That makes sense about the edge bias when letting them land on a table. However, there are ways to cheat when catching it in your hand. If you practice enough you can feel the difference between heads and tails on your skin, and know the result before you see the coin, because you already felt the result. Also, some people after catching simply open their hand, while other times they flip the coin over and set it on the palm of their other hand, changing the result. With enough skill you could do this to make sure you always win, even while letting the other person call heads or tails. It may lessen the bias of the coin, but it certainly makes it possible to cheat the toss by catching it.
I saw an interesting physics puzzle once which asked _How thick would a coin need to be such that there was a 1/3 chance of heads, 1/3 chance of tails and 1/3 chance of it landing on its edge?_ One answer is the thickness (t) has to be about 0.5774 times the diameter (d) *Reasoning* The coin can spin through 360 degrees. Dividing this full rotation into thirds means that 1/3 of the available rotation must result in heads, 1/3 tails and 1/3 edge. Viewing the coin from the side (imagine slicing it through it's diameter and looking edge on) the angle subtended by the heads face (length d) and the centre of mass must be 120 degrees. The angle subtended by the edge and centre of mass (length t) must be 60 degrees. t/d = tan(30) t = ~0.5774d
As a 'physics' puzzle rather than a maths puzzle, I suppose my only question regarding this is to do with the centre of mass (COM) of the thick coin. If the COM is higher when the coin is on its edge than when the coin is on one of the faces then we might imagine that, when landing on the ground, the coin is able to switch randomly (via wobbling, rotating, w/e as it lands) from edge to tails/heads because it lowers the COM, but it might struggle to return from heads/tails to the edge because it has to raise the COM to do so. Perhaps this would affect the result?
I think it's more complicated than that. I'm not sure how the energy and angular momentum would get distributed over the degrees of freedom. You know, some of the spin will end up rotating the cylinder along its axis of symmetry. This gives you a distribution in this 12 dimensional spinning cylinder space where you can analyze stuff.
Hey Brady, I'm a second year uni maths student and just started a module on Bayesian Statistics. I was wondering if you could do a video, similar to the Tau vs Pi one, where you have a Bayesian statistician and a classical/ frequentist statistician go against each other explaining why they prefer their type of stats. Thanks. Love the videos by the way!
That was my instinct, as well. Say a coin flip before a soccer game. It feels to me like the loner the coin is in the air, especially outdoors, the longer it spends being controlled by other factors than the person that flipped it, like wind and such, and the less biased the result should be. Assuming the grass doesn't let it spin any, of course. Someone who's really dedicated can totally learn to flip a coin in a way that makes it more likely to end up the way he wants to, if he's allowed to catch it when he wants to. That should eliminate that risk.
This year's Pi day is going to be at 3/14/15 and at 9:26.54 AM it's going to be the most accurate calendar depiction of PI until 2115. That is going to be epic
I'd like to know if the composition of the coin can make a difference, even slightly. The 1964 Kennedy half dollar as shown at 2:38 is made of 90% silver and was the only year it was made of 90% silver.
Letting a coin land on the ground allows more parameters to affect the outcome. Parameters such as ground restitution/bounciness, height at which the coin is tossed, ground friction, bumpiness/protrusion and sloping of the ground, et cetera.
So then if you add in the possibility of the catcher cheating, the fairest way would be to make it land on a bed? (That is assuming it won't spin on the bed, I haven't tried it out)
It depends what you mean by 'on its edge'. If a coin is spinning, the chances of it landing on one of its faces are very small, so it is pretty well guaranteed to land on its edge. If you mean landing perpendicular to the ground, it depends on the speed of rotation and descent. If you mean coming to rest on its edge, balanced upright -- I've seen it happen with a pound coin dropped on a bar counter; but it is quite a thick coin, and it bounced a few times first.
In theory, 1 in 6000, for an american nickel. In reality, its a lot less than that, due to the difficulty of finding a perfectly flat/horizontal surface. You'd also have to do it in a vacuum, otherwise force of millions of air molecules flying around would cause it to fall over.
Gammel Prutte >" If a coin is spinning, the chances of it landing on one of its faces are very small, so it is pretty well guaranteed to land on its edge." lol wut? Spin any coin right now and see that's not the case.
Consider than when it lands on the floor, it will have been in the air longer than if you stopped it partway down by catching it. This means that if the floor had similar properties to your hand in terms of bouncing (carpet probably has this), it has longer for random changes in the initial spin rate to add up.
But whether or not the coin is biased if you have no idea what the bias is, it's still "fair" in the sense that you have an equal chance of winning the toss up based on the information you have.
It's assuming that in your seach for fairness, you prevent cheating. Using your reasoning, you can used any rigged device and call it fair. You could secretly know the bias of the coin, or you could secretly know that the average bias of that specific type of coin (say a recent US nickel) is a particular way, without having tested that particular coin.
JWQweqOPDH well ya it would be fair if it's a fair 50/50 in choosing which side you go with. If in choosing the side that is rigged is fair, and you don't have any information related to the rigging, then it's fair. Very rarely will someone have studied any specific coin for its biases
Regtic One must make a distinction between the fairness of the randomizer itself and the fairness of the "game" based on the randomizer. You can bias the game both by using a biased randomizer or by making one of the win/loss conditions more or less difficult to fulfill (e.g. a game where you lose on one tails and win on two heads)
StarFox008 I wasn't trying to say that the video is pointless. The distinction is valid. I just wanted to point out that the "game" is still fair. Neither party will know anything about the coin before it's flipped, ideally. I can already see all the kids telling their teachers that coin tosses aren't fair games when they try and teach probability.
I know this video is kinda old, but, would it be more fairer to catch the coin in the middle of it either rising up or falling down in the air than to let it come back down to your hand? Say, you toss a coin and it goes 6 cm up in the air before it comes down, would catching it say 3 cm off going up or down make it more fair than letting that coin go up 6 cm and then fall down back where it started in your hand?
I once spent 6 hours learning to feel with my thumb which side up a coin was so that as i catch the coin and go to slap in on the back of my other hand I can roll the coin to the side that I win on. For fear of others having as much love of ridiculous skills as I do I always insist on the open palm catch or floor landing.
there might be people who can flip the coin so precise that they could influence the outcome of such an experiment. that would be a major reason for me to go for the no hands approach. when it comes to the coin still spinning often after it hits the surface after a flip i'd say it's bound to be less biased because the spin force of the coin would be nowhere near to what it would be when you spin it to start with.
I always feel that caught in the hand is less fair because some people grab it and show it and some place it on their other arm, thus reversing the result. If someone could feel or see which side was which quick enough, they could decide the result in their favor.
I would have guessed it would be more fair to let it drop on the floor because it bounces around like a dice rather than being stopped immediately by the hand.
How about if you throw the coin as far as you can and measure the distance, if when the measurement is rounded is even then you can call that heads, and if it is odd when rounded then you can call that tails.
So if you want to win a coin toss, you should (1) pick the face that's up from the start, and (2) catch the coin at the same height you tossed it. Or, if you're going to do that thing where you catch it, then flip it over onto the back of your other hand, you'd want to pick the face that's down from the start.
Interestingggg! People would actually think the hand is less fair because when it bounces on the ground that is super random and bouncing all over the place.. where as the hand alone.. well maybe the guy flips the same way a lot or something lol. But I didn't know about the edge bias. So yea.. catch it would be better. Just specify that they aren't to then flip it over into their hand after they see the result and don't like it lol.
Spinning a coin - how to get it to come up the way you want. When you start have the side you want to come up slightly on the top. Then it makes no difference if you just let it drop or spin it first, the result is the same. How to toss a coin and make the result you want. When you catch the coin feel one side. You should be able to feel it heads or tails. If that is wrong you can quickly flip the coin. Do it fast and it is hard to tell that you did it.
The odds of heads plus the odds of tails do not add up to 1. I remember flipping a coin and did not hear the sound of it landing. I couldn't find it until I noticed it standing on its edge on a hardwood floor - not in a crack or anything like that; just on the smooth surface of the hardwood floor. Now what are the odds of that???
1.53 My guess: Allowing the coin to hit and bounce on the table or floor or whatever, is less fair if the edge is beveled. Yes! You know, those coins with the serated edges are "milled" And they have "milled edges". Unless I'm misremembering.
Don't let me catch it in my hand, especially if you have picked heads or tails beforehand. There's a sleight of hand move that i have perfected where i, which i catch a coin, quickly run my thumb over the surface. I can sense the difference between heads and tails so i know what direction the coin is in when i caught it. Then (as is normally the procedure) you slap the coin on top of your other hand. In that move I am able to change the outcome of the coin flip if i need to by simply flipping the coin inside my hand as i make that final move. I have never abused this to my advantage but if i wanted to i could call what the result of the coin flip would be long before i have initiated the flip. Because at the end, i can always adjust the result. So dropping it on a table, edge bias or no edge bias is still the best option. By the way, the final "slap it on the upper hand" move isn't necessary but it makes it easier to adjust the result without anyone noticing.
Yes, cheating a caught coin toss is one of the most basic magic tricks. Therefore the most fair method is likely to let the coin drop onto a soft surface where it won't spin.
SAI Peregrinus The most easiest method is to catch it, then have the other one decide if it´s head or tails then reveal it, no trouble with searching for ideal material to let the coin drop on, no searching for lost coin.
Jan Věrný If that is the case i can just have the coin "accidentally" slip off my hand as i reveal it if i know i am going to lose. Then do a retoss... Chances are it will be the right side next time, or maybe i can just fool the other person to think his choice sticks for the next toss. Sleight of hand, sleight of mind.
How can you explain this.... In our childhood we find that the face we are looking at when we flip the the coin is more likely to come and we used to hide it from the two caption ( in cricket match) .....but this video show that coins are generally biased and more likely will be biased side.
What I always thought was unfair with the hand-catch method, often the person catching the coin will flip the coin by placing it on top his or her other hand.
Toss a bank note in the air...see how far it flies off before landing XD For bonus points, do it on a windy day, outside, in the middle of a crowded city.
One of the problems with this video is that he wants to eliminate the idea that the person catching the coin is going to tamper with the results. And while it's always good to look at things from a simplified version and expanding out, I don't think that's a factor you can easily discount. This is because you can easily train yourself to recognize either face of a coin when you close your hand around it. Then depending on how you open your hand it will reveal one face or the other. You might call it in the air, but as soon as you do it's a simple matter to manipulate the coin to be what I want it to be. You might think if you call it after the catch has happened and it's sealed in the hand that you would notice any slight of hand at this point, but it's not about slight of hand really at this point just simply how you open your hand. You might think, "Well if it's a matter of how the hand is opened, surely I would notice that" but why would you in the short run? Even if you played the best out of three tosses with someone, you are at most going to see them open their hand three times. And they are similar enough motions that you aren't likely to notice after only 3 times. This is because you have at most 1 chance to notice an odd opening of the hand. To understand why just think of each toss opening the hand naturally or with a twist... 1) You flip three times, and need to apply the twist each time. As you applied the twist each time, it looked like your natural way of opening your hand. No chance to notice anything odd. 2) You flip three times, and need to apply the twist once. Well there you go there is one chance to notice something odd. 3) You flip three times, and need to apply the twist twice. But as the natural one is the different one out of the three that's the one chance to notice anything odd. 4) You flip three times, and don't need to apply the twist at all. Well it was all natural so no cheating to be caught. And then it gets even worse. If you are doing best 2 out of 3, and you got your cheating down to a science, you'll rarely if ever need to make that 3rd toss. TL;DR: Don't trust people that want to insist on catching the coin. They likely know how to cheat the toy toss.
well you can say then that letting the coin landing on the ground is unfair because its not where the gravity is. pretty much it'll always have a bias no matter what you do.
I don't fully understand the comment about the "edge bias" at the end. Is he stating that the coin is tossed and when it hits the floor the probability is slightly skewed away from 50/50 due to edge bias? It seems to me that in both situations the coin is subject to stage one where it is flipped and allowed to move freely in the air with a probability of 50/50. However in the situation where it hits the ground the coin undergoes stage two where the probability is slightly skewed one way or another. But is the side it is bias towards not a function of the coin's position as it hits the ground? I.e. the initial conditions for the stage two system. So I understand both coins to be fair, but one undergoes a second process where the probability is a function of a random input. So aren't they both as fair? Moreover as you consider it's called in the air where the probability of choice and outcome is still .5. (Concerned about having misunderstood the comment and seemingly making a fool out of myself).
the side bias is constant for a coin, because they aren't perfectly shaped. if a side is angled, the spinning motion causes one of the sides to be upward
Information reduces the need to assign probability, and ultimately leads to the conclusion of a determinstic universe. Suppose you hand a spear to a blindfolded man and tell him to put his feet into slots in the floor so he can only throw the spear at one of two targets. He can orient his feet in either direction. Once the feet are set, the man throwing the spear, observes a 50 50 chance of throwing the spear at either target. To the observer the probability is 100% because he has information on the cause-effect relation of feet orientation.
It is deterministic 100%, but the ability to determine it is impossible because all influences could never be know. So we assign an unknown to the outcome called probability.
So if you spin a coin then when you catch it you dont look at it but spin it again you have a probability of 5.1*5.1+4.9*4.9 = 0.502 chance that it shows the same side as when you flipped it first. That is pretty fair IMO^^
It still seems 'fair' to me either way so long as you don't know what tendency your coin has; wouldn't any arbitrary coin be equally likely to tend towards heads as tails?
I think the fairest thing to do is have one person flip the coin and their opponent catch it. I'll try it with my kids and see how the results come out.
I reckon, you're reversing how a flipped coin will come up, if you catch it, as oppose to if you had left it fall, so if you're betting on the outcome, catching a coin, might make you lose a bet you would have won, though of course, the reverse could also be true, catching a coin, might cause you to win a bet you might have lost, if you had let it fall :) . But on the surface, letting a coin fall, feels fairer to me :) .
The edge bias from landing on the ground might also explain the skewed results of Super Bowl coin tosses since the referees let those coins hit the ground. If the refs caught it in the air the results might be more even.
I quickly looked at the super bowl coin toss statistics, and it seems to be a perfect 50/50 currently. Granted, I didn't give it much time. Would you care to elaborate on how the results are skewed?
This just comes to prove that it would be almost impossible for man to replicate randomness or in other words replicate something who's outcomes have the exact same probability of happening(this is the true meaning of randomness), being it a coin or anything else. The more time you allow a coin to flip, theoretically the more random the outcomes would be. Although if a coin is very biased, the time that it stays flipping would be of very low significance regarding it's outcome.
I'm sure it is, but this is irrelevant due to the assumption of no bet being involved. As he says: "You're just flipping coins for yourself, you're not trying to cheat anyone". The question is purely mathematical in the video.
Sasch Bengtsson Quite true, but, in my opinion, there is nothing wrong thinking about how the pure statistical question relates to a more practical situation.
Soliloquy Sure. Your original comment is likely a huge part, and possibly better explained than in the video, of why people tend to consider the absence of a hand fairer.
A while back I learned how to cheat with flipping a quarter by feeling which side was which and making sure the "correct" side came up. I think I got pretty good at making it look natural... though I've never used it to cheat someone, I swear.
dudelivestrong you have to learn the math curriculum, no one can know these things before they learn it. and everyone begins with the same level of ignorance, so go for it!
A coin toss isn't theoretically random, im sure with an extremely advanced piece of equipment that can just capture the first few seconds of flight, can predict accurately how it will land. Of course, this would have to be an extremely advanced and isolated test, preferably with a mechanical arm that flicks the coin so the computer knows the energy exerted and at what point on the coin, would probably have to be done in a vacuum too. Knowing what position the coin is in relative to the three different planes in space xyz and doing the math and physics and all, I think should be possible to predict the outcome. Of course, in reality, no two persons betting on who buys drinks can predict the outcome unless they have insanely advanced equipment xD The fact is is that there are simply too many variables to consider, making a coin toss essentially random during any average use. I wonder if a formula could be made considering what side the coin is first facing before flipping it, the force exerted, and what angle and at what position on the coin, to tell the outcome. That would be neat.
Sure, the coin that lands on the floor is subject to edge bias… AFTER it converts a bunch of its remaining linear momentum into erratic, multi-axis angular momentum, consequently dumping much of the coin's remaining bulk/translational kinetic energy into internal (rotational) degrees of freedom. Not to mention that the dynamics of any particular "post-bounce" phase of the coin's flight appear to be highly sensitive to the bounce's initial conditions, due to the highly elastic nature of the coin-floor collision and the huge variation in torque that such a flattened object will experience, depending on its exact orientation relative to the floor's surface. (That part depends on the collision being with a hard floor. But the inelasticity of the coin's collision with a soft floor, like a grass-covered football field, can't be any worse than that of a coin-hand collision.) There is just no way that this "post-bounce" phase, at least from a hard floor, doesn't scramble much of the residual predictability of the "flip" phase of the coin's flight. Which makes the edge bias a moot point, because the "dying" phase of the coin starts with completely unpredictable initial conditions.
But he showed in the previous video that, for a typical person flipping a coin the result is nearly 50/50 (50.5% chance to land on the side that it started on). That phase of the coin toss has relatively little predictability to begin with, compared to the edge bias which as he said in this video could be very significant (20% more likely to land on the favored side).
I can spin any coin, any time and get the outcome I want. Every time. I can also flip a coin and cheat too, but that depends on the situation... But to get the outcome I want flipping it, let's just say that I have to catch it and that's all I'll let on.
how is the coin landing on the ground "less fair"? i thought fairness in this situation would be the most random method, and landing on the ground seems to be it :/
he mentioned in the beginning of the video that coins tend to have a distinct bias for how they will land when spun on edge. The flip that ends on the table will often times spin for a short time on its edge, thus involving that bias.
screw it, i don't want to know which side it lands on until i learn how to spin it like persi. damn it, magicians are always doing something normal in an odd way. SHIBBY!
Half dollar coins have been produced every year since the conception of the United States Mint in 1794. Sometimes referred to as the fifty-cent piece, the only other U.S. coin that has been minted as consistently is the cent. -- WIkipedia
***** If I remember right, the Wikipedia article says they are made for collectors now. That's probably why you haven't seen any new ones in circulation.
I am sorry but i dont belive that catching the coin is more fair. Like you said the previous video one can calculate the speed and spin speed of a coin flip. but if you catch that coin you are dealing with a binary head or tails situation. If you let the coin hit the surface there is a hole new math involved. Each degree can make a huge difference on the coin behave. It can flip many time in both directions before decide the result. Sry my poor english
You kinda missed the point here, which is that if you let it hit a surface on which it can bounce/spin it's provably no longer 50-50 as to whether it lands heads or tails first. And since 'fair' in this instance is taken to mean "most random", then yes, catching a coin is fairer than letting it drop on a hard surface. The "new math", which you mention is precisely what's skewing the results so that it's not a 50-50 chance.
SatanicBunny From what i understood of the first video, the chances are not 50-50 when you catch, its more like 51-49 and depends on what face is up when u throw the coin. So if catching the coin its 51-49 how much is if you let it hit the surface? 52-48? Can you calculate that? I guess you can't b/c the number of variables increases so much, that is what i meant. By the way, i guess it gets closer to 50-50 since there is so much randomness included
Daniel Calou I think the point is that either way is not really random or fair in any case. You could only really say that it is more like the illusion of 'randomness' in fairer situations than in others. But really it is not random at all, but rather deterministic. If you have all the required information of course. While (like others have said) it is true that if both parties don't have the specific information about the coin or how it is flipped or span, it can be seen at a glance that it is fairer. But the deterministic and biased nature of it all means that there are particular exploitations (or key rules one might follow) which will potentially lead to one party winning the game in most cases. This is essentially defeating the purpose of the coin toss - in that it is supposed to be fair. As for the whole new area of maths involved... yes you could argue that. But in all fairness, is that new area of maths not as biased as the original area of maths for similar reasons since the coin is biased? Since I have no idea which area you are specifically refering to when you say a "whole new area of maths" it kind of makes it difficult to answer constructively. But I will say that if you want to get into the thick of it about more advanced variables interacting upon the coin when it has landed upon a hard surface, a hand is not perfectly flat. So if the coin collides with your hand on its edge, can the curvature of your hand act upon the coin? I'd say most definitely yes... but would the coin be tempted to still fall towards its bias in most cases? Stuff which could be considered I guess.
MrJC1 I am refering to the fact the coin bounce when it hits the ground. When you catch it its done, either head or tails the math is over. But i liked your answere.
The sound of a coin hitting the floor in slow motion is magical.
Damn I was thinking the same thing.
Sounds in slow motion are usually fake and added in afterwards btw
i.e. they used real magical sounds
Randomness expert AND FORMER MAGICIAN! I love both subjects - I want to see an entire channel featuring Persi Diaconis!
I THREW IT ON THE GROUND
Are you the hero lunk? (from cyanide and happiness)
WHAT DO YOU THINK? IM A JOKE?
Welcome to the real world jackass!
I'm not a part of this system!
Maaaaaaaan!
Are you an adult?
That's a 1964 kennedy coin, the last year that had 90% silver coins.
That makes sense about the edge bias when letting them land on a table. However, there are ways to cheat when catching it in your hand. If you practice enough you can feel the difference between heads and tails on your skin, and know the result before you see the coin, because you already felt the result. Also, some people after catching simply open their hand, while other times they flip the coin over and set it on the palm of their other hand, changing the result. With enough skill you could do this to make sure you always win, even while letting the other person call heads or tails. It may lessen the bias of the coin, but it certainly makes it possible to cheat the toss by catching it.
I saw an interesting physics puzzle once which asked
_How thick would a coin need to be such that there was a 1/3 chance of heads, 1/3 chance of tails and 1/3 chance of it landing on its edge?_
One answer is the thickness (t) has to be about 0.5774 times the diameter (d)
*Reasoning*
The coin can spin through 360 degrees. Dividing this full rotation into thirds means that 1/3 of the available rotation must result in heads, 1/3 tails and 1/3 edge.
Viewing the coin from the side (imagine slicing it through it's diameter and looking edge on) the angle subtended by the heads face (length d) and the centre of mass must be 120 degrees. The angle subtended by the edge and centre of mass (length t) must be 60 degrees.
t/d = tan(30)
t = ~0.5774d
As a 'physics' puzzle rather than a maths puzzle, I suppose my only question regarding this is to do with the centre of mass (COM) of the thick coin. If the COM is higher when the coin is on its edge than when the coin is on one of the faces then we might imagine that, when landing on the ground, the coin is able to switch randomly (via wobbling, rotating, w/e as it lands) from edge to tails/heads because it lowers the COM, but it might struggle to return from heads/tails to the edge because it has to raise the COM to do so. Perhaps this would affect the result?
I think it's more complicated than that. I'm not sure how the energy and angular momentum would get distributed over the degrees of freedom. You know, some of the spin will end up rotating the cylinder along its axis of symmetry.
This gives you a distribution in this 12 dimensional spinning cylinder space where you can analyze stuff.
standup maths is doing this now
Dear Brady, as much as I love your videos from sixty symbols and numberphile and ofcourse objectivity, this might be the most interesting one yet!
That means I could select or prepare a coin, so that it comes out in my favor. Great Explanation by the way!
Hey Brady, I'm a second year uni maths student and just started a module on Bayesian Statistics. I was wondering if you could do a video, similar to the Tau vs Pi one, where you have a Bayesian statistician and a classical/ frequentist statistician go against each other explaining why they prefer their type of stats. Thanks. Love the videos by the way!
I love all the videos from this professor
What if you toss it and it lands on carpet or dirt? Those wouldnt let the coin bounce and spin so theyd be fairer right?
They don't bounce or spin in your hand either. So that would be the same.
Elidan1012 except fairness increases as rotations increase. Hence if it is in air for longer, it becomes more random.
That was my instinct, as well. Say a coin flip before a soccer game. It feels to me like the loner the coin is in the air, especially outdoors, the longer it spends being controlled by other factors than the person that flipped it, like wind and such, and the less biased the result should be. Assuming the grass doesn't let it spin any, of course. Someone who's really dedicated can totally learn to flip a coin in a way that makes it more likely to end up the way he wants to, if he's allowed to catch it when he wants to. That should eliminate that risk.
Yet another video that's 3 minutes and 14 seconds long. I see a trend here...
😥😫 mines 3:15... I'm missing out on pi😩😭
natalie robinson breh do u evn math? :P
Shows 3:15 on mobile devices
This year's Pi day is going to be at 3/14/15 and at 9:26.54 AM it's going to be the most accurate calendar depiction of PI until 2115. That is going to be epic
blackridermidnite
Only in th the US because noone else writes dates in that weird order.
i frigging love this guy
Awesome video. I really liked the slow motion of the coins.
Thanks for creating amazing and entertaining content numberphile! :D
Love this! Never thought about it in my life
I'd like to know if the composition of the coin can make a difference, even slightly. The 1964 Kennedy half dollar as shown at 2:38 is made of 90% silver and was the only year it was made of 90% silver.
I think all of this just as easily applies to the 1971-present base metal halves, as well as all other denominations, reeded edge or otherwise.
Great video
Interesting videos with the superbowl comming up.
Counterintuitive but true, and convincingly explained. Thanks.
Letting a coin land on the ground allows more parameters to affect the outcome. Parameters such as ground restitution/bounciness, height at which the coin is tossed, ground friction, bumpiness/protrusion and sloping of the ground, et cetera.
So then if you add in the possibility of the catcher cheating, the fairest way would be to make it land on a bed? (That is assuming it won't spin on the bed, I haven't tried it out)
So how high is the probablity of a coin landing on it's edge?
It depends what you mean by 'on its edge'. If a coin is spinning, the chances of it landing on one of its faces are very small, so it is pretty well guaranteed to land on its edge. If you mean landing perpendicular to the ground, it depends on the speed of rotation and descent. If you mean coming to rest on its edge, balanced upright -- I've seen it happen with a pound coin dropped on a bar counter; but it is quite a thick coin, and it bounced a few times first.
In theory, 1 in 6000, for an american nickel. In reality, its a lot less than that, due to the difficulty of finding a perfectly flat/horizontal surface. You'd also have to do it in a vacuum, otherwise force of millions of air molecules flying around would cause it to fall over.
I've had it happen twice with Mexican 10 peso coins, but I wasn't counting.
Gammel Prutte >" If a coin is spinning, the chances of it landing on one of its faces are very small, so it is pretty well guaranteed to land on its edge."
lol wut? Spin any coin right now and see that's not the case.
1 in 6000.
Consider than when it lands on the floor, it will have been in the air longer than if you stopped it partway down by catching it. This means that if the floor had similar properties to your hand in terms of bouncing (carpet probably has this), it has longer for random changes in the initial spin rate to add up.
But whether or not the coin is biased if you have no idea what the bias is, it's still "fair" in the sense that you have an equal chance of winning the toss up based on the information you have.
It's assuming that in your seach for fairness, you prevent cheating. Using your reasoning, you can used any rigged device and call it fair. You could secretly know the bias of the coin, or you could secretly know that the average bias of that specific type of coin (say a recent US nickel) is a particular way, without having tested that particular coin.
JWQweqOPDH well ya it would be fair if it's a fair 50/50 in choosing which side you go with. If in choosing the side that is rigged is fair, and you don't have any information related to the rigging, then it's fair.
Very rarely will someone have studied any specific coin for its biases
Andy William yes, they do.
Regtic One must make a distinction between the fairness of the randomizer itself and the fairness of the "game" based on the randomizer. You can bias the game both by using a biased randomizer or by making one of the win/loss conditions more or less difficult to fulfill (e.g. a game where you lose on one tails and win on two heads)
StarFox008 I wasn't trying to say that the video is pointless. The distinction is valid. I just wanted to point out that the "game" is still fair. Neither party will know anything about the coin before it's flipped, ideally.
I can already see all the kids telling their teachers that coin tosses aren't fair games when they try and teach probability.
I know this video is kinda old, but, would it be more fairer to catch the coin in the middle of it either rising up or falling down in the air than to let it come back down to your hand? Say, you toss a coin and it goes 6 cm up in the air before it comes down, would catching it say 3 cm off going up or down make it more fair than letting that coin go up 6 cm and then fall down back where it started in your hand?
I once spent 6 hours learning to feel with my thumb which side up a coin was so that as i catch the coin and go to slap in on the back of my other hand I can roll the coin to the side that I win on. For fear of others having as much love of ridiculous skills as I do I always insist on the open palm catch or floor landing.
I like how even though the bias is 80% towards tails, both coins shown in the video land on heads.
How long is this video? 3.14?
You did it again Brady.
I was hypnotised by his shirt!
there might be people who can flip the coin so precise that they could influence the outcome of such an experiment. that would be a major reason for me to go for the no hands approach. when it comes to the coin still spinning often after it hits the surface after a flip i'd say it's bound to be less biased because the spin force of the coin would be nowhere near to what it would be when you spin it to start with.
I always feel that caught in the hand is less fair because some people grab it and show it and some place it on their other arm, thus reversing the result. If someone could feel or see which side was which quick enough, they could decide the result in their favor.
Sooo... Is it heads or tails for the superbowl?
I have a crisp £10 note riding on heads. But now i'm not so sure...
What about the coin bounced off the floor and catch method??
I would have guessed it would be more fair to let it drop on the floor because it bounces around like a dice rather than being stopped immediately by the hand.
How about if you throw the coin as far as you can and measure the distance, if when the measurement is rounded is even then you can call that heads, and if it is odd when rounded then you can call that tails.
So if you want to win a coin toss, you should (1) pick the face that's up from the start, and (2) catch the coin at the same height you tossed it. Or, if you're going to do that thing where you catch it, then flip it over onto the back of your other hand, you'd want to pick the face that's down from the start.
It's called a reeded edge in the minting business, not a serrated edge.
Interestingggg! People would actually think the hand is less fair because when it bounces on the ground that is super random and bouncing all over the place.. where as the hand alone.. well maybe the guy flips the same way a lot or something lol. But I didn't know about the edge bias. So yea.. catch it would be better. Just specify that they aren't to then flip it over into their hand after they see the result and don't like it lol.
Spinning a coin - how to get it to come up the way you want. When you start have the side you want to come up slightly on the top. Then it makes no difference if you just let it drop or spin it first, the result is the same.
How to toss a coin and make the result you want. When you catch the coin feel one side. You should be able to feel it heads or tails. If that is wrong you can quickly flip the coin. Do it fast and it is hard to tell that you did it.
The odds of heads plus the odds of tails do not add up to 1.
I remember flipping a coin and did not hear the sound of it landing. I couldn't find it until I noticed it standing on its edge on a hardwood floor - not in a crack or anything like that; just on the smooth surface of the hardwood floor.
Now what are the odds of that???
thanks, doc. keep working on that delorean time machine.
1.53
My guess: Allowing the coin to hit and bounce on the table or floor or whatever, is less fair if the edge is beveled.
Yes!
You know, those coins with the serated edges are "milled" And they have "milled edges". Unless I'm misremembering.
Don't let me catch it in my hand, especially if you have picked heads or tails beforehand. There's a sleight of hand move that i have perfected where i, which i catch a coin, quickly run my thumb over the surface. I can sense the difference between heads and tails so i know what direction the coin is in when i caught it.
Then (as is normally the procedure) you slap the coin on top of your other hand. In that move I am able to change the outcome of the coin flip if i need to by simply flipping the coin inside my hand as i make that final move.
I have never abused this to my advantage but if i wanted to i could call what the result of the coin flip would be long before i have initiated the flip. Because at the end, i can always adjust the result. So dropping it on a table, edge bias or no edge bias is still the best option.
By the way, the final "slap it on the upper hand" move isn't necessary but it makes it easier to adjust the result without anyone noticing.
Yes, cheating a caught coin toss is one of the most basic magic tricks. Therefore the most fair method is likely to let the coin drop onto a soft surface where it won't spin.
SAI Peregrinus The most easiest method is to catch it, then have the other one decide if it´s head or tails then reveal it, no trouble with searching for ideal material to let the coin drop on, no searching for lost coin.
Jan Věrný If that is the case i can just have the coin "accidentally" slip off my hand as i reveal it if i know i am going to lose. Then do a retoss... Chances are it will be the right side next time, or maybe i can just fool the other person to think his choice sticks for the next toss. Sleight of hand, sleight of mind.
is the sound of the dropping coin real ?
What if it's caught then flipped onto the back of a hand?
Suddenly the coin toss of every Super Bowl ever feels tainted...
How can you explain this....
In our childhood we find that the face we are looking at when we flip the the coin is more likely to come and we used to hide it from the two caption ( in cricket match) .....but this video show that coins are generally biased and more likely will be biased side.
What I always thought was unfair with the hand-catch method, often the person catching the coin will flip the coin by placing it on top his or her other hand.
OK we know about coins? How about flying banknotes ? They have two sides and can spin while falling... are they more fair?
Why would you flip a bank not?
Creased or even slightly bent bills ("notes" in the UK) will be completely unfair, virtually always landing on the same side.
Toss a bank note in the air...see how far it flies off before landing XD For bonus points, do it on a windy day, outside, in the middle of a crowded city.
IceMetalPunk And make it a $100 bill
Red Rogue
No, make it one of those limited-edition $100,000 bills from World War time :D
One of the problems with this video is that he wants to eliminate the idea that the person catching the coin is going to tamper with the results. And while it's always good to look at things from a simplified version and expanding out, I don't think that's a factor you can easily discount.
This is because you can easily train yourself to recognize either face of a coin when you close your hand around it. Then depending on how you open your hand it will reveal one face or the other. You might call it in the air, but as soon as you do it's a simple matter to manipulate the coin to be what I want it to be. You might think if you call it after the catch has happened and it's sealed in the hand that you would notice any slight of hand at this point, but it's not about slight of hand really at this point just simply how you open your hand.
You might think, "Well if it's a matter of how the hand is opened, surely I would notice that" but why would you in the short run? Even if you played the best out of three tosses with someone, you are at most going to see them open their hand three times. And they are similar enough motions that you aren't likely to notice after only 3 times. This is because you have at most 1 chance to notice an odd opening of the hand. To understand why just think of each toss opening the hand naturally or with a twist...
1) You flip three times, and need to apply the twist each time. As you applied the twist each time, it looked like your natural way of opening your hand. No chance to notice anything odd.
2) You flip three times, and need to apply the twist once. Well there you go there is one chance to notice something odd.
3) You flip three times, and need to apply the twist twice. But as the natural one is the different one out of the three that's the one chance to notice anything odd.
4) You flip three times, and don't need to apply the twist at all. Well it was all natural so no cheating to be caught.
And then it gets even worse. If you are doing best 2 out of 3, and you got your cheating down to a science, you'll rarely if ever need to make that 3rd toss.
TL;DR: Don't trust people that want to insist on catching the coin. They likely know how to cheat the toy toss.
well you can say then that letting the coin landing on the ground is unfair because its not where the gravity is. pretty much it'll always have a bias no matter what you do.
Interesting, I would never had guessed that it could do much difference how a coin toss is made...
I don't fully understand the comment about the "edge bias" at the end.
Is he stating that the coin is tossed and when it hits the floor the probability is slightly skewed away from 50/50 due to edge bias?
It seems to me that in both situations the coin is subject to stage one where it is flipped and allowed to move freely in the air with a probability of 50/50. However in the situation where it hits the ground the coin undergoes stage two where the probability is slightly skewed one way or another. But is the side it is bias towards not a function of the coin's position as it hits the ground? I.e. the initial conditions for the stage two system.
So I understand both coins to be fair, but one undergoes a second process where the probability is a function of a random input. So aren't they both as fair? Moreover as you consider it's called in the air where the probability of choice and outcome is still .5.
(Concerned about having misunderstood the comment and seemingly making a fool out of myself).
the side bias is constant for a coin, because they aren't perfectly shaped. if a side is angled, the spinning motion causes one of the sides to be upward
I'm the most unfair coin flipper. I say, "head I win, tails you lose" while the coin is in the air. 100% I win.
Information reduces the need to assign probability, and ultimately leads to the conclusion of a determinstic universe. Suppose you hand a spear to a blindfolded man and tell him to put his feet into slots in the floor so he can only throw the spear at one of two targets. He can orient his feet in either direction.
Once the feet are set, the man throwing the spear, observes a 50 50 chance of throwing the spear at either target. To the observer the probability is 100% because he has information on the cause-effect relation of feet orientation.
It is deterministic 100%, but the ability to determine it is impossible because all influences could never be know. So we assign an unknown to the outcome called probability.
This guy reminds me of Kripparrian .
So cool.
2 euro coin came up heads 8 out of 10 spins for me. granted 10 still allows for variance but interesting non the less.
so did anyone notice the easter egg that the video is 3:14? ha. haha. hahahaha.
So if you spin a coin then when you catch it you dont look at it but spin it again you have a probability of 5.1*5.1+4.9*4.9 = 0.502 chance that it shows the same side as when you flipped it first. That is pretty fair IMO^^
It still seems 'fair' to me either way so long as you don't know what tendency your coin has; wouldn't any arbitrary coin be equally likely to tend towards heads as tails?
Why do coins have numbers punched all the way to the other side??
I think the fairest thing to do is have one person flip the coin and their opponent catch it. I'll try it with my kids and see how the results come out.
at 2:30 it's kind of dramatic. Like when Two-face flips a coin and the camera is shooting in the ground
I reckon, you're reversing how a flipped coin will come up, if you catch it, as oppose to if you had left it fall, so if you're betting on the outcome, catching a coin, might make you lose a bet you would have won, though of course, the reverse could also be true, catching a coin, might cause you to win a bet you might have lost, if you had let it fall :) .
But on the surface, letting a coin fall, feels fairer to me :) .
The edge bias from landing on the ground might also explain the skewed results of Super Bowl coin tosses since the referees let those coins hit the ground. If the refs caught it in the air the results might be more even.
I quickly looked at the super bowl coin toss statistics, and it seems to be a perfect 50/50 currently. Granted, I didn't give it much time. Would you care to elaborate on how the results are skewed?
What about cricket matches? The coins there land on grassy soil! i think the soft grass and dirt sort-of absorbs any biases.
Could you also say that a coin hitting the floor dents The coin to make it more bias
This just comes to prove that it would be almost impossible for man to replicate randomness or in other words replicate something who's outcomes have the exact same probability of happening(this is the true meaning of randomness), being it a coin or anything else. The more time you allow a coin to flip, theoretically the more random the outcomes would be. Although if a coin is very biased, the time that it stays flipping would be of very low significance regarding it's outcome.
But maybe it’s possible to catch a coin and feel which way it is, and with a little sleight of hand flip of to your own side.
I'm sure it is, but this is irrelevant due to the assumption of no bet being involved. As he says: "You're just flipping coins for yourself, you're not trying to cheat anyone". The question is purely mathematical in the video.
Sasch Bengtsson Quite true, but, in my opinion, there is nothing wrong thinking about how the pure statistical question relates to a more practical situation.
Soliloquy Sure. Your original comment is likely a huge part, and possibly better explained than in the video, of why people tend to consider the absence of a hand fairer.
A while back I learned how to cheat with flipping a quarter by feeling which side was which and making sure the "correct" side came up. I think I got pretty good at making it look natural... though I've never used it to cheat someone, I swear.
just in time for the super bowl
That's a dirty ground
I wish I was this intelligent most things on this channel I do not understand but I try.
***** I like this element. I try to keep that in mind but my hybris often catches me before I can...
dudelivestrong you have to learn the math curriculum, no one can know these things before they learn it. and everyone begins with the same level of ignorance, so go for it!
when i flip a coin, i catch it in one hand and put it immediately on the back of the other
I spun a penny and it landed on tails 13 times in a row. This explains why that happened. :)
A coin toss isn't theoretically random, im sure with an extremely advanced piece of equipment that can just capture the first few seconds of flight, can predict accurately how it will land. Of course, this would have to be an extremely advanced and isolated test, preferably with a mechanical arm that flicks the coin so the computer knows the energy exerted and at what point on the coin, would probably have to be done in a vacuum too. Knowing what position the coin is in relative to the three different planes in space xyz and doing the math and physics and all, I think should be possible to predict the outcome. Of course, in reality, no two persons betting on who buys drinks can predict the outcome unless they have insanely advanced equipment xD The fact is is that there are simply too many variables to consider, making a coin toss essentially random during any average use. I wonder if a formula could be made considering what side the coin is first facing before flipping it, the force exerted, and what angle and at what position on the coin, to tell the outcome. That would be neat.
is it just me, or is the audio super low on this one?
Sure, the coin that lands on the floor is subject to edge bias… AFTER it converts a bunch of its remaining linear momentum into erratic, multi-axis angular momentum, consequently dumping much of the coin's remaining bulk/translational kinetic energy into internal (rotational) degrees of freedom. Not to mention that the dynamics of any particular "post-bounce" phase of the coin's flight appear to be highly sensitive to the bounce's initial conditions, due to the highly elastic nature of the coin-floor collision and the huge variation in torque that such a flattened object will experience, depending on its exact orientation relative to the floor's surface. (That part depends on the collision being with a hard floor. But the inelasticity of the coin's collision with a soft floor, like a grass-covered football field, can't be any worse than that of a coin-hand collision.) There is just no way that this "post-bounce" phase, at least from a hard floor, doesn't scramble much of the residual predictability of the "flip" phase of the coin's flight. Which makes the edge bias a moot point, because the "dying" phase of the coin starts with completely unpredictable initial conditions.
But he showed in the previous video that, for a typical person flipping a coin the result is nearly 50/50 (50.5% chance to land on the side that it started on). That phase of the coin toss has relatively little predictability to begin with, compared to the edge bias which as he said in this video could be very significant (20% more likely to land on the favored side).
Almost always when letting a coin drop on the floor it was on carpet. This rarely went outside of my opposite side guess when flipped by 5th graders.
Sometimes i catch a tossed salad if i play my cards right
I can spin any coin, any time and get the outcome I want. Every time.
I can also flip a coin and cheat too, but that depends on the situation... But to get the outcome I want flipping it, let's just say that I have to catch it and that's all I'll let on.
And yes... There's a hand there. If you allow someone to catch it, you allow them, with minimal training and practice, win ever coin toss.
how is the coin landing on the ground "less fair"? i thought fairness in this situation would be the most random method, and landing on the ground seems to be it :/
he mentioned in the beginning of the video that coins tend to have a distinct bias for how they will land when spun on edge. The flip that ends on the table will often times spin for a short time on its edge, thus involving that bias.
screw it, i don't want to know which side it lands on until i learn how to spin it like persi. damn it, magicians are always doing something normal in an odd way. SHIBBY!
Beautiful 90% silver half dollar. don't spend those :)
Better to let it fall on a soft surface, like a carpet or soil.
but if you carry a load of coins in your pocket and pick a random one it should be fair again
Well but if it is a hard surface then the coin can start to spin - then it could bee 80%.
I put a coin on a ceiling fan and turned it on. It hit the wall and fell on the ground. Tails
So the question is really: Should *an unbiased party* catch the coin or should we let it fall on the ground?
This dude finna listen to Platinum Plus by Big L
Coincidence the video lasted 3:14? I think not
A mathemagician!
this prof really reminds me of richard feynman for some reason
The video length though.
where'd this dude get a half-dollar coin (a U.S. coin which hasn't been minted since the 60s) in the middle of england
***** Persi is in the US - I got mine of the slow motions from ebay!
Half dollar coins have been produced every year since the conception of the United States Mint in 1794. Sometimes referred to as the fifty-cent piece, the only other U.S. coin that has been minted as consistently is the cent. -- WIkipedia
??? ive literally never seen one that was older than the 70s
If he was in England, he could probably go to a major bank and request it, and they might have it. You can request foreign currency at US banks too.
*****
If I remember right, the Wikipedia article says they are made for collectors now. That's probably why you haven't seen any new ones in circulation.
Can you possibly talk about Common Core math and state what your opinions on it compared to the "old method"
So... how do I get paid for doing this stuff?
I am sorry but i dont belive that catching the coin is more fair. Like you said the previous video one can calculate the speed and spin speed of a coin flip. but if you catch that coin you are dealing with a binary head or tails situation. If you let the coin hit the surface there is a hole new math involved. Each degree can make a huge difference on the coin behave. It can flip many time in both directions before decide the result. Sry my poor english
You kinda missed the point here, which is that if you let it hit a surface on which it can bounce/spin it's provably no longer 50-50 as to whether it lands heads or tails first. And since 'fair' in this instance is taken to mean "most random", then yes, catching a coin is fairer than letting it drop on a hard surface. The "new math", which you mention is precisely what's skewing the results so that it's not a 50-50 chance.
SatanicBunny From what i understood of the first video, the chances are not 50-50 when you catch, its more like 51-49 and depends on what face is up when u throw the coin. So if catching the coin its 51-49 how much is if you let it hit the surface? 52-48? Can you calculate that? I guess you can't b/c the number of variables increases so much, that is what i meant. By the way, i guess it gets closer to 50-50 since there is so much randomness included
SatanicBunny PS. Maybe i am really missing the point since my english is not that good. I may have miss interpreted the message
Daniel Calou
I think the point is that either way is not really random or fair in any case. You could only really say that it is more like the illusion of 'randomness' in fairer situations than in others. But really it is not random at all, but rather deterministic. If you have all the required information of course. While (like others have said) it is true that if both parties don't have the specific information about the coin or how it is flipped or span, it can be seen at a glance that it is fairer. But the deterministic and biased nature of it all means that there are particular exploitations (or key rules one might follow) which will potentially lead to one party winning the game in most cases. This is essentially defeating the purpose of the coin toss - in that it is supposed to be fair.
As for the whole new area of maths involved... yes you could argue that. But in all fairness, is that new area of maths not as biased as the original area of maths for similar reasons since the coin is biased? Since I have no idea which area you are specifically refering to when you say a "whole new area of maths" it kind of makes it difficult to answer constructively. But I will say that if you want to get into the thick of it about more advanced variables interacting upon the coin when it has landed upon a hard surface, a hand is not perfectly flat. So if the coin collides with your hand on its edge, can the curvature of your hand act upon the coin? I'd say most definitely yes... but would the coin be tempted to still fall towards its bias in most cases? Stuff which could be considered I guess.
MrJC1 I am refering to the fact the coin bounce when it hits the ground. When you catch it its done, either head or tails the math is over. But i liked your answere.
Yes, because hey: free coin