Why random results are NOT independent

[Bayes]

Don't hide behind semantics, don't see the tree and miss the forest...

Semantics are important because they are concerned with meaning. If you knew what independence meant then you wouldn't have written the following:

If you (or anybody else) can say that this event has slim chances to occur, this  is a certain definition.

If you also say that this or that event happens frequently, this is a specific definition.

If casinos didn't have a clue about what could happen, how would they be able to establish payouts for all bet types?

All of the above statements mean that there is a degree of certainty, which it could never existed  with completely independent outcomes!

Probability 101: Events are statistically independent if the occurrence of one doesn't affect the probability of the other. Notice that there are at least two events involved. This has nothing to do with the degree of certainty. Casinos can establish payouts because of the law of large numbers. Statistical independence means that given some previous results I can't predict future results; it doesn't mean that I can't say that events happen frequently, or that there are degrees of certainty.

You might as well say that just because an event has a probability then it is dependent, which is nonsense.

[Blue_Angel]

Events are statistically independent if the occurrence of one doesn't affect the probability of the other.

In a "closed" environment which its elements are finite, aka roulette with 37 or 38 numbers, each and every subsequent combination of the main 37 elements is finite too.
The event horizon is definitely not ever expanding, there might be fluctuations but within certain limits.
Don't you think the words limits and independence have contradicting meaning??
Try to imagine it as an artesian well, or as 2 connected jars filled with fluid, if you deduct fluid from one it affects the level of the other side and vice versa.
So if you keep on deducting you would eventually reach the bottom of the one, while the other would be topped up.
Probable, limits, degree of certainty, all of these meanings are contradicting independence!
By saying "I believe in Santa Claus despite that I've never seen him" makes thee same sense with what you are saying!
It's very contradicting!
I think it's not that you cannot understand but that you don't want to understand, either way is not my problem.

Statistical independence means that given some previous results I can't predict future results;

So why mr wiseman are you using trackers??
Why are you using past results to decide what to bet??!

[falkor2k15]

You should read the GUT ebook... there's some useful information in there about distribution/variance, and somebody once described it on here.

Rather than 2 jars affecting each other, it goes something like this...

When you begin a trot, the trot will try to keep within the mean or the line that we expect it to travel. When it goes astray it sometimes will correct it self - other times it doesn't correct itself - it just behaves randomly. So now we scrap that trot and move onto the next trot. Now, the next trot has no influence from the previous trot.... generally, we expect it to regress towards the mean as they say, but again it has a mind of it's own and can often deviate. And without the need to try to offer an opposing reaction to the previous trot, all trots together will still average out and resemble a rough line. So at the end of the day, it's all independent and random - unless we consider Priyanka's Non-Random methods.

[Blue_Angel]

You should read the GUT ebook... there's some useful information in there about distribution/variance, and somebody once described it on here.

Rather than 2 jars affecting each other, it goes something like this...

When you begin a trot, the trot will try to keep within the mean or the line that we expect it to travel. When it goes astray it sometimes will correct it self - other times it doesn't correct itself - it just behaves randomly. So now we scrap that trot and move onto the next trot. Now, the next trot has no influence from the previous trot.... generally, we expect it to regress towards the mean as they say, but again it has a mind of it's own and can often deviate. And without the need to try to offer an opposing reaction to the previous trot, all trots together will still average out and resemble a rough line. So at the end of the day, it's all independent and random - unless we consider Priyanka's Non-Random methods.

No, at the end of the day are not all random and independent, you perceive it this way because your personal permanence/session is just 1 "tree" out of a "forest"...it really comes down to perception.

[falkor2k15]

No, at the end of the day are not all random and independent, you perceive it this way because your personal permanence/session is just 1 "tree" out of a "forest"...it really comes down to perception.

No, it's from testing and experimentation. You take a trot and try to simulate the next trot or you take 3541 (3 not shown, 5 appeared once, 4 appeared 2 times, 1 number appeared 3 times or more). The independence doesn't always present itself as equally likely because of variance - but you know it's chaotic because the results are different across different data sets. So the next spin after 3541 is random and independent of the 3541. GUT can only potentially win because it knows when to scrap a bad trot (or how to handle losses; see Manrique's the perfect loser). Priyanka can go one step further with her methods.

[Blue_Angel]

No, it's from testing and experimentation. You take a trot and try to simulate the next trot or you take 3541 (3 not shown, 5 appeared once, 4 appeared 2 times, 1 number appeared 3 times or more). The independence doesn't always present itself as equally likely because of variance - but you know it's chaotic because the results are different across different data sets. So the next spin after 3541 is random and independent of the 3541. GUT can only potentially win because it knows when to scrap a bad trot (or how to handle losses; see Manrique's the perfect loser). Priyanka can go one step further with her methods.

What you see is never the whole picture, it's nothing more than a tiny fraction of a much larger picture...

So your "angle" defines your reality and your reality is just one of the many possible...nothing more than that.

[falkor2k15]

What you see is never the whole picture, it's nothing more than a tiny fraction of a much larger picture...

So your "angle" defines your reality and your reality is just one of the many possible...nothing more than that.

When it comes to Roulette that is pretty much the whole picture in terms of the random way of playing. Test triggers and you will see there is no pattern regardless of what you do - everything will break even on BV because is independent with the same constant odds. Check the leaderboard on Steve's multiplayer: 0.95 win ratio for most people. So in this scenario my tree is a microcosm for all types of random play. There exists no other fields within the forest other than Non-Random. We can test and confirm everything ourselves as being true through experimentation, so with a mathematical game like roulette we don't need to look at the bigger picture because we've gathered enough evidence already from the top down. Likewise, crossing the road isn't down to perception... we know the whole picture already... you got the distance from one side of the road to the other, the vehicles, the speed everything is moving, and potential hazards, so you know you will get across safely most of the time. You go to a third world country the same laws apply - but the drivers are just more crazy.  The bigger picture need only come into it when the subject is less clear cut and certain evidence is lacking or we have no direct way of testing.

[Bayes]

Don't you think the words limits and independence have contradicting meaning??
Try to imagine it as an artesian well, or as 2 connected jars filled with fluid, if you deduct fluid from one it affects the level of the other side and vice versa.
So if you keep on deducting you would eventually reach the bottom of the one, while the other would be topped up.
Probable, limits, degree of certainty, all of these meanings are contradicting independence!

No, they don't contradict independence as defined. You're getting confused (just as R.D.Ellison did) because you refuse to understand the difference between the word "independence" as used in everyday language, and the technical definition of independence. Independence as applied to probability does not mean "free from influence". If you're going to make an argument, first define your terms.

It means the occurrence of one event doesn't affect the probability of the other. If you can't see the difference between the definitions it's not my problem.

Yes I use trackers, but these are for tracking my own targets and success rate, and for money management. I don't track for triggers, which are useless.

[Blue_Angel]

Independence as applied to probability does not mean "free from influence".

Yes I use trackers, but these are for tracking my own targets and success rate, and for money management. I don't track for triggers, which are useless.

Those statements made the situation a bit more clear, I cannot argue this way.

[Blue_Angel]

Those statements made the situation a bit more clear, I cannot argue this way.

But independent in its broader sense does mean free from influence.

[Blue_Angel]

I've borrowed a small part from Mad Professor (professional dice roller)

''Their logic is to “Ignore the rainstorm and just consider that it is single droplets of water that are flooding your basement. 
It doesn’t matter if it is pouring cats and dogs; a storm is only made up of individual drops of water. 
Therefore, storms only happened in the past-tense, and whatever is happening now can only be considered as individual raindrops. 
You have to overlook and disregard the totality of the deluge, no matter how much damage is being wrought”. 
Obviously, their logic is just plain FLAWED, and they don’t use the brains that God gave dogs, to have enough sense to come in out of the rain. ''

Devoted to all ''math experts'' like Turner.

[The General]

Blue,

There are a lot of naive craps players as well.

Perhaps you can articulate why we should believe some craps player instead of all mathematicians and recorded history itself?   

[Blue_Angel]

Blue,

There are a lot of naive craps players as well.

That's simply a lie, or attempt of deception.
You cannot judge a book by a single page...

Do you pretend the loser? That's why you've changed your avatar?

Regardless what people might think of him, I like him better than Hillary, she looks like a typical American housewife, she is in wrong place.

I can understand why aliens/immigrants hate him, but why the rest dislike him is beyond my understanding. 

Wait a minute, I had a glimpse, perhaps because he reminds them their boss or dad...!

[The General]

Blue,

Please articulate your position.  Why do you believe that results are NOT independent when all of the experts, mathematicians, and history say that you're wrong? 

Why are you so eager to believe some craps player over the experts?  Is he a mathematician/actuary perhaps?

[Turner]

Devoted to all ''math experts'' like Turner.

I did degree level Maths in my HND Electronics and Electrical Engineering

Maths interests me. I read a lot of Astophysics and Quantum Mechanics type books. A good knowledge of Maths is essential or you get lost in that genre of literature.

I don't know why you describe me as a Maths Expert. Perhaps it was sarcasm.

I hope I didn't use too many big words in my little rambling soliloquy