How random is a coin toss? - Numberphile

Randomness, coins and dental floss!
Featuring Professor Persi Diaconis from Stanford University.
More links & stuff in full description below ↓↓↓
To catch or not to catch: • Should you catch a tos...
Extra footage (Numberphile2): • Coin Flipping (extra f...
Superbowl coin tosses: • 14 Super Bowl Coin Tos...
Paper shown in this video (Dynamical Bias in the Coin Toss): bit.ly/Dynamica...
Support us on Patreon: / numberphile
NUMBERPHILE
Website: www.numberphile...
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberph...
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumb...
Videos by Brady Haran
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanb...
Sign up for (occasional) emails: eepurl.com/YdjL9
Numberphile T-Shirts: teespring.com/...
Other merchandise: store.dftba.co...

[@sm64guy28]

0:53 Feet per second : American Révolutions per second : French

[@michaelg8841]

Crazy people per second: Florida

[@CTcuber4K]

@@michaelg8841 never have a read anything more true in my life

[@OnionBorn]

Tea per second: Britain

[@___________aing]

nuclear per second: north korea

[@shiloranxxer]

Water crisis per second: Nigeria

[@baGGan]

thank you hector salamanca

[@vinaychandak9930]

he is tortuga.

[@rising5948]

jesse we have to cook

[@nutranger]

Ding Ding

[@sharpnova2]

literally came here to say this

[@schmarpsywinkleurnklabean659]

Ring that Bell!

[@DeathBringer769]

3:17 I like how his thumbnail is literally bruised from flipping coins so much. Now that's dedication!

[@bundiderp5109]

Videos on this channel are always worth a thumb!

[@numberphile]

Bundi Derp thanks!

[@YoungColCol]

Numberphile A thumb down though ;)

[@Load_the_ducks]

fred col noh. a fum uhp

[@Danielkaas94]

And it's comments ^^

[@Triantalex]

??.

[@CustomGrow420]

I love this stuff

[@Gustavo321372]

and we love you

[@bigcountrymower4263]

Never expected to see CustomGrow comment on a math video. Awesome.

[@abdullahalmosalami2801]

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.

[@DustinRodriguez1_0]

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.

[@samba272]

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

[@ctejada-0]

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.

[@alephii]

so what......

[@Master2594212]

What do you do if you want to resolve something randomly?

[@rogeriocosta1035]

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!

[@claytonharring8514]

Edgy

[@darraghtate440]

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.

[@SoberBro]

"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.

[@animal_shorts1]

That's a mathematical way of talking.

[@subvind]

@@animal_shorts1 i'm going to flip it horizontal so that it's centrifugal force keeps it spinning like an alien space ship.

[@edwarddoernberg3428]

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.

[@MatthewBaka]

"We did the analysis in the 12 dimensional space" Something you should not here in a video regarding coin tosses.

[@Soliloquy084]

For deciding on a restaurant, when even asking for all the Oks didn't come up with the answer, it’s close enough ;)

[@fliguyman]

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

[@Dr.HazharGhaderi]

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

[@JimCullen]

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.

[@robosergTV]

wrong, it doesnt matter when flipping. Loaded coins have still 50 50 chance.

[@kamebwoi]

RobosergTV - прохождение и летсплей игр How so? :)

[@AkiSan0]

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". ;)

[@JimCullen]

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.

[@robosergTV]

David Aceituno kzbin.info/www/bejne/b4OufKKOrJyqgNk

[@lladerat]

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.

[@Saibrock]

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.

[@leafster9273]

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.

[@edhozell]

Right in the middle of watching this i asked myself... Why do i watch this video... Why do i wanna know this...

[@RkoRocks1525]

I had to turn my volume all the way up to 100 just to be able to hear what he's saying

[@Natalie-cx3cp]

Same

[@Benobot99]

Mine was on 32 out of 100 and I heard him fine.

[@AuroraNora3]

Are you deaf?

[@z121231211]

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.

[@Markus9705]

You're not alone.

[@mrestko]

The dental floss idea was a very clever way of measuring the number of spins.

[@Hythloday71]

Nothing is Random - No probability without uncertain mechanism - therefore YOU HAVE NO FREE WILL.

[@CupCakeArmy1]

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.

[@kimf.wendel9113]

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.

[@nerdbot4446]

Interesting! But you´re doing science, so please use the metric system

[@miguelguerrero3394]

I was going to say the same thing!

[@klutterkicker]

*pulls out ten-sided coin

[@chsxtian]

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.

[@eldizo_]

For once I agree with you, Patrick.

[@Reitenshii]

Hey! Even if I use metric system, he has the right to use non-metric systems whenever he wants to!

[@Ken-S]

These videos are awesome!

[@billyzummo7934]

I was recommended this for a class. It blows my mind that even 212 people could dislike this video

[@RandomWalker39]

I wonder how many of these views were Bill Belichick?

[@StrangerInTheTubb]

😂😂 but just one....he recorded it.

[@ispinozist7941]

The scariest thumb ever videoed.

[@skevoid]

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.

[@gabemerritt3139]

skevoid yeah, but if it hits the ground all bets are off

[@LordSwordbreak]

When I heard him say "miles per hour" I instantly knew there were going to be comments about it below...!

[@philippenachtergal6077]

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)

[@gyes99]

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.

[@thenewsebs]

dots and boxes, rock paper scissors, coin flipping? I assume the next one is about how to properly throw a stone for hopscotch.

[@770pratik]

Brady can you get a slow motion video of Prof. Diconis doing false deals? He is an "Expert On the Card Table".

[@rabidamio]

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.

[@bradster00]

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.

[@DMitsukirules]

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.

[@Myndale]

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.

[@Andersl201]

Random = when you don't know the variables to find the result. Red machine always tosses a head Blue machine always tosses a tails Now if you dont know which machine that is tossing, you can call it random.

[@LibertyWaxlips]

The real question is what's the most you've ever lost on a coin toss.

[@jonaswinklmann1925]

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?

[@TonyHammitt]

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.

[@dinh.6398]

Catching the coin makes it more random, therefore it is more fair.

[@SometimesCompitent]

This is one of my favorites for a long time!

[@alexbeepboop]

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?

[@UnknownXV]

A lot of what we call random, is merely a lack of information and / or an inability to process the information in the given amount of time.

[@Reitenshii]

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.

[@kamebwoi]

"Schrödingers coin" :D

[@Lordderpest]

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.

[@Makron5]

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.

[@Seth_M-T]

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?

[@Dronebertios_World]

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.

[@adamelekes]

If you flip it to the moon, it would be 0.49 leaving you with the same side you started with! :D

[@Onoma314]

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 ?

[@allyourcode]

I'm confused. Is the bias something that happens to "typical human toss", or does that include all combinations of translational and angular speeds?

[@nomarsenrab]

I heard the coin toss in the previous 48 Super Bowls has come up 50-50.

[@CxC2007]

No Country For Old Men.... That Coin toss scene

[@StroalOutdoors]

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!

[@Kaesekuchen002]

Actually a pretty interesting topic. I like his explanations!

[@rjlee3112]

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?

[@andrehena]

The dental floss method was brilliant!

[@Tangobaldy]

Please increase microphone level. Can hardly hear u on ipad at full volume

[@TheViralClovers]

How come he didn't take the probability of the coin landing on its side?

[@nychold]

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?

[@PokemonDiamondUS]

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

[@CompoundInterest-SG]

Is this Richard Feynman's son? He sounds and looks so much like Feynman it is quite funny. And I am pretty sure Feynman would also be interested in something like this.

[@JoostMehrtens]

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.

[@teekanne15]

He looks like a good italian chef.

[@gageboan3961]

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

[@BerkSarikaya]

He looks so pissed.

[@sunyboy333]

FEET PER SECOND?! Disliked video. Reported for repulsive content. Unsubscribed. Deleted youtube account. Uninstalled Firefox. Smashed computer. Set house on fire.

[@willdeary630]

Voted UKIP

[@EddyMac1903]

Will Deary Let's not be irresponsible here, c'mon...

[@Markus9705]

My reaction as well. :P

[@culwin]

Spaghetti falls out of pocket.

[@RockSmacker]

This made my day :P

[@schnapps77]

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?

[@kairosofbabylon6564]

Nah if you flip it to the moon the bias is no longer. 51, but almost exactly .50

[@Erblack3]

Ich you actually manage to flip the coin to the moon, it's propably not coming back :P and if it came back, you wouldnt want to catch it :D

[@TheKevinFanClub526]

Since you mentioned that coin flipping is a 12 dimensions problem. What are the 12 dimensions?

[@Javiercav]

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 ?

[@Treebornfrog5383]

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.

[@jakebricker697]

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?

[@asdasdasdasd7483]

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

[@cwjalexx]

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.

[@unvergebeneid]

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.

[@eliethesaiyan]

I think the problem comes from the human hand.Once you do something over and over again your body gets used to the rhythm.I would be curious to see the results of different people throwing the coins at random times to avoid their hand getting the rhythm of tossing.

[@TheSLK66]

It isn't random at all, like he said partly, if you input in a computer the initial conditions of the coin, the momentum you apply on it to flip it, the air fluctuations and the conditions of the place where it's going to land, you could have a computer tell you 100% accurate the result, the only randomness that could exist (not sure if it does since some deterministic interpretations exist) is quantum superposition and the act of measuring the system.

[@g-gamer4747]

Is it weird that I just finished listening to metal and than start listening to a man talking about maths?

[@JBinero]

No? Why would it be?

[@OlDurtyGurty]

It's weird that you thought this information was useful to anyone, for any reason.

[@emilbuchmueller9899]

metal and maths, both begin with m

[@mustafakulbay5943]

Emil Buchmueller Obama has an M in its name, just sayin. Coincidence, I don't know, you tell me.

[@Hogibaer]

"...actually describing a moving coin is a twelve-dimensional problem, it's not something I can draw a picture of..." Maybe Picasso could have?! ;-) Yes, you lost me at that point, but great video anyway! :-)

[@vinniciusg]

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.

[@1814Custom]

I could listen to his voice all day long.. Dont know why..

[@BeastOfTraal]

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

[@vain8876]

My teacher made me watch this, LOL 😂

[@qorilla]

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.

[@Tacsponge]

Clearly the 'solution' is to not let the guesser's see the initial state of the coin.

[@kilorat]

Someone could make an app that takes input from a high speed camera and predict what side will come up before it hits the ground.

[@elhugo13]

good thing Brady address the catching of the coin at the end I was starting to worry.

[@donniedamato]

Wait, so if you jiggle it in your hands to randomize it before the flip, why even flip at all after that if the flip is scientifically proven to have some bias?

[@EliosMoonElios]

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?

[@jackdumanat49]

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.

[@Kahadi]

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

[@jackdumanat49]

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.

[@jeebersjumpincryst]

proferrors voice - accent, rhythm, pace, manner - many things - strongly are reminiscent of feynmans. to me.

[@XouZ88]

You can also practice to make it more likely to get the result you want. I did this as a kid for my dad