How Truly Random is Random

[acroman08]

This thought has been nagging me since I first saw the pic below (taken from here):



The image on the left features a uniform distribution (which many erroneously come to think of as random), while the points on the right image are allegedly distributed randomly (read, it is a random distribution). But if we think about it, we may come to the idea that random is not truly random at a higher level. Really, if you hit some random outcome, you could in fact expect more of such outcomes in close vicinity of that first outcome as the image above clearly reveals. So how truly random is what universally considered random?

I'm starting the thread in the Gambling discussion section because this domain (i.e. gambling) is where the idea of randomness and whether random is truly random have most applications and implications. Yeah, you thought it right, for gambling and our success at it

you are overthinking it. reading the meaning of random on a dictionary will already give you the answer to what is considered random. but in your case, you are looking for another meaning
(or not or was just intrigued) or other reason why random isn't random and that is mostly associated with supernatural(god) that has planned everything and what people consider random
isn't actually random but was planned.

[IadixDev]

This thought has been nagging me since I first saw the pic below (taken from here):



The image on the left features a uniform distribution (which many erroneously come to think of as random), while the points on the right image are allegedly distributed randomly (read, it is a random distribution). But if we think about it, we may come to the idea that random is not truly random at a higher level. Really, if you hit some random outcome, you could in fact expect more of such outcomes in close vicinity of that first outcome as the image above clearly reveals. So how truly random is what universally considered random?

I'm starting the thread in the Gambling discussion section because this domain (i.e. gambling) is where the idea of randomness and whether random is truly random have most applications and implications. Yeah, you thought it right, for gambling and our success at it

Ever heard of poisson distribution ?

https://en.m.wikipedia.org/wiki/Poisson_distribution

Its the law that govern certain category of random events.

If you flip a coin, the average distribution will tend toward 50/50, and the occurrence of ten time the same result will be lower than occurrence of 50/50 with a distribution law.

[deisik]

Indeed galaxies are bound by gravity

But what makes galaxies in the first place? Why are there many and not just one conglomeration of stars, all tightly packed together? If this is random (in fact, it is kinda a scientific fact), you have to accept that patterns are a distinctive feature or property of randomness. The Universe has innumerable billions of stars, and that's more than enough to evaluate its properties

Universe is expanding and has been doing so since the Big Bang. So it can't be in one big clump. It would probably be a very neatly organized sparse cloud of particles if not for randomness, which caused it to stick into various blobs

Should it be construed in the way you think that the distribution of galaxies in the Universe is not random?

Besides, you can't have it any other way from a purely mathematical point of view (the approach which you seem to be particularly fond of). How come? The reason is simple. If it were not for patterns, you would have a uniform distribution which is not random by definition, as simple as it gets. Stated differently, you can't have a random distribution without patterns given sufficient sample size

Uniform distribution is a very distinctive pattern

Indeed it is patterned, but it has only one pattern, while in a random distribution you can see plenty of them. They are random too, but it is exactly their randomness (which leads to them being many) that distinguishes the latter from the former. If you remove these patterns, you will get a uniform distribution, which violates the assumption of randomness (though the opposite is not necessarily true). So any way you twist the semantics of it, a random distribution without patterns (as in plural) turns into a uniform distribution (with just one repetitive pattern), and thus stops being random

So it's the other way round. Random doesn't stop being random because you spotted a pattern. It either wasn't random to begin with, or you're wrong and there is no pattern

There's not only one pattern in a random distribution as there are many, and their very existence makes a random distribution somewhat less random, from a practical point of view (superstitions or otherwise)

[Debonaire217]

It may worth adding that usually in computer science pseudo-random numbers are generated. Truly random (?) values are only to be found in nature. And pseudo-randomness may, strangely(?), be closer to what you expect in statistics.

In my computer programming class, we're task to random out numbers and sometimes, tutorials are saying that random numbers mostly comes from the current time you have in your computer's clock. In this case, the system is basing the random number which is not actually random at all. Applying it to the context of gambling, random chances could possibly have a basis of it being random and might not be random at all.

[Patatas]

The source for the data should have been provided to see how they actually mined it to generate those charts. I mean I want to know which algorithm produces that distribution. You could argue but will the output be different if the test data is feed into a more efficient algorithm?

Speaking generally, the randomness use on the gambling sites that is the seed and hash work quite differently than just filliping a coin and expecting a random result every time.

[IadixDev]

It may worth adding that usually in computer science pseudo-random numbers are generated. Truly random (?) values are only to be found in nature. And pseudo-randomness may, strangely(?), be closer to what you expect in statistics.

In my computer programming class, we're task to random out numbers and sometimes, tutorials are saying that random numbers mostly comes from the current time you have in your computer's clock. In this case, the system is basing the random number which is not actually random at all. Applying it to the context of gambling, random chances could possibly have a basis of it being random and might not be random at all.

The rationale for gambling is different from the problematic of RNG in computer science, for gambling you still want something that will have poisson like distribution to have a "fair" game where the chances of winning are still known.

Chaotic mechanical processes in the end tend toward poisson distribution if the parameters stay constant, like dice or roulette or coin tossing, even at quantum level on long enough time you can find average with good statistcal match.

Turing machine are not good at creating randomness they are not made for this, on the contrary. They are perfect exemple of closed system with very low entropy.

[buwaytress]

Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing.

I love thinking about the concept of randomness, too. Not so much from a mathematical perspective though.

When you flip a coin, the air, the way you flip, the way the coin is manufactured, all affect the outcome in ways we can't really calculate. When you roll a 10-sided die or 6-sided one, the manufacturing of it, the way some sides might have more density than others. The way a "10" is grooved means that side is ever so lighter than the side that has a "1". For sure all these affect the outcome, and, therefore, have a say in how random the coinflip or dice throw is. I've seen people manipulate dice throws, coin flips, measuring exactly how much strength to flip the coin, ensuring every throw has the same number of flips.

The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel.

How random is random? It's a lovely question!

[Debonaire217]

Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing.

I love thinking about the concept of randomness, too. Not so much from a mathematical perspective though.

When you flip a coin, the air, the way you flip, the way the coin is manufactured, all affect the outcome in ways we can't really calculate. When you roll a 10-sided die or 6-sided one, the manufacturing of it, the way some sides might have more density than others. The way a "10" is grooved means that side is ever so lighter than the side that has a "1". For sure all these affect the outcome, and, therefore, have a say in how random the coinflip or dice throw is. I've seen people manipulate dice throws, coin flips, measuring exactly how much strength to flip the coin, ensuring every throw has the same number of flips.

The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel.

How random is random? It's a lovely question!

I like the way you explain things that affects its random outcomes, but what if we consider randomness of a computer system? All physical tangible things could be impacted by their physical characteristics on how they were created. What about the computer system who uses random generating functions, do they have any basis at all? Are they really random? How come they are programmed to provide random numbers if computers are precise and absolute.

[Ucy]

This thought has been nagging me since I first saw the pic below (taken from here):



The image on the left features a uniform distribution (which many erroneously come to think of as random), while the points on the right image are allegedly distributed randomly (read, it is a random distribution). But if we think about it, we may come to the idea that random is not truly random at a higher level. Really, if you hit some random outcome, you could in fact expect more of such outcomes in close vicinity of that first outcome as the image above clearly reveals. So how truly random is what universally considered random?

I'm starting the thread in the Gambling discussion section because this domain (i.e. gambling) is where the idea of randomness and whether random is truly random have most applications and implications. Yeah, you thought it right, for gambling and our success at it

you are overthinking it. reading the meaning of random on a dictionary will already give you the answer to what is considered random. but in your case, you are looking for another meaning
(or not or was just intrigued) or other reason why random isn't random and that is mostly associated with supernatural(GOD) that has planned everything and what people consider random
isn't actually random but was planned.

I totally agree. Random is not in the dictionary of the CREATOR of the universe and everything. That word is for those whose knowledge are limited.
There is definitely something responsible for falling chaff to be scattered randomly on the ground after being thrown in the air. If you can know, understand and control those things which cause the scattering or randomness, you could  prevent the so called randomness from occurring or make the chaff land on the ground exactly how you want.

[deisik]

Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing

But that's what I'm talking about

Randomness is all about patterns, even if those patterns are random on their own. With this in mind, you can try to exploit this property consciously once you definitely see or assume that you are dealing with random events, or if you know that beforehand (which is often the case in real life). In fact, we are all using this subtlety of randomness in everyday life without even thinking about it, without even being aware of it

The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel

I see what you are getting at, but in this topic I'm speaking mostly about the outcomes which are considered the representation of the built-in randomness of the world. Whether they are truly random in this sense is another question. Technically, our assumptions about these outcomes can just reflect our lack of knowledge (read, God doesn't play dice)

[IadixDev]

Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing.

I love thinking about the concept of randomness, too. Not so much from a mathematical perspective though.

When you flip a coin, the air, the way you flip, the way the coin is manufactured, all affect the outcome in ways we can't really calculate. When you roll a 10-sided die or 6-sided one, the manufacturing of it, the way some sides might have more density than others. The way a "10" is grooved means that side is ever so lighter than the side that has a "1". For sure all these affect the outcome, and, therefore, have a say in how random the coinflip or dice throw is. I've seen people manipulate dice throws, coin flips, measuring exactly how much strength to flip the coin, ensuring every throw has the same number of flips.

The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel.

How random is random? It's a lovely question!

All thèse things you describe are things that actually make the game "less random". If the roulette is not perfectly oiled and the ball is not round leading to number 21 having 2% more occurrence than number 11, then you got a rigged game, which doesnt follow a poisson distribution. If one rely on such knowledge to win the game he is essentially cheating.

[IadixDev]

Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing.

I love thinking about the concept of randomness, too. Not so much from a mathematical perspective though.

When you flip a coin, the air, the way you flip, the way the coin is manufactured, all affect the outcome in ways we can't really calculate. When you roll a 10-sided die or 6-sided one, the manufacturing of it, the way some sides might have more density than others. The way a "10" is grooved means that side is ever so lighter than the side that has a "1". For sure all these affect the outcome, and, therefore, have a say in how random the coinflip or dice throw is. I've seen people manipulate dice throws, coin flips, measuring exactly how much strength to flip the coin, ensuring every throw has the same number of flips.

The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel.

How random is random? It's a lovely question!

I like the way you explain things that affects its random outcomes, but what if we consider randomness of a computer system? All physical tangible things could be impacted by their physical characteristics on how they were created. What about the computer system who uses random generating functions, do they have any basis at all? Are they really random? How come they are programmed to provide random numbers if computers are precise and absolute.

In computer science there are lot of different kind of random number generators, not all of them are suited for gambling.

You can have Perlin noise or fractal noise which can be used in computer graphics like to generate landscape or Marble or in audio synthesis etc but they will have certain distribution that doesnt make them suitable for gambling.

Uniform distribution is white noise but there are other kind of distribution and algorithm that can be suited for some specific purpose.

But you can easily say there will always be a known pattern in anything generated by a computer program, and the séquence can always be reproduced if you know the initial parameters ( seed etc) and the algorithm.

[IadixDev]

Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing

But that's what I'm talking about

Randomness is all about patterns, even if those patterns are random on their own. With this in mind, you can try to exploit this property consciously once you definitely see or assume that you are dealing with random events, or if you know that beforehand (which is often the case in real life). In fact, we are all using this subtlety of randomness in everyday life without even thinking about it, without even being aware of it

The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel

I see what you are getting at, but in this topic I'm speaking mostly about the outcomes which are considered the representation of the built-in randomness of the world. Whether they are truly random in this sense is another question. Technically, our assumptions about these outcomes can just reflect our lack of knowledge (read, God doesn't play dice)

Then the answer is 42

Montgomery had found that the statistical distribution of the zeros on the critical line of the Riemann zeta function has a certain property, now called Montgomery’s pair correlation conjecture. He explained that the zeros tend to repel between neighboring levels. At teatime, Montgomery mentioned his result to Freeman Dyson, Professor in the School of Natural Sciences.

In the 1960s, Dyson had worked on random matrix theory, which was proposed by physicist Eugene Wigner in 1951 to describe nuclear physics. The quantum mechanics of a heavy nucleus is complex and poorly understood. Wigner made a bold conjecture that the statistics of the energy levels could be captured by random matrices. Because of Dyson’s work on random matrices, the distribution or the statistical behavior of the eigenvalues of these matrices has been understood since the 1960s.

Dyson immediately saw that the statistical distribution found by Montgomery appeared to be the same as the pair correlation distribution for the eigenvalues of a random Hermitian matrix that he had discovered a decade earlier. “His result was the same as mine. They were coming from completely different directions and you get the same answer” says Dyson. “It shows that there is a lot there that we don’t understand, and when we do understand it, it will probably be obvious. But at the moment, it is just a miracle.”

The unexpected discovery by Montgomery and Dyson at teatime in the 1970s opened a tantalizing connection between prime numbers and mathematical physics that remains strange and mysterious today. Prime numbers are the building blocks of all numbers and have been studied for more than two thousand years, beginning with the ancient Greeks, who proved that there are infinitely many primes and that they are irregularly spaced.

More than forty years after the teatime conversation between Dyson and Montgomery, the answer to the question of why the same laws of distribution seem to govern the zeros of the Riemann zeta function and the eigenvalues of random matrices remains elusive, but the hunt for an explanation has prompted active research at the intersection of number theory, mathematical physics, probability, and statistics. The search is producing a much better understanding of zeta functions, prime numbers, and random matrices from a variety of angles, including analyzing various systems to see if they reflect Wigner’s prediction that the energy levels of large complex quantum systems exhibit a universal statistical behavior, a delicate balance between chaos and order defined by a precise formula


https://www.ias.edu/ideas/2013/primes-random-matrices


This is the zero of riemann zeta function

[buwaytress]

I see what you are getting at, but in this topic I'm speaking mostly about the outcomes which are considered the representation of the built-in randomness of the world. Whether they are truly random in this sense is another question. Technically, our assumptions about these outcomes can just reflect our lack of knowledge (read, God doesn't play dice)

And as such we are always in the pursuit of more knowledge, not the completion of knowledge (as Asimov so properly and comprehensively explains in The Last Question).

But even if there is built in randomness, all the laws of physics still can apply -- wear and tear, different points of gravity having different effects on how things should work. Take a system and place it into another environment and it works differently.

Then, how we view and perceive the random results even have an effect on that randomness. The images you show, for example, to a colour-blind person, and then maybe viewed on a different monochrome, or a different resolution.

But you're right, our assumptions cannot even possibly comprehend new understandings and even new definitions of random.

[ralle14]

I am just curious about how the online gambling site generated winners like on dice, it is truly random and not pre-programmed? how can they prove it? Is their programming can be checked and verified online by the public or these gambling sites has license to operate? Do they need to get a license? So many questions came out in mind.

Imo it is random since there are days where high rollers could take a piece of the bankroll or suddenly hit a very big multiplier like that one time on stake where a guy hits several x10 multipliers in a row which add up to a million. Before, gambling sites don't have licenses from what I know they only put restrictions on a few countries but now most of them have a verified curacao license on the bottom of their page.

[AicecreaME]

If you remove these patterns, you will get a uniform distribution, which violates the assumption of randomness (though the opposite is not necessarily true).

I disagree. Uniform distribution doesn't violates the assumption of randomness, besides, it is still random, for example, if a certain program will distribute 0-9 integers with the same interval (uniform distribution) the numbers that will be distributed will still random, and it will not stop being random, in my opinion.

This randomness topic of yours is a bit tricky if you are going to let it go deeper in your mind.

[Ranly123]

Being random is how a person understand and translate something. Example of which is our thoughts, if we think of something some people will think of it randomly but for us it's planned.

[AniviaBtc]

Being random is how a person understand and translate something. Example of which is our thoughts, if we think of something some people will think of it randomly but for us it's planned.

What are you trying to say? Being random is not like that, random is unpredictable and it is the outcome without pattern. It's just simply as that, don't make yourself overthink about being random.

In relation to gambling, random is very random because im gambling there are many outcomes and if you try to bet at random, your chances to win is very small. There are a lot of combinations in the gambling, and random is just 0.00000001% depends on the number of choices.

[GSpgh]

Universe is expanding and has been doing so since the Big Bang. So it can't be in one big clump. It would probably be a very neatly organized sparse cloud of particles if not for randomness, which caused it to stick into various blobs

Should it be construed in the way you think that the distribution of galaxies in the Universe is not random?

That's literally the opposite of what I said. This discussion is going in circles now.

There's not only one pattern in a random distribution as there are many, and their very existence makes a random distribution somewhat less random, from a practical point of view (superstitions or otherwise)

Again, that doesn't fit the basic dictionary definition of random. By definition random doesn't have patterns. If you're seeing patterns then your randomization algorithm is not good (which technically is the case with almost any human-devised algorithm) or you're not actually seeing patterns.

Going forward you probably should establish if you're discussing a specific algorithm or the hypothetical ideal randomness. There is no doubt that most algorithms have flaws limiting their entropy (but nonetheless are good enough for many practical purposes like gambling). But that doesn't mean a contradiction the way you're presenting it.

[Darker45]

Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing.

I love thinking about the concept of randomness, too. Not so much from a mathematical perspective though.

When you flip a coin, the air, the way you flip, the way the coin is manufactured, all affect the outcome in ways we can't really calculate. When you roll a 10-sided die or 6-sided one, the manufacturing of it, the way some sides might have more density than others. The way a "10" is grooved means that side is ever so lighter than the side that has a "1". For sure all these affect the outcome, and, therefore, have a say in how random the coinflip or dice throw is. I've seen people manipulate dice throws, coin flips, measuring exactly how much strength to flip the coin, ensuring every throw has the same number of flips.

The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel.

How random is random? It's a lovely question!

And it is also lovely how a seemingly simple gambling question quickly escalated into a metaphysical one.

If we look for absolute randomness, I am afraid there is none. Not in a toss of a coin or a roll of a dice, not even in the movements of the atoms in a single object, and not in the workings of the universe. Everything factored in, there is no result which we can consider an absolute random one.   

Or perhaps, just like in freedom, justice, joy, and everything else, there are no absolutes. That applies to randomness as well.