there are some outlying setups that make it very non random. when I do the coin flip, tossing with the thumb as shown in the video, catching in my hand and placing on the back of my other hand (a common way to display results of a toss where i grew up) with an Australian 20 cent coin it is almost certain (~50 tosses in a row, no counter examples) to be the opposite way up to the starting orientation. i don't get the same level of consistency with other coins.
I've always wondered if the 51/49 odds were due to the different types of coin available, or if it was all done off a standardised piece - be it a perfectly balanced metal circle or a US quarter, or if it was due to mechanics.
When I was a teenager I decided I was going to master the coin toss to get the result I wanted, and I did. I can safely say that 99.9% of the times I got the result I wanted setting up specific initial conditions (not in a mathematical fashion, but in a trial an error one): initial side, initial position, force applied, point of impact of the thumb on the coin, point of interception of the hand and the coin in the air. I can't tell how long it took me to master it, because I can't remember. I can now think many other parameters that one could take into consideration, but those were the ones that I thought about by that time.
It is not soo dificult to learn to flip a medium size coin and catch then in some way you can "force" 80-90% of the results. It is not about predicting the moviment, it is most like a sport. Your brain can automatically do it for you with some training, like throwing a ball in a basket or thowing a knife. (I'm sorry about my English, it is not my language). Regards!
One point this video missed (and hopefully the "very soon" video will cover the issue) is that many coins are not weighted evenly, and this _can_ give them a bias towards a certain side. For example, I believe the American penny has a bias towards the tails side.
oh boy. if you just count in the rotation / speed its biased. if you start with other factors like weight, weight distribution, aero dynamic, inertia, inital energy input (like if you know how to flip a coint at a certain speed, you could more or less get what you wanted). you can go forever that its not random. but thb, i think they should stay at "is it random" and "can you flip it in a way, that favors your decision". ;)
David Aceituno it turns out that they explain this is the second video. See the description for a link. The article I linked didn't make it clear (and hence I misinterpreted it), but it was talking about spinning the coin like a spinning top, rather than tossing a coin.
Those graphs remind me of the graphs in my microeconomics textbook describing two different factors of production producing a specified amount produced, so there are an infinite number of combinations producing a specified amount of production, and infinitely many production amounts. I'm mentioning it cuz it just points to the way math describes the world and I find it very interesting.
When talking about the difference introduced by attaching dental floss to the coin, he said 'we hope it's a third-order effect'. What does that mean? What is a third-order effect? From context I assume it means that the influence is small? Given that we're specifically talking about a system which has chaotic behavior (sensitive dependence on initial conditions), I would think knowing the influence is small would be useless. Even tiny differences would result in it being entirely different.
The system you use doesn't matter, as long as you always write down and pay attention the units. Once a mars -lander- probe crashed into mars, because they used different units without noticing it. Edit: not a lander. Or at least, it wasn't supposed to.
does the amount of metal (or the picture) on each side of the coin not count for any irregularity? I've always heard that a coin toss is effected by how the coin is printed or forged or whatever the process is that distributes the mass of the coin across the 2 faces For instance some of the state coins in the US have very little 3D metal on the state side which would make the head side hold more of the mass for the coin
Nice, I love investigating these simple questions. For you bicycle riders out there with O-locks on your bikes: Have you guys noticed how frequent your lock hit the spokes when trying to lock your bike? The high rate of occurrence caught my attention so much that I calculated the probability for the O-lock to hit the spokes and found P(36) ~ 0.23 for an ordinary bike having tire diameter of .6m and 36 spokes. That's almost 1 in 4 :-O
I wonder if their calculations took into account the fact that the coin-flipper often doesn't catch the coin at the same point where it was flipped. So the speed of the coin isn't really a determining factor, since the coin isn't simply moving up and down the same distance.
Find it humorous people say they down-voting for use of Imperial units even though it has very little to do with the video. I am sure their mommies would love to hear about how much they were offended.
Benobot99 Different headphones/monitors have different impedance. The smaller the impedance the louder he'd sound (a kindof simplified explanation). OP might need an amplifier.
I can get a coin flip to land the way I want it to with 80%+ accuracy (as long as the choice is made before the throw, and I can choose which side is up before the throw), so the short answer is: not very.
I always get heads. Or almost anytime. I think an experiment from when I was child showed a 90% chance of heads no matter how the coin initially started. But didn't check if the probability of tail was bigger if tail was upwards at initiation.
Love videos about randomness! More! We tend to call something is "random" just because it is too complicated for us to predict, but its not random at all.
when you look at a coin that is being flipped in the air, the side that the light reflects off of is the side that will be up when it lands. same goes with spinning it.
FEET PER SECOND?! Disliked video. Reported for repulsive content. Unsubscribed. Deleted youtube account. Uninstalled Firefox. Smashed computer. Set house on fire.
Are coins usually equally heavy on both sides (sliced so discs would be created) and if not how much could a reasonable weight difference change the outcome of the coin toss?
Out of 100 starting at heads: average 51, but out of 100 starting at tails: average 51. I was the only in my class who had the reasoning. They thought I was some genius.
To try to explain the bias towards landing on the side on which it started: If you could tally the side facing up after every "flip" during its time in the air, the starting side would either be one ahead, or equal to the side initially facing down. This would lead to that 51% chance mentioned in the video. Does that make sense?
This completely changes the game of "Two-up" played here in Australia, which is illegal on all days other than April 25 (Australia Day). The rules of two-up state that two coins are placed tails-up on a flat board and then flipped, with bets being made on how they fall. If flipping with a paddle exhibits the same kind of bias that flipping by hand does, then it would result in the most catastrophic undermining of Australian culture since Crocodile Dundee.
i was a kid i did a similar experience with coin tosses. I remember hypothesising that no matter how high or how fast you flip the coin the outcome will be the same from the starting side, But only if the coin's displacement was more or less 0. I never knew if i was correct or not, but i came to a conclusion to always pick the side that is up from the start. At least now i know that my hypothesis is completely crap but my conclusion is more or less on par.
so your hypothesis was that, but what did the experiment itself end up showing? because the hypothesis is what you think will happen before the actual experiment, so if you did it right, you were more likely to be correct
it kept showing that the top side that it started with, whenever it landed. I can't remember how many trials i did or the exact percentage but almost always landed top side. I won a fair bit of coin toss with that idea, with slight variation if they do a catch and flip at the end.
Shouldn't you also take into account the design of each face? Because one side of the coin must be slightly heavier than the other side. Does that have any significant effect?
The beauty of SI units is that it can be easily derived from base units like meter, secs, and kg. 1 Watt = 1 Watt, no matter where the power is coming from, electrical, mechanical or thermal. The time of horses being the source of power is over. Plus, the base units are easily extended by factors of 10: meters, mm, km. No complicated conversion factors between inch, feet and mile needed. And, despite english is a good language for communication round the world, this doesnt mean we all need to like fish eaten with a newspaper wrap and a soak of vinegar.
A while back I used some old parts out of an R/C plan I built and ended up crashing, to make a coin flipping machine. At one point I was able to get a 70% chance of landing heads. That is, after repeated attempts, and flipping 1 coin 100 times, It averaged 70 heads, and 30 tails. I'm sure someone who is much more skilled in mathematics could do better, but I was pretty happy with that!
I really liked the use of the half dollar in the video. It's a seldom used but great coin. I'm assuming you used it because it's easier to see on camera? Does the size of the coin make any difference at all in this experiment?
6:25 isn't the problem only six dimensional? From Chasles' theorem the most general movement of a rigid body is a translation of the centre of mass, and then a rotation about an axis through it's centre of mass. Using generalised coordinates, the position of the centre of mass is then specified by three coordinates as it exists in three-space, and the rotation about the centre of mass is described then by three coordinates also. So, in configuration space, there is a single path, in six-space, that describes the motion.
Instead of flipping it, start on the floor and flick it under your finger, then how do you determine the probability of heads / tails when the starting state isn't one of the faces ?
Hey Brady for a long time I've been wondering how mathematicians work in other dimensions and even fathom things with 12 dimensions could you make a video talking about this please
The randomness comes from the assumption no two flips have the same initial conditions, especially the energy being put into the coin by an imperfect human doing the flipping.
Use a machine to flip a coin inside a box. While the coin is unobserved inside, it is *both heads and tails*. When you open the box, it appears either heads or tails.
Both yes and no a perfect example of a reversed Schrödinger's cat. Its such a splendid question. Though i'm not going to type any more because it would be too long so i'm going to leave this up to the minds of ones reading this comment.
Why would you have the x axis stand for speed instead of the duration that the coin is in the air? Because if the coin is flipped at different heights the coin would be able to flip more, right?
+Seth Wyatt the assumption is that the coin has an initial velocity at height 0 and it returns to height 0 as well -- so if the initial velocity is close to 0 then the time to come back is also close to 0. He should have clarified that as I also found it confusing a bit.
+tgwnn I was looking at the chart he made and noticed that he just gives you the velocity of the coin and how fast it is turning. And this would leave a third variable, the distance he flipped the coin up into the air, unaccounted for. This being a problem because, he could have a different outcome even if he had the same velocity and the same rpm on both flips. For example, if he had flipped the coin 2ft into the air or 3ft at a high velocity and low rpm the coin would have a higher chance of turning over. And the reason I said duration in my previous comment was because it would cover both speed and distance. But I do agree that we can assume he started the flip at height 0 and at a velocity of zero.
+Seth Wyatt no sorry that's not what I meant, I meant that the assumption he made is that the toss is made at h=0 (and the toss also finishes at h=0) at some initial v and some initial omega and these two parameters are given by the two axes. Now if the v is small enough, tbe coin falls right down. I'm actually quite sceptical about the other assumption, namely that at a low enough initial omega the coin doesn't flip as the coin could easily start turning from air friction if the toss is a bit asymmetric. This is probably covered by the paper but I'm too lazy to download and read it.
I find it hard to believe that this bias is the same for all people, I am sure there is a variance. If you hardly give it any rotation the bias will be more, I would guess. But moreover he didn't include a 3rd typical variable: height! Do you drop it on the ground, or catch it in the air, and if you catch it, at a higher height, or lower, or does it depend how far away from your body you need to catch it.
Next would be what about a magician ? Someone with nimble hands, how predictable can he become ? (Requires some parameters : a player would reject a coin toss that looks too flat or small)
I wonder if the professor's analysis takes the possibility of a projectile trajectory into account, because I doubt I could ever throw a coin as vertically as it is demonstrated in this video. Most of the times it will drop some 20 cm away from the finger that threw it.
Yea ok but when the coin lands on the ground it bounces off randomly (more or less) and keeps on flipping. And it does that a couple times before coming to rest. So how do you account for that and come up with the .51 bias of it coming to rest the same way it went up?
The number of people complaining about the use of feet is insane. If you cannot follow the video or understand this because feet were used then you should stop trying to learn this material, and go learn addition and subtraction again so you can just convert them on the fly if it means that much to you.
Quarters are not 50-50 if I recall correctly and I prefer a computer for my randomness because it works a little better. Every time I flip a coin it tends to just switch sides.
I'm curious, do coaches in the NFL teach this to their players? Idk if they can even see how the ref places the coin before they make their decision, but if they can then this seems worth knowing.
I like to proof my hand made dices dividing the sides for 100%, give 30% of margin of error and toss 100 times and see if the numbers fit the percent's ranges. · A question: Any advise in more acurate percent per sides and/or margin of error?
Does the weight of the coin play a factor? Coins differ from country to country and denominations of a coin vary in weight, albeit minuscule, does this play a factor? I would assume that in an ideal world where both sides of the coin weigh the same that this video holds true (or testing the exact same coin over and over would yield these conclusions), due to the images on either side of the coin altering the weight slightly, or is this negligible?
Would coin denomination make a difference. In the video he flipped a half dollar what if you flip a quarter on a 1 pound coin, or a 1 yen coin. Are the weight, size, center of mass some of those 12 dimensions he mentioned
Brady, could you switch off your subpixel rendering? It looks really ugly when you zoom into screenshots. I don't know if the Mac lets you do this but given the decent pixel densities of today's displays, I don't think you'd notice if you did.
The coin landing on the ground is a lot more fair, as it has so much things that can happen then simply landing flat. That calculating process to dictate what it will land as it a whole other discussion and in my thoughts much harder to calculate.
Is this not more Physics related than maths? And therefore better suited to Sixty Symbols? Is it because this particular interview was not with Uni of Nottingham?
It feels more physicsy, but I don't know if it would really fall under a physics department umbrella. All of the principles are known and understood, the mechanics that are used are that of Lagrangians, and drag arguments. I would call this a statistics problem, that exists in a real situation, and so requires a grounding in the physical characteristics of the applied system. The problem could probably be tacked by anyone with a strong maths background.
But you don't exactly catch it at the same height where you tossed it. There will be a distance between the thumb and the palm. You may also move your hand a bit.
when i was a kid, in school we tosed a coin for everything. Soon i noticed that if you put the coin with X side up in your hand, when you toss it and grab it back, it had a large chance of landing in your hand witht he same side up. Dont know if im crazy and i just imagined that, but thats how i remember i won most of the times xD
recently I was bored at work and I started to flip an American quarter and catch it in my palm and then flip it over. after only about 3 flips I got tails 8 times in a row. i was pretty surprised.
I wonder what the twelve dimensions are. Velocity in 3 dimensions, rotation about 3 axes, mass/density/surface area of the coin, air density? Any ideas?
***** 6:20 He clearly states there are 12 parameters involved in flipping a real coin. Don't feel obliged to answer a question that you don't know the answer to my friend.
When I was in elementary school I won a lot of quarters. I trained myself to flip a quarter in the same way every time so that over 90% of the time it would land on the opposite face that it started on. Chocolate milk instead of regular milk for three years in a row just because I taught myself to flip any quarter the same way every time.
0:53
Feet per second : American
Révolutions per second : French
Crazy people per second: Florida
@@michaelg8841 never have a read anything more true in my life
Tea per second: Britain
nuclear per second: north korea
Water crisis per second: Nigeria
thank you hector salamanca
he is tortuga.
jesse we have to cook
Ding Ding
literally came here to say this
Ring that Bell!
3:17 I like how his thumbnail is literally bruised from flipping coins so much. Now that's dedication!
Videos on this channel are always worth a thumb!
Bundi Derp thanks!
Numberphile A thumb down though ;)
fred col noh. a fum uhp
And it's comments ^^
??.
there are some outlying setups that make it very non random.
when I do the coin flip, tossing with the thumb as shown in the video, catching in my hand and placing on the back of my other hand (a common way to display results of a toss where i grew up) with an Australian 20 cent coin it is almost certain (~50 tosses in a row, no counter examples) to be the opposite way up to the starting orientation.
i don't get the same level of consistency with other coins.
I've always wondered if the 51/49 odds were due to the different types of coin available, or if it was all done off a standardised piece - be it a perfectly balanced metal circle or a US quarter, or if it was due to mechanics.
When I was a teenager I decided I was going to master the coin toss to get the result I wanted, and I did. I can safely say that 99.9% of the times I got the result I wanted setting up specific initial conditions (not in a mathematical fashion, but in a trial an error one): initial side, initial position, force applied, point of impact of the thumb on the coin, point of interception of the hand and the coin in the air. I can't tell how long it took me to master it, because I can't remember. I can now think many other parameters that one could take into consideration, but those were the ones that I thought about by that time.
so what......
What do you do if you want to resolve something randomly?
It is not soo dificult to learn to flip a medium size coin and catch then in some way you can "force" 80-90% of the results. It is not about predicting the moviment, it is most like a sport.
Your brain can automatically do it for you with some training, like throwing a ball in a basket or thowing a knife.
(I'm sorry about my English, it is not my language). Regards!
Edgy
There is a recent study published on that. They used volunteers and made 350k coin tosses with different coins. It was 50.8 to 49.2
One point this video missed (and hopefully the "very soon" video will cover the issue) is that many coins are not weighted evenly, and this _can_ give them a bias towards a certain side. For example, I believe the American penny has a bias towards the tails side.
wrong, it doesnt matter when flipping. Loaded coins have still 50 50 chance.
RobosergTV - прохождение и летсплей игр How so? :)
oh boy. if you just count in the rotation / speed its biased. if you start with other factors like weight, weight distribution, aero dynamic, inertia, inital energy input (like if you know how to flip a coint at a certain speed, you could more or less get what you wanted). you can go forever that its not random. but thb, i think they should stay at "is it random" and "can you flip it in a way, that favors your decision". ;)
David Aceituno it turns out that they explain this is the second video. See the description for a link.
The article I linked didn't make it clear (and hence I misinterpreted it), but it was talking about spinning the coin like a spinning top, rather than tossing a coin.
David Aceituno th-cam.com/video/9RKKoXw7wJw/w-d-xo.html
Those graphs remind me of the graphs in my microeconomics textbook describing two different factors of production producing a specified amount produced, so there are an infinite number of combinations producing a specified amount of production, and infinitely many production amounts. I'm mentioning it cuz it just points to the way math describes the world and I find it very interesting.
I love this stuff
and we love you
Never expected to see CustomGrow comment on a math video. Awesome.
When talking about the difference introduced by attaching dental floss to the coin, he said 'we hope it's a third-order effect'. What does that mean? What is a third-order effect? From context I assume it means that the influence is small? Given that we're specifically talking about a system which has chaotic behavior (sensitive dependence on initial conditions), I would think knowing the influence is small would be useless. Even tiny differences would result in it being entirely different.
Interesting!
But you´re doing science, so please use the metric system
I was going to say the same thing!
*pulls out ten-sided coin
The system you use doesn't matter, as long as you always write down and pay attention the units.
Once a mars -lander- probe crashed into mars, because they used different units without noticing it.
Edit: not a lander. Or at least, it wasn't supposed to.
For once I agree with you, Patrick.
Hey! Even if I use metric system, he has the right to use non-metric systems whenever he wants to!
"I don't care how hard you flip it, you could flip it to the moon!" Just the way he says it makes me laugh.
That's a mathematical way of talking.
@@animal_shorts1 i'm going to flip it horizontal so that it's centrifugal force keeps it spinning like an alien space ship.
does the amount of metal (or the picture) on each side of the coin not count for any irregularity? I've always heard that a coin toss is effected by how the coin is printed or forged or whatever the process is that distributes the mass of the coin across the 2 faces
For instance some of the state coins in the US have very little 3D metal on the state side which would make the head side hold more of the mass for the coin
"We did the analysis in the 12 dimensional space"
Something you should not here in a video regarding coin tosses.
Nice, I love investigating these simple questions. For you bicycle riders out there with O-locks on your bikes: Have you guys noticed how frequent your lock hit the spokes when trying to lock your bike? The high rate of occurrence caught my attention so much that I calculated the probability for the O-lock to hit the spokes and found P(36) ~ 0.23 for an ordinary bike having tire diameter of .6m and 36 spokes. That's almost 1 in 4 :-O
I wonder if their calculations took into account the fact that the coin-flipper often doesn't catch the coin at the same point where it was flipped. So the speed of the coin isn't really a determining factor, since the coin isn't simply moving up and down the same distance.
Find it humorous people say they down-voting for use of Imperial units even though it has very little to do with the video. I am sure their mommies would love to hear about how much they were offended.
I had to turn my volume all the way up to 100 just to be able to hear what he's saying
Same
Mine was on 32 out of 100 and I heard him fine.
Are you deaf?
Benobot99 Different headphones/monitors have different impedance. The smaller the impedance the louder he'd sound (a kindof simplified explanation). OP might need an amplifier.
You're not alone.
I wonder how many of these views were Bill Belichick?
😂😂 but just one....he recorded it.
I can get a coin flip to land the way I want it to with 80%+ accuracy (as long as the choice is made before the throw, and I can choose which side is up before the throw), so the short answer is: not very.
skevoid yeah, but if it hits the ground all bets are off
I always get heads. Or almost anytime. I think an experiment from when I was child showed a 90% chance of heads no matter how the coin initially started. But didn't check if the probability of tail was bigger if tail was upwards at initiation.
Love videos about randomness! More!
We tend to call something is "random" just because it is too complicated for us to predict, but its not random at all.
when you look at a coin that is being flipped in the air, the side that the light reflects off of is the side that will be up when it lands. same goes with spinning it.
FEET PER SECOND?!
Disliked video.
Reported for repulsive content.
Unsubscribed.
Deleted youtube account.
Uninstalled Firefox.
Smashed computer.
Set house on fire.
Voted UKIP
Will Deary Let's not be irresponsible here, c'mon...
My reaction as well. :P
Spaghetti falls out of pocket.
This made my day :P
Are coins usually equally heavy on both sides (sliced so discs would be created) and if not how much could a reasonable weight difference change the outcome of the coin toss?
Out of 100 starting at heads: average 51, but out of 100 starting at tails: average 51. I was the only in my class who had the reasoning. They thought I was some genius.
To try to explain the bias towards landing on the side on which it started: If you could tally the side facing up after every "flip" during its time in the air, the starting side would either be one ahead, or equal to the side initially facing down. This would lead to that 51% chance mentioned in the video. Does that make sense?
This completely changes the game of "Two-up" played here in Australia, which is illegal on all days other than April 25 (Australia Day). The rules of two-up state that two coins are placed tails-up on a flat board and then flipped, with bets being made on how they fall. If flipping with a paddle exhibits the same kind of bias that flipping by hand does, then it would result in the most catastrophic undermining of Australian culture since Crocodile Dundee.
i was a kid i did a similar experience with coin tosses. I remember hypothesising that no matter how high or how fast you flip the coin the outcome will be the same from the starting side, But only if the coin's displacement was more or less 0. I never knew if i was correct or not, but i came to a conclusion to always pick the side that is up from the start. At least now i know that my hypothesis is completely crap but my conclusion is more or less on par.
so your hypothesis was that, but what did the experiment itself end up showing?
because the hypothesis is what you think will happen before the actual experiment, so if you did it right, you were more likely to be correct
it kept showing that the top side that it started with, whenever it landed. I can't remember how many trials i did or the exact percentage but almost always landed top side. I won a fair bit of coin toss with that idea, with slight variation if they do a catch and flip at the end.
The dental floss idea was a very clever way of measuring the number of spins.
The scariest thumb ever videoed.
Shouldn't you also take into account the design of each face? Because one side of the coin must be slightly heavier than the other side. Does that have any significant effect?
The beauty of SI units is that it can be easily derived from base units like meter, secs, and kg. 1 Watt = 1 Watt, no matter where the power is coming from, electrical, mechanical or thermal. The time of horses being the source of power is over.
Plus, the base units are easily extended by factors of 10: meters, mm, km. No complicated conversion factors between inch, feet and mile needed.
And, despite english is a good language for communication round the world, this doesnt mean we all need to like fish eaten with a newspaper wrap and a soak of vinegar.
Wouldn't the variations of carvings or engravings on the coin also affect how the coin flips, just based on a non-uniform distribution of mass?
I was recommended this for a class. It blows my mind that even 212 people could dislike this video
These videos are awesome!
When I heard him say "miles per hour" I instantly knew there were going to be comments about it below...!
A while back I used some old parts out of an R/C plan I built and ended up crashing, to make a coin flipping machine. At one point I was able to get a 70% chance of landing heads. That is, after repeated attempts, and flipping 1 coin 100 times, It averaged 70 heads, and 30 tails. I'm sure someone who is much more skilled in mathematics could do better, but I was pretty happy with that!
I really liked the use of the half dollar in the video. It's a seldom used but great coin. I'm assuming you used it because it's easier to see on camera? Does the size of the coin make any difference at all in this experiment?
Right in the middle of watching this i asked myself... Why do i watch this video... Why do i wanna know this...
6:25 isn't the problem only six dimensional? From Chasles' theorem the most general movement of a rigid body is a translation of the centre of mass, and then a rotation about an axis through it's centre of mass. Using generalised coordinates, the position of the centre of mass is then specified by three coordinates as it exists in three-space, and the rotation about the centre of mass is described then by three coordinates also. So, in configuration space, there is a single path, in six-space, that describes the motion.
You can all just ignore my comment. I didn't take the time derivatives for the remaining six. This is probably why I failed my dynamics exam.
Joshua Mcateer Dumbass
How come he didn't take the probability of the coin landing on its side?
Brady can you get a slow motion video of Prof. Diconis doing false deals? He is an "Expert On the Card Table".
Instead of flipping it, start on the floor and flick it under your finger, then how do you determine the probability of heads / tails when the starting state isn't one of the faces ?
Hey Brady for a long time I've been wondering how mathematicians work in other dimensions and even fathom things with 12 dimensions could you make a video talking about this please
Catching the coin makes it more random, therefore it is more fair.
Don't forget that, with practice, people can flip coins really consistently and catch the coin as they've called it nearly all of the time.
This is one of my favorites for a long time!
Please increase microphone level. Can hardly hear u on ipad at full volume
For deciding on a restaurant, when even asking for all the Oks didn't come up with the answer, it’s close enough ;)
The randomness comes from the assumption no two flips have the same initial conditions, especially the energy being put into the coin by an imperfect human doing the flipping.
Use a machine to flip a coin inside a box.
While the coin is unobserved inside, it is *both heads and tails*.
When you open the box, it appears either heads or tails.
"Schrödingers coin" :D
What about using this data to create a coin spinning robot that flips the coin in the desired result. It's possible to do that ?
Both yes and no a perfect example of a reversed Schrödinger's cat.
Its such a splendid question.
Though i'm not going to type any more because it would be too long so i'm going to leave this up to the minds of ones reading this comment.
Why would you have the x axis stand for speed instead of the duration that the coin is in the air? Because if the coin is flipped at different heights the coin would be able to flip more, right?
+Seth Wyatt the assumption is that the coin has an initial velocity at height 0 and it returns to height 0 as well -- so if the initial velocity is close to 0 then the time to come back is also close to 0. He should have clarified that as I also found it confusing a bit.
+tgwnn I was looking at the chart he made and noticed that he just gives you the velocity of the coin and how fast it is turning. And this would leave a third variable, the distance he flipped the coin up into the air, unaccounted for. This being a problem because, he could have a different outcome even if he had the same velocity and the same rpm on both flips. For example, if he had flipped the coin 2ft into the air or 3ft at a high velocity and low rpm the coin would have a higher chance of turning over. And the reason I said duration in my previous comment was because it would cover both speed and distance. But I do agree that we can assume he started the flip at height 0 and at a velocity of zero.
+Seth Wyatt no sorry that's not what I meant, I meant that the assumption he made is that the toss is made at h=0 (and the toss also finishes at h=0) at some initial v and some initial omega and these two parameters are given by the two axes. Now if the v is small enough, tbe coin falls right down. I'm actually quite sceptical about the other assumption, namely that at a low enough initial omega the coin doesn't flip as the coin could easily start turning from air friction if the toss is a bit asymmetric. This is probably covered by the paper but I'm too lazy to download and read it.
Please tell me, that the shuffle video snippet at the end slate is from a video about the faro shuffle and its group theory aspects :)
The dental floss method was brilliant!
I'm confused. Is the bias something that happens to "typical human toss", or does that include all combinations of translational and angular speeds?
I find it hard to believe that this bias is the same for all people, I am sure there is a variance. If you hardly give it any rotation the bias will be more, I would guess.
But moreover he didn't include a 3rd typical variable: height!
Do you drop it on the ground, or catch it in the air, and if you catch it, at a higher height, or lower, or does it depend how far away from your body you need to catch it.
You can also practice to make it more likely to get the result you want. I did this as a kid for my dad
The real question is what's the most you've ever lost on a coin toss.
Next would be what about a magician ? Someone with nimble hands, how predictable can he become ? (Requires some parameters : a player would reject a coin toss that looks too flat or small)
For any coin nerds out there:
This is a 1964-P(no mint mark) Kennedy Half Dollar. It has a composition of 90% silver and 10% copper.
i can always control what side it lands on by lowering my hand and not spinning the coin to fast.
I wonder if the professor's analysis takes the possibility of a projectile trajectory into account, because I doubt I could ever throw a coin as vertically as it is demonstrated in this video. Most of the times it will drop some 20 cm away from the finger that threw it.
Actually a pretty interesting topic. I like his explanations!
Yea ok but when the coin lands on the ground it bounces off randomly (more or less) and keeps on flipping. And it does that a couple times before coming to rest.
So how do you account for that and come up with the .51 bias of it coming to rest the same way it went up?
Nothing is Random - No probability without uncertain mechanism - therefore YOU HAVE NO FREE WILL.
The number of people complaining about the use of feet is insane. If you cannot follow the video or understand this because feet were used then you should stop trying to learn this material, and go learn addition and subtraction again so you can just convert them on the fly if it means that much to you.
Quarters are not 50-50 if I recall correctly and I prefer a computer for my randomness because it works a little better. Every time I flip a coin it tends to just switch sides.
How do tou account for catching the coin lower that you tossed it, or that some people flip the coin once more after they catch it?
I'm curious, do coaches in the NFL teach this to their players? Idk if they can even see how the ref places the coin before they make their decision, but if they can then this seems worth knowing.
I like to proof my hand made dices dividing the sides for 100%, give 30% of margin of error and toss 100 times and see if the numbers fit the percent's ranges.
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A question: Any advise in more acurate percent per sides and/or margin of error?
Does the weight of the coin play a factor? Coins differ from country to country and denominations of a coin vary in weight, albeit minuscule, does this play a factor? I would assume that in an ideal world where both sides of the coin weigh the same that this video holds true (or testing the exact same coin over and over would yield these conclusions), due to the images on either side of the coin altering the weight slightly, or is this negligible?
Would coin denomination make a difference. In the video he flipped a half dollar what if you flip a quarter on a 1 pound coin, or a 1 yen coin. Are the weight, size, center of mass some of those 12 dimensions he mentioned
Brady, could you switch off your subpixel rendering? It looks really ugly when you zoom into screenshots. I don't know if the Mac lets you do this but given the decent pixel densities of today's displays, I don't think you'd notice if you did.
Speaking of coins, can you do a video that explains which parts of a coin are visible when you spin it?
dots and boxes, rock paper scissors, coin flipping? I assume the next one is about how to properly throw a stone for hopscotch.
Since you mentioned that coin flipping is a 12 dimensions problem. What are the 12 dimensions?
The coin landing on the ground is a lot more fair, as it has so much things that can happen then simply landing flat. That calculating process to dictate what it will land as it a whole other discussion and in my thoughts much harder to calculate.
No Country For Old Men.... That Coin toss scene
I follow your instructions and flipped it to the moon. You owe me a quarter
This also made me wonder what kind of calculable bias dice of varying "sizes" have.
So, I should call for heads if its heads when tossed ?
Is this not more Physics related than maths? And therefore better suited to Sixty Symbols? Is it because this particular interview was not with Uni of Nottingham?
It feels more physicsy, but I don't know if it would really fall under a physics department umbrella. All of the principles are known and understood, the mechanics that are used are that of Lagrangians, and drag arguments. I would call this a statistics problem, that exists in a real situation, and so requires a grounding in the physical characteristics of the applied system. The problem could probably be tacked by anyone with a strong maths background.
Brady, can you please get one of your professors to walk through Bayes theorem, and its implications in applied mathematics?
But you don't exactly catch it at the same height where you tossed it. There will be a distance between the thumb and the palm. You may also move your hand a bit.
If you flip it to the moon, it would be 0.49 leaving you with the same side you started with! :D
This channel is awesome
when i was a kid, in school we tosed a coin for everything. Soon i noticed that if you put the coin with X side up in your hand, when you toss it and grab it back, it had a large chance of landing in your hand witht he same side up. Dont know if im crazy and i just imagined that, but thats how i remember i won most of the times xD
recently I was bored at work and I started to flip an American quarter and catch it in my palm and then flip it over. after only about 3 flips I got tails 8 times in a row. i was pretty surprised.
First of all, that thumb.
Secondly, I can influence coin flips by changing the height of which I catch the coin. That or I'm bat shit crazy
I wonder what the twelve dimensions are. Velocity in 3 dimensions, rotation about 3 axes, mass/density/surface area of the coin, air density? Any ideas?
It has too wide of a range in the variables so no one really knows.
***** 6:20 He clearly states there are 12 parameters involved in flipping a real coin. Don't feel obliged to answer a question that you don't know the answer to my friend.
wazzmastermax It wasn't an answer.
***** "No one really knows" is an answer - the wrong answer. The gentleman in the video does indeed know.
The variables have too much range to come to an answer. So tell me if i flip a coin Heads or Tails
When I was in elementary school I won a lot of quarters. I trained myself to flip a quarter in the same way every time so that over 90% of the time it would land on the opposite face that it started on. Chocolate milk instead of regular milk for three years in a row just because I taught myself to flip any quarter the same way every time.
I could listen to his voice all day long.. Dont know why..
My volume was over 9000 and I still had trouble hearing this
I'd love to back to school and tell my Maths teacher a coin flip is 51/49. That would rustle his Jimmy's so bad.
My teacher made me watch this, LOL 😂