at all. Betting on the same side that's up doesn't give you an advantage. It's crock 'scientists' like this that ruin actual science.
You can also know with near 100% accuracy whether a coin will show heads or tails when you spin it on a flat surface. Just watch the coin closely as it spins and you'll see one side much more often than the other. That's the side that will be up when it stops spinning. My hypothesis for why that works is that the coin never spins perfectly perpendicular to the surface. The side that has the obtuse angle to the surface is either lighted better or is angled so that it's easier to see or some combination of both. Since the coin is already leaning that way, it will continue like that until it stops, with the obtuse angle getting larger and larger as time passes. Finishing with that side up is effectively inevitable.
Randomness is tricky! Definitely DON'T use a computer simulated coin toss to eliminate bias -- you just get a different kind of bias. The simple truth is that there is nothing in nature that is 'unbiased' -- we shouldn't waste our time with questions like: "Is this random?" and instead ask "Is this random enough?" A single 50/50 decision (like who gets the slightly bigger piece of cake, or what team starts with the ball) can be confidently handled with a coin toss from most coins. Just remember to call it in the air-- Heads I win, Tails you lose!
You can simulate randomness using a computer to the degree of randomness you require. There are several excellent statistical tests for randomness. Write your own algorithm to generate the random numbers and test the generated series. When you are satisfied make up a good method to ensure that the seed is never the same. The possibilities are endless.
I used the "heads I win, tails you lose" thing when calling a coin toss bet in New World (back in the initial period of popularity after the game released). The person I was betting against agreed to play, and when he realized after the toss, he still paid me for making him laugh 😂
Unfortunately, what is often not made clear in the media is that the tendency to land on the same side is not a property of the coin, but rather a property of the thrower. When I plotted the results in a funnel chart, I noticed that 14 of the 48 individual results, or 29%, were outside the 95% CI at p = 0.508. In my opinion, the funnel plots illustrate the bias in each experiment quite well. In particular, a graph for p = 0.5 shows that there is no tendency to throw to the other side.
Job interview: What was your last job and how long have you worked there? I was flipping coins in the past 2 years. 5000 coin flips a day. I was quite good at it.
to add onto this. If you build a physical coin flipping machine, you can configure it to flip the coin to land on the side you want with 100% accuracy. Same applys with humans flipping the coin if they know special techniques Coin flips randomization is like computer randomization, it's not actually random, it's based off an inputted seed. if you input the same "seed", you get the same output.
This makes sense since there is a way to “flip” a coin and force it to land on the same side as it started. With enough practice you can get really good at making the coin appear to be flipping but in reality it’s just wobbling.
I can prove that a coin is not 50/50 quite easily. There is a real, but rare, chance for the coin to land on it's edge. Thank you for coming to my TedTalk
The test was done flipping the coin and catching it, with a 51% chance of landing the same side. But, the common coin tossing method is: when you catch the coin you then then turn your hand over and place the coin on the back of your other hand. The coin is being turned over one last time. Is that taken into consideration?
Is it also possible that one side of a coin is slightly heavier than the other side because of the different images having more or less material than the other? One could impress both sides of the coin in modelling clay, fill the impression with water then weigh the water to see if they are equal.
The paper linked in the description shows 175,420 heads in 350,757 tosses. There were multiple currencies and denominations, so any bias to the heavier side would have been canceled out by variation in which side is heavier on, for example, a nickel vs a quarter. That said, I suspect the weight and aerodynamic differences of the faces would be very small. The citation for a lack of heads tails bias is: Gelman A, Nolan D. You can load a die, but you can’t bias a coin. The American Statistician 2002; 56(4): 308-311 But I'm too lazy to hunt down the web link :)
One way of looking at why there may not be much of a bias for such things is to look at how the leverage works in the system. The faces of the coin are very close to the center plane of the coin, and to each other, so they don't really have much leverage to be able to pull the coin one way or another. The difference in forces between the slightly heavier side being up and it being down don't really make the system unstable enough to flip the coin around.
There was a lesser-known study of this with different results. They performed over 350,000 coin tosses _in a zero-gravity environment._ Now, there are over 350,000 coins lost in space.
I think I should confess, I've always known that coin toss are predictable in it's outcome. That's why I learned the muscle memory so that the coin will always land on the desired side, but I never told anyone before.
You appear to have misunderstood the physics. There isn't an inherent bias if the coin is flipped. The bias is in whether or not the person who is supposed to flip the coin is coordinated enough to actually flip the coin or whether they just toss it upwards without providing a large enough flip to get it rotating around its diameter. So, the lesson is to teach people whose job it is to flip a coin to actually impart 'flip' along with the initial vertical velocity.
Yes. All that paper did was prove some nerds didn't know how to flip a coin. They were throwing coins up and watching them wobble. A proper flip will have a coin ring out like a bell.
Would you consider this effect "essentially" negated by tossing 3 times, throwing out the first two? You would of course keep the orientation when you flip #2 & #3 from the results of the previous throw. If 0.8 is the advantage, what would you estimate the advantage would be on the 3rd throw?
Somewhat similar to what you suggest, von Neumann came up with an elegant solution for how to get fair results from a biased coin. The procedure is as follows: 1. Toss the coin twice. 2. If the two coin flips match, start over, forgetting both results. 3. If the two coin flips differ, use the first result, forgetting the second. Since a biased coin still produces independent results from trial to trial (i.e., no autocorrelation between trials), the process produces a fair result (50% of calling Heads or Tails) because a the probability of flipping Heads then Tails is the same as the probability of flipping Tails then Heads.
@@davetannenbaum I'm not statistician but to me that only sounds fair if you enforce the same starting position for both throws. Because the probability of same + different is the same as different + same. But If you just use the side it landed on for the second throw, then it becomes same + different vs. different + different, which isn't fair.
There are two problems with the study that is behind this. The biggest is that the people who tossed the coins knew the predictions of the theory that was under test. Their unconsciously acting to bias the outcome is probable, as it is almost impossible not to bias it under such test conditions. Secondly, some people actually do toss the coin in such a way that it is unbiased by starting position, ie. 50/50. So what this shows, if unconscious biasing of the outcome is not in play, is that just as some people are good at golf, or any physical activity, and others are bad at it, some are bad at flipping coins fairly and others are good at it. We might have thought everyone was equally good at it, but either they are not, or those who are bad at it are because they unconsciously wanted to see the theory verified and somehow slightly tilted the outcome in that direction.
Also, if you’re the one flipping the coin, and the other person chooses the face-up direction, you can also just choose the catch method. I see some people catch the coin and then that is the result, but some people also put it onto the back of the other hand, flipping it in the process, so as the flipper, you can choose which side gets the bias
When I was a kid, I had an 80% chance of getting the same face when I caught the coin mid-air with a slap. I knew coin toss was not fair. I won several bets this way
"Bias" is an understatement. 0:55 shows "...With careful adjustment, the coin started heads up always lands heads up-one hundred percent of the time." this meant the coin, in the right condition, could be manipulated 100%.
I'm not sure I understand. If you flip a coin, it will rotate. If you do not let it fall to the ground but catch it in the air, you catch it mid-rotation, so it does not matter how it would have landed. The wobble introduced can not possibly mean that at any point of it being airborne, the probability of it being the same side you started with is higher, can it. So what gives?
Considering how many times I or even anyone used a coin flip to decide something, I'd say it's a pretty good research. Newton got hit by an apple and that was his inspiration. The point of research is to look into everything.
You actually want to pick the opposite of the side shown. Because when the coin is caught in the hand most people flip it over onto their other hand changing the side
There are several comments that flipping a coin twice is fair, regarding TT + HH as one outcome and TH + HT as the other. In fact, there will still be a bias as (.495)^2 + (.505)^2 i not equal to 0.5. But that is pedantry in practice, it is much much closer: 50.005% instead of 51%
What is the p-value? In coin flipping for NFL football games the coin hits the ground which means that the coin can bounce, which should re-randomize the odds.
Important to know though, if you're the one making the toss, whether the catcher will flip the coin after catch or not. If they do, then you should pick the opposite side as it will more likely land same side. And if you are the flipper, then just do or do not decide to flip after the catch depending on if they pick same side or not, as long as it's not agreed upon beforehand.
The way that coins are tossed here is that they are tossed, caught and then turned over onto the back of the hand. That would give a bias to the opposite side.
does the engravings and carvings on the design of the two sides of the coin affect how it flips? like a standard quarter might have a slightly different bias from a nickel or one of the state quarters because of differences in a cut.
Given the fineness of detail on the average coin face, any effect on its aerodynamics is probably very minor; factors like the coin’s shape, its metal composition, and how worn it is probably have more of an effect on how fairly it flips. I’m no minter, though, so take all of this with a grain of salt.
It's probably just down to center of mass and moment of inertia to have notable effects. But I didn't read the paper so I'm not sure if either factor cancels out in the math somewhere.
Also remember that the coins themselves were fair. if the engravings would matter, than some of the coins should show a heads/tail bias. but they did not.
With practice, you can deliberately pizza spin a coin and get it to land same side up nearly 100% of the time. If I'm rigging a coin toss, I do this, catch the coin in one hand, and then slap the coin down on the back of my other hand to reveal it- when I transfer to the other hand, knowing which side was up when it landed in my palm, I just control which side shows up after the transfer based on what my opponent called. Because of this, I'm careful to say "we'll settle this with a coin toss" and not "coin flip", because I am tossing the coin, but I am not flipping it.
I think there is a way to counteract the problem. First,decide which person or group is heads and which is tails. Then you flip the coin twice. the first time you start the flip with heads facing up, the second flip, you start with tails facing up. If the result of the two flips is heads twice, whomever picked heads wins, if the result is tails twice, tails wins. If the result is mixed, you do the two coin flips the same way, and you repeat until you get either heads, heads or tails, tails.
start with heads up, then flip. if it’s heads, leave it heads up then flip again, if (the first flip) is tails, turn it heads up then flip. if the first flip is heads and the second flip is tails, side A wins, if the first flip is tails and second flip is heads, side B wins. any other scenario and you restart from scratch.
The physics must be interesting. Is a wobble more likely to create a type of gyroscopic effect that stabilises the coin's atitude and reduce the number of flips? Or are more complex things going on?
The comparison between coin tosses and pancakes is flawed. Pancakes don't flip 40 times in the air so the wobble can affect the bias to one flip. Coins will land on the same side if it flips an even number of times and the opposite an odd number of times. The wobble would create just as much bias for a coin to flip 32 over 31 times as there would bias for 33 over 32 flips.
This has always been my concern with coin toss. Which side do you start with? Who gets to toss the coin? Who gets to call it? And on the catch, do you flip it or alternatively, let it drop? Or do you toss a coin to answer the above questions?
At 2:15 it says the starting position of the coin was decided randomly. Why don’t we all just start using whatever that random decision process was, and forget about coins altogether? 😊
Actually, wouldn't you want to predict the opposite face in a coin toss? the experiment only had the tossers catch the coin, but when ever I have tossed a coin it is flipped at the end as I place the coin on the back of my other hand, concealing it with the catching hand.
coins being tossed then caught are always caught at a different height, this causes differing results and throws off the perceived bias. a person's muscle control might flip the coin more times than previous, so would their tiredness. you would need a machine to flip the coin with a consistent amount of force, then allow the coin to land on the same flat surface and settle on its own.
I spent weeks in middle school practicing flipping a coin to make it look like it was flipping when it reality it was just spinning while remaining with the same face up. It worked about 60% of the time. Won a lot of bets.
Interesting! I did a bit of another thing at about the same age. I have found, that with the right size of the coin (15-20 mm in diameter) and training you can just capture the coin at the right time from the air to get the desired result. Somehow I managed to make ~80 percent same-side captures and ~60 percent other-side captures (in comparison with initial orientation).
Know what I do is, when I catch the coin out of the air I try to catch it while swiping my hand towards my face so I have a split second to glimpse how it is resting on my palm. Then you can either open your hand and reveal the coin as is or open your hand sort of tilted down so that the coin flips onto your fingers. Works nearly every time @@man0fstraw
is that 60% of the time getting the result you wanted, or 60% of the time getting the technique right with a 40% chance for it to be an honest coin flip?
Good question. Its a fine line because if you want the coin to look like it's flipping you have to toe the line between a spin and real, fair flip. So I would say that it was more that 60% of the time the technique worked well enough that it looked like a convincing coin flip while still being reliably on the side I wanted. The other 40 percent was split evenly between it either not look convincing enough or it flipping so that I couldn't tell which side it would land on. @@catkook543
Me, I used a half dollar.
Since the heads side is smoother than the tails side, I would flip the coin, often as high and as rapidly spinning as possible, telling my mark to "call it in the air." I make a show of catching the coin, then I open my hand to reveal that the person guessing got it wrong.
Of course, when I catch it, I can tell which side is facing my fingers. I practiced making the motion of opening my hand almost perfectly identical, but I could control which side came up.
Making them figure out how I did the trick was the most fun for me, especially as after the second or third go, almost every guy will wind up suckered into having to try to win.
So, in order to make a coin toss fair, you just have to not look at the starting state XD
Which is just what he says at 3:26
Just flip a coin to determine the starting state 😂
Schrödinger's Coin
No.
First you need an ACTUAL fair coin (that is not slightly heavier on one side or that has a bias in air resistance).
Then you need to flip it in a fair way.
And even then, there is likely to be a very small bias.
But this bias is small even in the case of an unbalanced coin - generally within the margin that cannot easily disprove the null hypothesis.
Spinning a coin is even more unfair, as it magnifies the weight effect.
@@eurovisioncyan9550GMTA
I recall reading many years ago that most coins do have a bias because heads/tails are not perfectly symmetrical, with 1 side slightly heavier. However, this bias appears at the 1 part in 10k-100k level, so is completely drowned out by the same side bias.
Thst bias only happens when spinning a coin, not flipping it
wrong
Right. I find this video uncompelling
@@mlthornton1 Doesn't matter what you think, this is not a matter of opinion. Statistically, it's compelling enough to matter and consider when flipping a coin.
@@GamestaMechanicthink critically my friend. This "experiment" was run by people. But SCIENCE! you say. Sure. If you say so
I'm a soccer referee and this will actually change the way I do the coin flip. I kind of knew that there was a face up bias, but I never thought through my mechanics to hide the coin before the flip. Now it'll be a little more fair. 2% more.
your changes actually make it less fair for the disadvantaged teams because without your changes, their disadvantage would have been an advantage instead
@@itskittymewhat
@@itskittyme nvm she edited the comment now it doesn't make sense
You could even shake it around in your hands where no one can see it and then flip the coin from cover so it's only revealed for an instant, making it extremely difficult to spot.
@@itskittyme A coin toss is intended to randomly select from between two options. "Fair" in a coin toss means it has an equal chance of landing heads or tails. The closer you can approach to exactly even chances the more fair it is, by definition. Losing an unintended advantage is not "less fair," it's more fair.
A note on coin flip strategy - some people routinely flip the coin upside down (usually catching the coin and then slapping it face down on the back of their other hand) - in that case you should bet on the opposite side instead
And because you usually don't know if the other person does this, the flip ends up being fair out of the randomness from this factor alone
@literallybest4482 Which is why the person flipping the coin should ask the other person if they wish to pick heads or tails after the flip
That is a George Castanza. When everything do do always comes out wrong, do the opposite of what you usually do and your winning streak will be😅 endless.
As a magician in my youth, I spend a lot of time learning how to make a cointoss look fair when in fact I controlled the result. It was this exact wobble effect..
You can make the coin toss a little more complicated to ensure that it's fair:
Flip the coin two times. If it shows heads-tails, you win. If it shows tails-heads, your opponent wins. If it shows the same side twice in a row, repeat the process. That way, whatever the probability p of heads is, your chance of winning is p*(1-p), while your opponent's chance is (1-p)*p.
this does'nt work.
lets assume heads is up and I win with heads-tails you win with heads-tails. i am gonna assume that the 51% figure shown here is correct
i have 0.51*0.49 chanse to win
you have 0.49*0.49 chanse to win
In the case of a reroll i am also more likely to have adventge in the next flip
the chanse for head-heads is 0.51*0.51
the chanse of tails-tails is 0.49*0.51
And to add to that, you should do it in a liquid like water.
@@נירמנחמי
No, if you have the same side up in the re-roll as initial side up, then it is the same for both!
Say, we begin with "Heads" up.
I win if it is HT and you win if it is TH
Now, if you keep heads up in the re-roll too, then my chances of winning are :
0.51 * 0.49
(according to the video's probability)
And your chances of winning are :
0.49 * 0.51
So our chances are equal! Fair.
P(HT) = 0.49*0.51 = P(TH)
P(HH) = (0.51)²
P(TT) = (0.49)²
@@dhruvgupta6389 you are assuming independent probability. You ignore the fact that the result of the second flip is effected by the result of the first
@@נירמנחמי The key is you don't just re-roll the Duplicate, you chuck them BOTH out and start from scratch. EG. if you roll Heads, then roll Heads again, then roll Tails, Heads tails don't win, since you chucked out the heads. It's now Tails-head with the advantage. If it comes up Tails again, then it's back to no advantage to either side. And you always flip with heads up.
You can get a lot closer to 50:50 by flipping two coins, one starting on heads and the other on tails, and calling whether they will both land the same way up as each or not. The chances of them landing the same way up are 2*(0.51*0.49)=0.4998.
feinman's coin flip says to flip twice and if outcomes are same - reflip
otherwise choose first (or last) of the two
that ensures 50:50 no matter the bias (still has trouble with correlations)
@@NoNameAtAll2Not If u make the same starting position, that means make all throws with the same side up at start
@@NoNameAtAll2No, that only works for unfair flips where p(heads) =/= p(tails). It doesn't work with p(same side) =/= 50٪.
If the coin starts heads, heads tails has p(same) * p(different) odds, or .51*.49. If the coin starts heads, tails heads has p(different) * p(different) odds, or .49*.49, which is a lower chance.
@@autumn4442 It still works then, you can just redeclare heads to be when the coin landed on the same side it was initially and tails as when it changes sides when you flip it.
@@flameofthephoenix8395 Yeah, I realized that later in a different comment I made to someone making the same observation as the person I was responding to.
Someone else also suggested always starting the next flip with heads up, that way you deal with p(tails|heads start) and p(heads|heads start). Since you always start with heads up regardless of the previous flip result, it returns to the same problem/solution as simple unfair coins between heads and tails
I remember when this paper first came out.
All the paper did was convince me that the researchers didnt know how to flip a coin.
As long as you can actually flip the coin wobble will be totally irrelevant. If you have a decent coin, you can clearly hear when you've flipped it properly and when you've screwed it up.
The height of your catching hand vs. the peak height of the coin and the rotational (flipping) speed are going to be the determining factors. They are NOT going to be controlled or predictable in real life. They are the random action. The coin is just a means of measuring it.
Yeah like what does wobbling have to do if it's gonna flip
But doesn't the fact that more people much smarter than you support the paper prove that you're just ranting online?
And also, you can OPENLY look up people who are experts in coin flips and dice throws to get EXACTLY the outcome they want, and they use "wobble" to their advantage, and YES, they CAN predict when and where to put their catching hands to get what they want or throw how hard with how much "spin" or "wobble"
@BrianStewart126 wait, explain to me how you plan to check if someone "can actually flip the coin" and "flipped it properly"?
@@acmhfmggru my question was how do you plan to check. do you plan to ask someone to perform 5 before allowing them to do one that decides something? is the deciding flip not valid if it doesnt make a ringing sound?
I agree. The whole premise of the argument is that in the flip you introduce radial spin that provides a slight gyroscopic element that makes the coin less likely to flip over. If you flip it properly, flicking the edge so that the coin does indeed rotate heads over tails I still believe that's going to be random as the coin will spin heads over tails multiple times in flight. The slight radial spin is just not going to matter.
Something else to throw in here. The physics result of unintentional bias is for a defined axis of rotation through the face of the coin. However, there's another form of intentional bias that results from the rotational speed of the flip using an axis across the coin, not through its center. With a little practice, you can deliberately determine the flip result with a nearly 100% accuracy. I used to do this with my students all the time. Show them the coin, including its face. Ask them to call the toss before the toss, then control the toss's flip speed to affect the outcome - always coming up opposite of what they called. (I think I lost a handful of times over a decade)
Very important for when I go on a coin flipping marathon competition with my friend
Tradionally in soccer, the coin is flipped caught in the hand and then placed on the back of the other hand for the reveal. Which means the the 51% bias up face, becomes the down face. ❤
Surely this bias depends on the height the coin is flipped and how far it drops.
In American football the coin is tossed and lands on the ground, so there are probably more time for turns there.
Back when I was younger, I was able to make a coin almost always land on the same side by flicking it in such a way where it would wobble without actually flipping (it would look like it was flipping to the naked eye, but it wasn't). It’s been many years, but I believe I recall it involving flicking such that your thumb skims the edge of the coin in a somewhat outwards motion. There is most definitely an amount of precision required for it.
That's really cool! I am able to make a fully spinning coin land on one side most of the time, (practiced doing one rotation, up to five which is believable), but can only do it with quarters since different sized coins are too tricky. Yours seems way more versatile
i think you were trying to rotate the coin vertically while it is in a slanted position (not perfectly flat). As it rotates, it looked like it wobbled.
Kinda like those beyblade toys that wobble when slowing down.
"Back when I was younger" a bit redundant eh? 😉
@@mlthornton1 haha true
@@mlthornton1 i guess technically but due to the connotation of those words more detail and context is added (or implied) as a result of them being used. Strictly speaking denotatively, you are right.
Heads I win, tails you lose
Unoriginal, but funny.
@@auserwitha404original but unfunny
Unoriginal but unfunny
I liked your suggestion about dealing with unfair coins from your other coin-flipping video where you flip it twice (with the same side starting up based on this research). If you get heads followed by tails, it's Heads. If you get tails followed by heads, it's Tails. If you get two of the same, then the bias kicked in, and you should throw out that result. I always like thinking of this as the first flip being "provisional", and the second flip confirming the validity of the provisional flip by returning the opposite.
That is the Von Neumann debiaser algorithm.
Not bad. There will still be a bias as (.495)^2 + (.505)^2 i not equal to 0.5. But that is pedantry in practice, it is much much closer: 50.005% instead of 51%
@@hippophile I think you got your math wrong there; what you calculated is the odds of flipping a coin twice and getting either HH or TT, but that doesn't matter for this scenario. They're talking about this process:
1) Flip a coin twice
2) Check if the results are different
2a) If they're different, take the first value
2b) If they're the same, ignore this result and go back to step 1
For a coin whose flipping has probability p of returning heads and probability (1-p) of returning tails, the chance of getting heads followed by tails is (p(1-p)) = p-p^2, and the chance of getting tails followed by heads is ((1-p)p) = p-p^2. That means that no matter the actual value of p, if you flip the coin twice then the odds that you got "heads and then tails" is equal to the odds that you got "tails and then heads".
And the odds that you got "heads and then heads" or "tails and then tails" doesn't matter for the fairness of the result, because if you get either of those then you just flip the coin two more times instead.
Unfortunately, that method doesn't work for this type of unfairness. To fix it, you have to know the starting orientation, then one person calls same as initial position & different from previous flip, and the other calls different from initial flip, but same as the previous flip.
If the coin starts heads, one person calls heads tails, while the other person calls tails tails.
@@autumn4442 The Von Neumann doesn't work for serially correlated data at all. It's a debiaser for uncorrelated data. This is explained in the original paper, but the improved version (The Yuval Peres debiaser) is a lot more explicit and the paper is easier to find. Take SCC=-1 data "0101010101010101" the output is 00000000. It failed to debias it because it's serially correlated. So the Von Neumann debiaser is not a good algorithm to use for this kind of statistical property.
You can always bias it in your favor if you're flipping, because you can either catch it, or catch it and then flip it on the back of your other hand, making the other person's choice meaningless.
Just have someone random flip it
I'm SO happy a paper was finally written on this subject. I had a friendly, but extended debate with my teacher in high school about this part of this subject:
My argument: Flipping a coin cannot possibly be a true 50/50 chance. The reason we believe or assume so, is because calculating or counting the number of spins a coin makes before hitting the ground is incomprehensibly complex for us to do in such a short period of time. We just agree it's 50/50.
The counter argument is that "flipping a coin" in the abstract sense is always 50/50, as that's what the example is there to demonstrate.
The conclusion is that they don't contradict each other: It's just that inconclusively stating something as fact, even observed from the perspective of something as "pure" as math, is extremely difficult.
Which is why I'm so happy someone did a paper on this! Having geniuses define and describe the very thing my high school brain was trying to comprehend is incredibly cathartic!
"It's too complex, therefore it can't be X" is not a solid argument...
You were right but, ironically, you could just as accurately have arrived to that conclusion by flipping a coin 😅
@@BillyViBritannia The argument isn't that the action "is too complex" - it's that our perception of it is.
For example, if I were to flip a pineapple pizza instead of a coin - would you say there an equally likely chance of the throw being fair? Probably not, for reasons that should be intuitive.
Those reasons are why we agree a coin is "random" - because we perceive it as "too complex" - while reality is different. Whereas flipping a pizza isn't "random" but it depends on the person throwing the pizza.
@@nivyan the fact that reality is or isn't complex says nothing about the probability of a random (for all intents and purposes) event being 50\50.
The mechanism may be complex and non deterministic like the spin of a particle or it can be simple like a person flipping a switch. In either case the probability of either outcome could very well be 50%
Where I disagree with you is that regardless of whether the coin flip, the pizza or anything is or isn't easy enough to calculate, that alone is no reason to reject the 50% hypothesis. And in fact when you are not sure it's the best guess.
@@BillyViBritannia We don't disagree about the points you're making. My point is about how we perceive something. My point is that, in reality, it's impossible to replicate a perfectly 50/50 coin. Because you'll eventually flip the coin in a way where it lands on its side - standing up. It's extremely improbable, but that one throw makes the 50/50 impossible. This has been demonstrated on video on many occasions (mostly in uncontrolled environments, because why would you test that?).
That's the "reality" of flipping a coin - that we perceive it as a perfect 50/50 throw and or consider it to perfectly overlap with theoretical probability - but it just doesn't.
Alternative example for clarity: Even if you were to program a piece of software that spits out a random number - it's still not random. It's determined by whatever the algorithm does to spit out that number. The reason we PERCEIVE it as random, is because that algorithm is too complex for a normal human to understand.
Coin tosses are not fair.
Heads: I win. Tails: you lose.
With practice you can actually flip a coin consistently so it spins the same number of times before catching. It only spins at like 5 revolutions per second so you need to catch it with an accuracy of 100ms. Very doable.
I was actually capable of getting face almost every time back when I was playing Pokémon TCG. I was getting huge advantage with that
With practice you can do a terrible, fake flip, yes.
Or you can properly flip a coin and have it flipping several dozen times per second and ringing like a bell.
@@acmhfmggru I'll have you know my terrible dice throws aren't fake. I very naturally suck at throwing them.
It is the 50/50/90 rule.
If you have a 50/50 chance of getting something right there is a 90% chance you will get it wrong.
I DO remember a paper about 10 years ago or so predicting this going over the physics and calculations and said that it would need flips above 250,000 to be able to detect and prove. Never realized there was a team that ACTUALLY DID IT.
edit: Just saw the video description, I guess it was more than 10 years ago. I went back and saw that it was referenced in text in the video. wish it was mentioned in the voiceover too
Technically, it's not a bias, it's serial correlation. The bias is 50/50 over a large number of tosses. But there is bias conditioned on the previous toss which is what binary serial correlation is.
No. The bias is towards the face that's up just before the toss not towards the previous flips outcome. He only says that bit at the beginning because he assumes that you when you pick the coin up after a toss, you put it the same side up. You can then say that the coin is biased towards the previous outcome which is not strictly true
@@feliksporeba5851A single flip doesn't have a measurable bias. Over a large number of flips, the bias would approach 0.5 but the serial correlation could be easily computed.
Ackshuallly, no. Serial correlation would be independent of how you place the coin on your thumb
@@Trizzer89 Serial correlation is exactly what the paper described. The tendency for the next result to be the same as the previous (positive SCC) or different to the previous (negative SCC). SCC tests measure that tendency and gives it a number from -1 to +1 with 0 being no SCC (serial correlation coefficient). See Knuth's books for a full definition, or my book on the topic (Random Number Generators - Principles and Practices). If the coin on your thumb is 50/50 uniformly randomly placed then the outcome is also 50/50 because you don't know the starting state. If you do know the starting state then you can predict the next with slightly higher chances of being right. Over many coin flips, where the landing state is also the starting state of the next flip, the average outcome over time will be 50/50, but with small positive SCC (which is what the paper describes) you would expect to see the distribution of runs (sequences of the same value) be skewed towards longer sequences. If you know the starting state of a single flip, you would be able to predict the next one so you could call that bias, but over many flips where you don't control the starting state, the average will be 50/50 while the predicability of the next flip will remain 49/51 when you know the starting states.
Who would have a thought real life coins are not perfectly symmetrical and thus not really 50/50 ? Color me baffled
This must have been inspired by one of the recent top Hacker News articles. One of the comments said that a way to negate this is to do flips in groups of two. When you eventually get to a group of two that is not the same (heads-tails, or tails-heads) then you take the first flip of that group as the result.
Although I can see that a manual coin flip is an inexact operation, and so may not give a 50% chance of the coin landing the other way up, the actual deviation from 50% surely depends on the coin-flipping technique: Coins more accurately flipped will give a probability of either face closer to 50%. It depends on how close the initial spin axis of the coin is to one of its principal axes of rotation; if your flip is closer to throwing the coin like a Frisbee you will get a higher probability of same-side results.
All this really shows is that the chance of a same-side result is at least 50%.
So I put the same amount of trust in that 51% figure as I do in results from people who have demonstrated that bread really does fall butter-side down, but whose results are only valid for a certain range of table heights.
In science something isn't statistically significant until there's a 5% difference. So it being merely 50.8% means it doesn't come close to being statistically significant. That and like you said, it's an inexact operation. Many people will flip it in many different ways at many different speeds. And skilled ones can actually manipulate the result in their own favor.
@@thenonexistinghero That's now how statistical significance works, at all. Something is considered statistically significant if there is a 5% chance or less that the difference between two groups is due to chance alone. Or in other words, a 95% chance that the difference between two groups is due to an actual, existing difference. You calculate a p value to determine this. p < 0.05 is considered significant.
50.8% vs 49.2% over a sample of 300k trials is MASSIVELY statistically significant. I bet their p value was < 0.001 - less than a 1 in a thousand chance that the results were due to chance alone.
50/50 is for ballanced coin. That means heads and tails have to be symetric and have same weight. For 1 PLN "eagle" side has about 52% chance to win.
So in other words, coin tosses are completely fair until somebody tells you how to make them unfair! 😂
This feels like watching speed runners:guys i saved 0.0001NS"
Like dam how would we ever recover from 51% vs 49%
This actually gives me more questions than it answers. First of all, how were the coins flipped? Just so that they land on the flooror so that they're caught in the air and then turned around on the other hand? How strongly did they snap the coin at the start? This influences how many turns it will make in the air. How high did they throw the coin? And so on, and so forth. I think it would be more telling if there mere more different testers, than if few testers make a lot of throws but always with the same method.
read the paper
@@djcortex8635 No need to read the paper, it's a sham. First of all, a statistical difference of 0.8% is nothing and falls well within the margin of error (something is not statistically significant until there's a difference of about 5%). Second, coins are tossed in many different ways by many different people and at many different speeds. And 3rd, if you're really good you can actually achieve the result you're aiming for a lot of the time by tossing the coin in almost exactly the same way with the same force every time (and yes, there's also research that proves people can do this. Even ones that aren't that skilled can still get their preferred result over 2/3rds of the time).
Statistically in perfect testing conditions the chance of getting a result that's the same side as the one you toss might be 50.8%, but in reality that's not the case at all. Betting on the same side that's up doesn't give you an advantage. It's crock 'scientists' like this that ruin actual science.
read the paper
read the paper
You can also know with near 100% accuracy whether a coin will show heads or tails when you spin it on a flat surface. Just watch the coin closely as it spins and you'll see one side much more often than the other. That's the side that will be up when it stops spinning.
My hypothesis for why that works is that the coin never spins perfectly perpendicular to the surface. The side that has the obtuse angle to the surface is either lighted better or is angled so that it's easier to see or some combination of both. Since the coin is already leaning that way, it will continue like that until it stops, with the obtuse angle getting larger and larger as time passes. Finishing with that side up is effectively inevitable.
I once witnessed a coin toss land on the edge. There were 50 people with their jaws on the ground in astonishment.
0:20 oh, you mean which of the Wright Brothers would fly the world's SECOND airplane? #teamDumont
👏👏👏
Please explain why “all sorts of other biases” are introduced if the coin bounces. That’s stated as fact but sounds unintuitive to me.
In fact, I am thinking that the bouncing is totally random and that might make it 50% chance of heads and tails. Similar to dies in casinos.
It was a gloss-over to conceal the fact that he actually has no idea
I have known this for 20 years. I always look at the coin before they toss it. My family doesn’t let me look at it anymore.
I’ve been flipping a coin with more than 51% success on same side for years ! Introduce even more horizontal spin by not flipping directly up !
I like how the order of the authors was decided by the number of coins flipped.
Randomness is tricky! Definitely DON'T use a computer simulated coin toss to eliminate bias -- you just get a different kind of bias. The simple truth is that there is nothing in nature that is 'unbiased' -- we shouldn't waste our time with questions like: "Is this random?" and instead ask "Is this random enough?" A single 50/50 decision (like who gets the slightly bigger piece of cake, or what team starts with the ball) can be confidently handled with a coin toss from most coins. Just remember to call it in the air-- Heads I win, Tails you lose!
qubit.
You can simulate randomness using a computer to the degree of randomness you require. There are several excellent statistical tests for randomness. Write your own algorithm to generate the random numbers and test the generated series. When you are satisfied make up a good method to ensure that the seed is never the same. The possibilities are endless.
@@fuglbird Isn't that what I said? "Don't ask if it's random, ask it's random enough" = "simulate randomness to the degree you require."
I used the "heads I win, tails you lose" thing when calling a coin toss bet in New World (back in the initial period of popularity after the game released). The person I was betting against agreed to play, and when he realized after the toss, he still paid me for making him laugh 😂
that’s what I always thought about coin tosses; if I flip a coin with the heads side facing up at a similar force every time, I usually get a heads
Unfortunately, what is often not made clear in the media is that the tendency to land on the same side is not a property of the coin, but rather a property of the thrower.
When I plotted the results in a funnel chart, I noticed that 14 of the 48 individual results, or 29%, were outside the 95% CI at p = 0.508.
In my opinion, the funnel plots illustrate the bias in each experiment quite well. In particular, a graph for p = 0.5 shows that there is no tendency to throw to the other side.
This 0.8% bias is not significant if you toss just once. Ignore this and live this life as previously
Job interview:
What was your last job and how long have you worked there?
I was flipping coins in the past 2 years. 5000 coin flips a day. I was quite good at it.
There's this guy in our school, no matter who flips the coin, even if you close his eyes. He ALWAYS wins a toss.
to add onto this.
If you build a physical coin flipping machine, you can configure it to flip the coin to land on the side you want with 100% accuracy.
Same applys with humans flipping the coin if they know special techniques
Coin flips randomization is like computer randomization, it's not actually random, it's based off an inputted seed.
if you input the same "seed", you get the same output.
“Scientists just proved…”
“In 2007”
This makes sense since there is a way to “flip” a coin and force it to land on the same side as it started. With enough practice you can get really good at making the coin appear to be flipping but in reality it’s just wobbling.
I can prove that a coin is not 50/50 quite easily. There is a real, but rare, chance for the coin to land on it's edge.
Thank you for coming to my TedTalk
Damn. They broke my rule by requiring it to be caught.
So.. coin flip is 50/50 always, but the method might be faulty.
So it is 50/50.
The test was done flipping the coin and catching it, with a 51% chance of landing the same side.
But, the common coin tossing method is: when you catch the coin you then then turn your hand over and place the coin on the back of your other hand. The coin is being turned over one last time.
Is that taken into consideration?
Is it also possible that one side of a coin is slightly heavier than the other side because of the different images having more or less material than the other? One could impress both sides of the coin in modelling clay, fill the impression with water then weigh the water to see if they are equal.
That’s what I wondered, too, but he addresses that at 2:48. Apparently the answer is no.
@@leickrobinson5186but not experimented with all coins from all countries.
The paper linked in the description shows 175,420 heads in 350,757 tosses. There were multiple currencies and denominations, so any bias to the heavier side would have been canceled out by variation in which side is heavier on, for example, a nickel vs a quarter.
That said, I suspect the weight and aerodynamic differences of the faces would be very small. The citation for a lack of heads tails bias is:
Gelman A, Nolan D. You can load a die, but you can’t bias a coin. The American Statistician 2002; 56(4):
308-311
But I'm too lazy to hunt down the web link :)
One way of looking at why there may not be much of a bias for such things is to look at how the leverage works in the system. The faces of the coin are very close to the center plane of the coin, and to each other, so they don't really have much leverage to be able to pull the coin one way or another. The difference in forces between the slightly heavier side being up and it being down don't really make the system unstable enough to flip the coin around.
Look up:
You Can Load a Die, But You Can't Bias a Coin - Columbia Statistics
There was a lesser-known study of this with different results. They performed over 350,000 coin tosses _in a zero-gravity environment._
Now, there are over 350,000 coins lost in space.
Persi Diaconis is the king of randomness and probability, ever since he came up with "7 shuffles" for a 52-card deck.
I think I should confess, I've always known that coin toss are predictable in it's outcome. That's why I learned the muscle memory so that the coin will always land on the desired side, but I never told anyone before.
they encountered an edge landing ≈58 times
You appear to have misunderstood the physics. There isn't an inherent bias if the coin is flipped. The bias is in whether or not the person who is supposed to flip the coin is coordinated enough to actually flip the coin or whether they just toss it upwards without providing a large enough flip to get it rotating around its diameter.
So, the lesson is to teach people whose job it is to flip a coin to actually impart 'flip' along with the initial vertical velocity.
Yes. All that paper did was prove some nerds didn't know how to flip a coin. They were throwing coins up and watching them wobble.
A proper flip will have a coin ring out like a bell.
The result of 50.8% "same side" probability matches the 51% that was predicted by a _theoretical_ model.
@@yurenchu You haven't understood my comment.
I have no idea how to properly flip a coin. I usually resort to having people draw straws to avoid the embarrassment.
Would you consider this effect "essentially" negated by tossing 3 times, throwing out the first two? You would of course keep the orientation when you flip #2 & #3 from the results of the previous throw. If 0.8 is the advantage, what would you estimate the advantage would be on the 3rd throw?
Somewhat similar to what you suggest, von Neumann came up with an elegant solution for how to get fair results from a biased coin. The procedure is as follows:
1. Toss the coin twice.
2. If the two coin flips match, start over, forgetting both results.
3. If the two coin flips differ, use the first result, forgetting the second.
Since a biased coin still produces independent results from trial to trial (i.e., no autocorrelation between trials), the process produces a fair result (50% of calling Heads or Tails) because a the probability of flipping Heads then Tails is the same as the probability of flipping Tails then Heads.
@@davetannenbaum I'm not statistician but to me that only sounds fair if you enforce the same starting position for both throws. Because the probability of same + different is the same as different + same. But If you just use the side it landed on for the second throw, then it becomes same + different vs. different + different, which isn't fair.
There are two problems with the study that is behind this. The biggest is that the people who tossed the coins knew the predictions of the theory that was under test. Their unconsciously acting to bias the outcome is probable, as it is almost impossible not to bias it under such test conditions. Secondly, some people actually do toss the coin in such a way that it is unbiased by starting position, ie. 50/50. So what this shows, if unconscious biasing of the outcome is not in play, is that just as some people are good at golf, or any physical activity, and others are bad at it, some are bad at flipping coins fairly and others are good at it. We might have thought everyone was equally good at it, but either they are not, or those who are bad at it are because they unconsciously wanted to see the theory verified and somehow slightly tilted the outcome in that direction.
Matt Parker did a video where he tried to find the height ratio of a fair, balanced three-sided (heads, tails, edge) "coin."
Also, if you’re the one flipping the coin, and the other person chooses the face-up direction, you can also just choose the catch method. I see some people catch the coin and then that is the result, but some people also put it onto the back of the other hand, flipping it in the process, so as the flipper, you can choose which side gets the bias
And here I was thinking the bias would be from the two sides not using the same amount of metal for the patterns and therefore being weighted
Now we just need a coin toss to determine the starting face of the coin.
The 1% is when the coin is on your hand.
If you toss a coin while the coin is vertically standing up, now it is 50-50%
On my way to show this to my stats teacher
When I was a kid, I had an 80% chance of getting the same face when I caught the coin mid-air with a slap. I knew coin toss was not fair. I won several bets this way
"Bias" is an understatement. 0:55 shows "...With careful adjustment, the coin started heads up always lands heads up-one hundred percent of the time."
this meant the coin, in the right condition, could be manipulated 100%.
Either that or they determined that an unknown percentage of scientists don't know of to flip a coin properly consistently.
I'm not sure I understand.
If you flip a coin, it will rotate. If you do not let it fall to the ground but catch it in the air, you catch it mid-rotation, so it does not matter how it would have landed.
The wobble introduced can not possibly mean that at any point of it being airborne, the probability of it being the same side you started with is higher, can it.
So what gives?
This is the reason why calls in cricket are made after the coin is tossed and is in mid-air
Anyone else roll coins like dice? I always struggled to flip them the normal way.
I'm so glad these scientists are working on matters that are critical to the betterment of mankind.
Considering how many times I or even anyone used a coin flip to decide something, I'd say it's a pretty good research. Newton got hit by an apple and that was his inspiration. The point of research is to look into everything.
You actually want to pick the opposite of the side shown. Because when the coin is caught in the hand most people flip it over onto their other hand changing the side
This proves the fairest way to decide is
“Paper, Rock,Scissors!”
From Ernest Goes to Camp
There are several comments that flipping a coin twice is fair, regarding TT + HH as one outcome and TH + HT as the other. In fact, there will still be a bias as (.495)^2 + (.505)^2 i not equal to 0.5. But that is pedantry in practice, it is much much closer: 50.005% instead of 51%
What is the p-value?
In coin flipping for NFL football games the coin hits the ground which means that the coin can bounce, which should re-randomize the odds.
Important to know though, if you're the one making the toss, whether the catcher will flip the coin after catch or not. If they do, then you should pick the opposite side as it will more likely land same side. And if you are the flipper, then just do or do not decide to flip after the catch depending on if they pick same side or not, as long as it's not agreed upon beforehand.
The way that coins are tossed here is that they are tossed, caught and then turned over onto the back of the hand. That would give a bias to the opposite side.
Tossing a coin digitally is practically also not really random, but probably not foreseeable for a normal human
"What's the most you've lost in a coin toss?"
"About one percent apparently."
The coin tosses I've seen for NFL games are not caught in the hand. The coin lands on the turf, and the referee looks at it and announces the result.
does the engravings and carvings on the design of the two sides of the coin affect how it flips? like a standard quarter might have a slightly different bias from a nickel or one of the state quarters because of differences in a cut.
Given the fineness of detail on the average coin face, any effect on its aerodynamics is probably very minor; factors like the coin’s shape, its metal composition, and how worn it is probably have more of an effect on how fairly it flips. I’m no minter, though, so take all of this with a grain of salt.
It's probably just down to center of mass and moment of inertia to have notable effects. But I didn't read the paper so I'm not sure if either factor cancels out in the math somewhere.
Also remember that the coins themselves were fair. if the engravings would matter, than some of the coins should show a heads/tail bias. but they did not.
As a kid, I noticed that I had some control over which side it landed on.
Doing one set of tests is the lowest form of science, your result will "always" show a bias.
With practice, you can deliberately pizza spin a coin and get it to land same side up nearly 100% of the time. If I'm rigging a coin toss, I do this, catch the coin in one hand, and then slap the coin down on the back of my other hand to reveal it- when I transfer to the other hand, knowing which side was up when it landed in my palm, I just control which side shows up after the transfer based on what my opponent called.
Because of this, I'm careful to say "we'll settle this with a coin toss" and not "coin flip", because I am tossing the coin, but I am not flipping it.
I would like to see a video of you demonstrating this.
A coin toss depends statistically on the center of mass relative to the geometric center plane.
Crazy how people can affect probabilities like this, its crazy
If I did the math right, using a coin toss to decide how to flip the coin would reduce the bias to 50.02%.
Know this puzzle: How to make a fair result from a biased coin?
I think there is a way to counteract the problem. First,decide which person or group is heads and which is tails. Then you flip the coin twice. the first time you start the flip with heads facing up, the second flip, you start with tails facing up. If the result of the two flips is heads twice, whomever picked heads wins, if the result is tails twice, tails wins. If the result is mixed, you do the two coin flips the same way, and you repeat until you get either heads, heads or tails, tails.
What's the most you've ever lost on a coin toss?
start with heads up, then flip. if it’s heads, leave it heads up then flip again, if (the first flip) is tails, turn it heads up then flip. if the first flip is heads and the second flip is tails, side A wins, if the first flip is tails and second flip is heads, side B wins. any other scenario and you restart from scratch.
life is unfair
it makes no sense to expect the fairness from flip coin
The physics must be interesting. Is a wobble more likely to create a type of gyroscopic effect that stabilises the coin's atitude and reduce the number of flips? Or are more complex things going on?
It would be such a funny thing if people actually thought this was real lol
The comparison between coin tosses and pancakes is flawed. Pancakes don't flip 40 times in the air so the wobble can affect the bias to one flip. Coins will land on the same side if it flips an even number of times and the opposite an odd number of times. The wobble would create just as much bias for a coin to flip 32 over 31 times as there would bias for 33 over 32 flips.
This has always been my concern with coin toss. Which side do you start with? Who gets to toss the coin? Who gets to call it? And on the catch, do you flip it or alternatively, let it drop?
Or do you toss a coin to answer the above questions?
At 2:15 it says the starting position of the coin was decided randomly. Why don’t we all just start using whatever that random decision process was, and forget about coins altogether? 😊
When I flip a coin, I catch it in one hand and then flip it onto the back of the other hand, so the bias would actually be the other way.
Also, the coin bias doesn't matter if the users don't know what the bias is.
Actually, wouldn't you want to predict the opposite face in a coin toss? the experiment only had the tossers catch the coin, but when ever I have tossed a coin it is flipped at the end as I place the coin on the back of my other hand, concealing it with the catching hand.
coins being tossed then caught are always caught at a different height, this causes differing results and throws off the perceived bias.
a person's muscle control might flip the coin more times than previous, so would their tiredness.
you would need a machine to flip the coin with a consistent amount of force, then allow the coin to land on the same flat surface and settle on its own.