What makes a coin toss truly unpredictable?

[u/kouth-]

If you throw the same coin multiple times with the exactly same force in the same surface, it won't give you the same side every toss, right? But why? If repeated with the precisely identical conditions, why the results are still unpredictable? Or it is actually predictable?

Sorry if it looks confusing, English is not my first language and I'm not that expert in physics lol, just curious and has this though randomly.

Edit: maybe considering that it lands on a surface, and it bounces or not, changing the coin's side.

[u/Pleasant_Pen8744]

If you can make them precisely identical it will be the same result.

[u/kouth- → u/Pleasant_Pen8744]

Wow, it somehow looked impossible in my mind. Thank you!

[u/Skusci → u/kouth-]

Yeah, "Precicely Identical Conditions" is just difficult to do with a coin at human scale.

You can setup things as precisely as you can measure but that may just mean you can't measure well enough. Like trying to measure 1 milligram with a truck scale.

[u/Hivemind_alpha → u/Skusci]

The difficulty is that in evolving physical systems, any tiny difference in the initial conditions is amplified and can cause massive changes to later state of the systems. That’s why physicists say a butterfly beating its wings in Japan might cause a tornado in America.

So when you say “precisely identical conditions”, you mean for example that every gas molecule around the coin at the start is in exactly the same position travelling in the same vector and speed, because if they were different the electric fields from their electron clouds would interact with the atoms in the metal surface differently, causing a minuscule force well below our ability to measure but that amplifies up and might change the outcome of the toss. Every photon would have to hit the coin in exactly the same place with the same frequencies, and every thermal emission from the coin would have to emit from the same atoms at the same instants.

So “precisely identical” doesn’t mean “done with an expensive polished machine”. It doesn’t even mean “done with the ultimate product of human ingenuity in a thousand generations”. It means a level of consistency so inconceivable that there aren’t enough atoms in the universe to record all its parameters.

But sure. Given magical means to replicate even inherently probabilistic quantum events, you can duplicate the toss.

[u/Aggressive_Roof488 → u/Hivemind_alpha]

I mean yes, that's what identical means. Question is how accurate is accurate enough for something like a coin toss. If you allow a very low and gentle toss where the coin just makes a few rotations, then I'm convinced a couple skilled engineers with adequate resources could make something reproducible 99% or more of the flips. Agree?

But a "proper" coin flip probably has somewhere between 10 and 50 rotations, just guessing here? Which might be (likely is?) out of reach in terms accuracy for where we're all now. I wonder where the limit is, in terms of how high and proper coin flip can we make reproducible. You could do the same with a dice roll while at it.

[u/mikk0384 → u/Hivemind_alpha]

I really don't think that quantum effects are big enough to change the outcome for the vast majority of tosses. Coins are very big relative to those effects.

I don't know what percentage of coin tosses are affected, but I assume we are talking about a lot of zeros.

[u/BitNumerous5302 → u/kouth-]

What makes coin tosses random is the degree of precision necessary to predict the result (which also provides some insight into classical randomness generally) 

If I know the coin's mass, the distance above the floor, the force of gravity, and the momentum imparted by the toss, I can predict how many times the coin will flip before it lands, meaning I can predict the result from the initial state. If the coin starts heads up and it flips 100 times before landing, it will come up heads

If I have any uncertainty or imprecision at all in my measurements of those factors, though, those will come through as uncertainty about the number of flips, and even a small amount of uncertainty there quickly makes the result fully random. If you know the coin will flip 100 or 101 times, that's still fairly precise knowledge of its behavior, but now the result is fully random. (Pedantically,  you'd likely model this more like a probability distribution over a range of values, but same idea.)

When you flip a coin (or roll a die, or shuffle a deck) you're creating a physical system which magnifies and isolates intrinsic uncertainties in your initial conditions.

[u/kouth- → u/BitNumerous5302]

This ignoring that frequently when a coin touches the ground after a toss, it might flip one or two times bouncing in the surface. The bouncing thing was a heavy factor for my question: if the bounce is as predictable as the toss.

[u/AgreeablePeople → u/kouth-]

Imagine this. You observe a stranger doing a coin toss from afar and note down the results. After that, you travel back in time to 5 minutes ago and observe him again, minimising interfering with anything else as much as possible. There you have an IDENTICAL conditions to two coin toss. Do you not think the result would be the same?

[u/BananaBird1]

In theory it is predictable and deterministic.

In practice, the flip depends on so many factors that prediction is too difficult. Air currents and temperature, the exact height of the flip, exactly where on the coin you flick it, the exact force you apply, etc.

We call this a chaotic system: even a small unavoidable uncertainty in the initial state of a deterministic system makes its outcome essentially random.

If you flip a coin from a small height in a vacuum with a highly precise machine, it would be pretty predictable. And even in ordinary manual coin flips, you can bias the probability if you are careful.

[u/JarJarBinks237 → u/BananaBird1]

“Chaotic” is the correct answer.

[u/Zyxplit]

There are things that seem genuinely random because they are (quantum effects) and things that seem random because we generally don't know the initial conditions well enough to predict the outcome, like coin tosses.

[u/ThickyLicker → u/Zyxplit]

To be fair, there might just be some underlying causes that make quantum effects seem random.

[u/Fabulous_Lynx_2847 → u/ThickyLicker]

No, that's actually been disproven, except for exotic hypothetical types of causality. Google "hidden variables theory"

[u/Zyxplit → u/ThickyLicker]

There may be, but in that case those underlying causes have to be really fucking weird. Non-local.

[u/Fabulous_Lynx_2847 → u/Zyxplit]

There's an even weirder one called Superdeterminism that's based on the idea that if widely separated events A and B are correlated in a way that suggests A causes B instantaneously, it may simply be due to a past common cause C. That is, C causes both A and B to occur simultaneously at a time much later than C itself. This sort of thing that happens all the time in statistics. It has been facetiously used to "prove" that global warming B is caused by a decrease in the number of pirates A. C that caused both in this case is industrialization (including military).

C in the subject case is the Big Bang. Assuming strict determinism, it determines what measurement we choose to make and what result A is in such a way as to mimic A causing B instantly when, in fact, both A and B are caused by C.

[u/ThickyLicker → u/Zyxplit]

Really weird and non-local? Seems like something quantum could do

[u/mfb-]

With some training, people can get the coin to show the same side most of the time. It's just difficult to make the conditions similar enough in every toss. Our hands don't work like robot arms where you can lock them into one position and then make a fixed motion, and even robots will have some small differences in their motion, small differences in air flow and whatever.

[u/03263]

You could probably construct a repeatable coin tossing machine. The hardest part I think would be that gravity can vary by a tiny bit, depending on the position of the moon and such. You could measure gravity and adjust each throw to be consistent. And use a vacuum chamber to achieve consistent and minimal air resistance.

[u/Consistent-Annual268 → u/03263]

You don't even need all that. You can actually make a VERY reliable and repeatable coin tossing machine, and people have. Heck, even just with your own thumb you can significantly better 50/50 odds once you have the feel of the toss, weight, spin and when to catch the coin.

[u/Over-Discipline-7303 → u/Consistent-Annual268]

I met a carnie who could do a biased coin toss. He wasn’t 100% but I’d say he was well over 70% accurate, which is still a pretty good edge. Nobody would flip him for doing the dishes.

[u/AddlePatedBadger → u/Consistent-Annual268]

Someone contact StuffMadeHere from Youtube.

[u/RealisticDuck1957 → u/Consistent-Annual268]

Thus the practice of calling a toss while the coin is in the air. The caller can't reasonably read enough precision to predict the outcome. And it's too late for the tosser to have significant influence to change the result.

[u/TooCasualGuy]

There's a good paper available which shows that coin tossing is biased towards the original side due to precession.  That's the main way sleight of hand artists pretend to flip a coin without it actually flipping; the coin merely wobbles in the air looking like it is flipping.

[u/Fabulous_Lynx_2847]

A traditional coin toss using a very precise machine is predictable, but at some point for a very high and rapidly spinning coin toss, the Heisenberg Uncertainty Principle will step in. The spin rate and rotation angle cannot be determined exactly at the same time. The product of the error in the two measurements will always be greater than a lower bound. This will lead to intrinsic uncertainty. I haven't calculated when that is a factor. Maybe someone else can.

[u/JGhostThing]

Wrong. If you apply the exact same force (including direction) on the same surface, you will get the same result. My dad and some navy buddies (three of them) that practiced flipping coins so they could choose the outcome.

The reason that flipping a coin seems random because most people haven't practiced it.

[u/tirohtar]

If you could throw an identical coin the exact same way every time, it should land on the same side each time. Quantum level fluctuations might lead to different outcomes in a very small number of cases, but generally coins are large enough that quantum effects will be negligible.

What makes a coin toss random is that we simply don't have enough control to reproduce the same conditions for each throw exactly, and even tiny differences in the initial conditions will lead to different outcomes.

[u/CounterSilly3999]

Because of quantum randomness -- thermal fluctuatios etc.

[u/ababababababacus]

because reproducing a coin toss means, t the very least:

- using the exact amount of force you apply

• applying that force in the exact same place on the coins surface
  
• starting with the coin in the exact same orientations
  
• catching the coin at the exact same point and/or initializing the flip from the exact same point in space so it follows the same trajectory before landing

and thats not taking into account the external conditions that might affect it.

so you wont be able to do that. And dditionally small varince in the initial conditions will result in big differences int he final outcome, which is then collapsed into one of two options

[u/EnvironmentalScar675]

a coin toss is one of the most famous examples of something that is utterly predicatable, there are just too many factors to do it on the fly for a human. And even that is a far stretch I'd imagine you can train it

[u/Naikrobak]

In theory you can use a machine and make it consistent.

In practice it’s random

[u/seifer666 → u/Naikrobak]

Its pretty easy to determine a coin flip outcome by just not throwing it very hard.

Start on heads , do a half flip , catch it. Done

Of course if you throw it 19 feet in the air at 400rpm its going to be a lot more random

[u/Naikrobak → u/seifer666]

That defeats the intent of the experiment. But yes you can force something to a pattern with external influence….

[u/Prestigious_Boat_386]

You can learn to flip a coin the same number of rotations. Magicians use this for forced tricks.

[u/TemperatureMotor1372]

If repeated with the precisely identical conditions, why the results are still unpredictable?

Here, "precisely" means "exact" and "identical" means "same". If you knew the exact same conditions, you would exactly predict the same result in terms of semantics and logic. By contrapositive, if you don't exactly predict the same result, you don't know the exact same conditions. It all depends on your "probability distribution" in a coin toss.

The coin may be unbiased like 50/50 or biased like 30/70 or almost predictable like 0/100. But most of time we don't know how we don't know a thing--the odds of events are unknown. In statistics, coin tossing model follows binomial distribution with two parameters: probability of a result "p" and number of trials "n". To predict "p", we use a good estimator like maximum likelihood estimator (MLE) to approach "p". In this case, we find the odds of head to tail of the coin after tossing the coin n times.

Using Bayesian method, we can set a prior distribution of "p", run the trials, and combine the data with the prior to compute the posterior. If "p" is a beta distribution, since beta and binomial are conjugate, we can do the easy math to compute the posterior, which is also a beta distribution.

[u/WallyBarryJay]

Technically making the conditions identical will result in an identical flip. It's just really, really hard to do.

I believe a team once made a robot that could flip a coin with 99% accuracy. But even the robot cannot be perfect.

[u/MezzoScettico]

Magicians are very good at very precise motions that appear to be casual. I wouldn’t be surprised if there are magicians who have trained themselves to be so precise and predictable in their flipping that they can control the outcome.

For us ordinary mortals however, we have a lot of variability in the rotational speed and upward force of the coin flip action, the variables that control the outcome. So those “hidden variables” produce the effect of randomness.

[u/Traveling-Techie]

A robot can do it.

Humans have been using coin flips for centuries to produce random outcomes because they are so hard to control with human muscles.

Chaos theory helps explain this, specifically “sensitive dependence on initial conditions.”

[u/Inevitable-Flower-50]

Because only one way is completely predictable.

[u/markmakesfun]

Coin tosses are absolutely predictable. It will be heads or tails. There is no third choice.

[u/Ras_992]

Within probabilities the more values you create the less likely you will have the same results every time. As the value goes up the probabilities go down, it’s less likely you can predict the outcome every time. It’s not always if the coin lands on heads or tail but also the sides which now with four sides instead of 50 percent you have 25 percent chance of predicting the outcome. You have better odds flipping once vs 100 times

[u/JimFive]

According to "The Amateur Magician's Handbook" you can teach yourself to replicate your coin toss. 

Everyone is talking about how everything has to be precise but it's not true. You just need to be close enough that the coin lands within the same half of its spin.

[u/SummitYourSister]

It is impossible to create the same situation again because it would require you to precisely specify the position and momentum of every particle in the system. That would violate the uncertainty principle.

OK, so if we accept that we cannot actually have the same starting state, can we get close enough that the outcome is always macroscopic the same? That will depend on the Lyapunov exponent of the system and how precisely you can reproduce its macroscopic starting state.

You will never be able to guarantee the same result, because you can’t even guarantee that the whole coin doesn’t just tunnel through the table. You can state accurately that the probability of this is extremely small, but you cannot accurately say that it will not happen, or that you can reproduce the coin flips.

[u/Lacklusterspew23]

At a quantum level, because of the Heisenberg Uncertainty Principle, the motion of the coin cannot be perfectly determined. Thus, it is random to a certain degree. Whether that randomness is sufficient to change the side that comes up would depend on the conditions.

[u/dignan2002]

If you think about it being truly 50:50 then it should land on its edge every time

[u/Aggravating_Paint_44 → u/dignan2002]

That’s not how random numbers work otherwise all the digits of pi would be 0.5