Understanding variance

[falkor2k15]

I was a bit confused about variance. We are more likely to get 2 dozens in 3 spins, so shouldn't that form the benchmark in terms of measuring it?

111 = extreme
121 = normal/expected
123 = extreme

However, it seems variance is based on maths expectation, and that's how we should analyse it:

111 = extreme
123 = normal/maths expectation
121 = extreme

In the short term we expect more repeats (121) instead of uniques (123) due to the Birthday Paradox and Law of the Third (if I'm not mistaken).
However, in the long run the Law of Large Numbers/Regression Towards Mean will start to enforce brick design, and this is also affected by an increasingly larger sample size.

I decided to do a visual test to show just how LOTT starts out and how brick design eventually sets in, and I believe I've found the perfect way to represent this. I would measure the variance of the 3 dozens after every repeat cycle to see how things had changed. After a wild start the dozens began to get closer to the 33% maths expectation, but as the sample size increased the changes become smaller in terms of their percentage overall. For example, if dozen 1 is ahead of dozens 2-3 and above maths expectation, it needs to be a lot more ahead further down the line in order to maintain the same lead %; if it's 5 hits ahead then that will become less and less significant as time goes on unless that lead continues to increment.

Conclusion: we are guaranteed to get caught by the Law of the Large - not so much when everything levels out at 33% - but more so when the periodic changes in variance become less than, say, 1%.

000 > 111 - we have already got caught early!
676 > 787 - no detectable change in variance, i.e. less than 1%.

Any thoughts?

[ego]

I have many times show the inside of variance using even money bets, but people don't seem interested.
When I look at your attempt to define variance it seems wrong.

I could copy a 3 SD chart for one dozen group of three not showing, then you could measuring and explore the true values.
Will get back to this topic and post the chart if you would like it for reference.

I quote a member with the name Harry ...

In any large series of random trials, every possibility would tend to occur in proportion to
its probability. In short, the odds would "Average out" along the way. The larger the
series of trials the closer the result would be to the expected average(Mean). In an
infinite series, every possibility would occur in exact proportion to its probability.

This became known as the "Law of Averages", and was the basis of probability for
100 years.
" In any series of EQUALLY DISTRIBUTED Random Trials, in which the individual
trials were MUTUALLY EXCLUSIVE. The larger the number of trials the closer the
percentage result would be to the expected (Theoretical) MEAN. Although the actual
deviation would tend to get larger." -- Pascal/Bernoulli
This became known as the "Law of Large Numbers", and is the basis of modern
probability.

The extent to which the actual result will diverge from the theoretical expectation is a
function of the square root of the number of trials. This divergence, known as the
STANDARD DEVIATION can be calculated using the formula:

"That 68.3% of the time the divergence would be one SD or less. Either side of the
MEAN.

"That 95% of the time the divergence would be 2 SD's or less. Either side of the
MEAN.

"That 99.7% of the time the divergence would be 3 SD's or less. Either side of the
MEAN.

"That only 0.3% of the time would the divergence exceed 3 SD's
Not only does this Theorem offer an explanation of "Regression Toward the Mean",
But it allows us to roughly calculate, and assess the deviations, that are a common factor
in any series of random trials.

There is no way known to man to accurately calculate a probability! If you use them
"Law of Large numbers" or SD's to calculate. About the best you can hope for is that
2/3rds of the time you might only be 1 SD off target. Much of the time you could be up
to 2 SD's off target! How does this translate into figures? Not well for the punter! The
number of trials is far too small for any degree of accuracy. The "fudge factor" is just
too large.

There is one other factor that must be taken into account when working with short
random trials. It is a theory, and no proof is offered. That is the 'RANDOM WALK
THEORY" It is obvious that every trial in a series changes the percentage of deviation,
and possibly it's DIRECTION. Unlike the SD the "random walk produces sharp zigzags
in the short term, rather than the slower, average, waves of the SD. It is in the peaks and
valleys of these short-term zigzags that the punter will find the best chance of defeating
probability.

[ego]

 First, you have the true value and after that, the SD rounding up.
Here you can see that one group missing for five attempts still is 0 SD ...

1. 0.00 SD 0
2. 0.04 SD 0
3. 0.11 SD 0
4. 0.22 SD 0
5. 0.36 SD 0
6. 0.53 SD 1
7. 0.73 SD 1
8. 0.96 SD 1
9. 1.22 SD 1
10. 1.51 SD 2
11. 1.82 SD 2
12. 2.16 SD 2
13. 2.52 SD 3
14. 2.91 SD 3
15. 3.32 SD 3
16. 3.75 SD 4
17. 4.20 SD 4
18. 4.67 SD 5
19. 5.16 SD 5
20. 5.67 SD 6
21. 6.20 SD 6
22. 6.75 SD 7
23. 7.31 SD 7
24. 7.89 SD 8
25. 8.49 SD 8
26. 9.10 SD 9
27. 9.73 SD 10

[falkor2k15]

Hi Ego,

I'm not a mathematician and don't really understand what you mean by SD and all these theoretical descriptions. Could you please give some examples as applied to roulette using dozens?

I am thinking the test would be more informative if the first scenario was benchmarked:
111 = extreme
121 = normal/expected
123 = extreme

That would indicate tighter extremes in the short term and still arrive at maths expectation in the long run.

[The General]

In the random game the random walk moving forward is always just expectation, regardless of what has hit in the past, and regardless of the deviation from the normal.  For example if a section of the wheel or a color is 50 hits behind the average, then the expectation moving forward is that it will remain 50 hits behind as it's hit rate is predicted to be "just expectation."  The standard deviation however will likely decrease as the sample size increases.  This is NOT in ANY WAY WHATSOEVER anything that can be exploited.  Believing otherwise is to fall victim to the gambler's fallacy.

It all comes down to time.  The past is in the past and it does not reach forward in the game of roulette to influence future spins.

[nottophammer]

In the random game the random walk moving forward is

See you do know of the trot, or as Winkel say's the march of the non-hit going forward at 1/37

[The General]

Instead of variance, replace the word with luck.  "Understanding luck."

Regarding Winkel...so?  And the "trot?"

If the trot worked you'd be able to win something more than the dirt on the MPR, but you can't.

[nottophammer]

there's always a or in the group it's you

[winkel]

Instead of variance, replace the word with luck.  "Understanding luck."

Regarding Winkel...so?  And the "trot?"

If the trot worked you'd be able to win something more than the dirt on the MPR, but you can't.

It works, that´s why you hate me.

[The General]

Winkel,

I don't hate you.  But I suspect we both know the GUT doesn't work.  Regardless we can just agree to disagree.

Hope you're in good health.

Cheers!

-The General

[winkel]

Winkel,

I don't hate you.  But I suspect we both know the GUT doesn't work.  Regardless we can just agree to disagree.

Hope you're in good health.

Cheers!



-The General

Since 10 years you attack me and GUT without even looking at it. If thats not hate what is it?

and pls don´t use "we" as an attack. And pls. If you atttack others opinionions don´t use my name and don´t argue with GUT. You simply don´t understand it.

[The General]

Winkel,

Don't mistake attacking the message with attacking the messenger.  It's nothing personal.


No, I know the GUT doesn't work.  It's not an attack on you.  I'm just saying that the system doesn't work for obvious reasons.
If you want to debate it, then fine.  Go ahead.  Lay out solid reasons why it should work.   While you're at it show us how you can beat the MPR while playing it.   

Best of luck. 

-The General

[Turner]

Caleb

"Hmmm....no one is getting upset. I know....I"'ll have an unprovoked attack on Winkel. He usually bites"

LOL....so transparent. So sad

[nottophammer]

How you doing Mr T
The reason he picked on Winkel is from my reply to his understanding of the Trot or march of the starting 37 non-hit.

In the random game the random walk moving forward is always just expectation

Oh yeah 1/37 will see all 37 #'s hit once

A good place for random numbers is random.org.   

Oh look Random. org

Now the usual Blah,blah not enough data, COBBLERS

[TurboGenius]

While you're at it show us how you can beat the MPR while playing it.

Isn't it interesting how anyone who is supposed to "prove" something is told to do it on "MPR".  Strange isn't it...
There's a ton of testing apparatus available, live wheels on sites, various forms of rng both on sites or imported spins into RX that can be live or rng, there's math....there's actual casino play results..
There's someone posting that beat(s) them all but nope - it has to be MPR or there's
no proof whatsoever, sorry.
General pushed this as well because...well.... there's a reason.
Clearly even he knows that proof of something comes from the math and testing - not from 1 specific source of spins on 1 forum where he happens to hang out. Weird.