The key to the final solution - Marigny de Grilleau - Even money

[ego]

The key to the final solution - Marigny de Grilleau
Is a book from a Swedish author (Sten Nordland) and the main titel of the book is International Roulette.
Its two books.
Part two is exclusive about basics and advance new development about Marigny de Grilleau's work.

I will write about this to become a reference area for cut point methodology or also known as regression towards the mean.
This will based upon my understanding about the subject.

[ego]

Its based upon my understanding about the work in general.
I start from this position to solve the core about the subject.

First we do is using some kind of playing model.
With this example i will referring to singles contra larger series.

We look for imbalance or bias within a window of events / trails.
This means we are measuring overrepresented events and underrepresented events.

When we reach a benchmark around 3.0 STD (could be any) then we have a pretty strong imbalance / bias.
Then it can continue to grow stronger as the nothing is due or that the bell curve has no limit.
This does not effect us.

This window of bias or overrepresented events following strict rules and values based upon math and probability to be valid.
With the example singles contra larger series so do we have the following values or playing model.

Singles has the value of 1
Series of two has the value of 0
Series of three has the value of 1
Series of four has the value of 2
Series of five has the value of 3
Series of six has the value of 4
Series of seven has the value of 5
And so it continues ...

Look at this values again, here you have singles contra series of three and both with the same value.
This is because when you measuring the random flow or distribution of random events you want to make sure you have overrepresented events and underrepresented events or a true bias into one direction.

This way with this example larger series are underrepresented.
Now you can pick how many windows you want with 14/2 and you will for the next 50 100 150 200 250 300 trails get larger series.
You know they will show, but you don't know when, this is why cut point methodology only attack when change is present.
More about that later.

Example 14 singles and 2 series of three is 3.0 STD.
it's a window of 16 events with a strong bias or a strong window with overrepresented events.

This is the starting point or core about this subject.
To measuring the random flow and find overrepresented events or strong bias (around 3.0 std)
Different methods or measuring other events has other values based upon math and probability.

With this example we have find and observe a window with 14 singles and 2 series of three.
From this moment and further into the future so do we have some degree of expectation.

I am not saying we have a crystal ball.
But we have what we can call vacuum pressure or a hole or a window with strong imbalance of overrepresented events.
So our expectation is that sooner or later the underrepresented events will start to show.

I know that the bias can grow and get stronger and hit 4 5 6 STD but it does not effect us.
In this case we would only observe.

Cut point methodology is about to capture the drop point after a strong bias.
The drop point or the underrepresented events can come as tiny, medium or large drop points.

The main idea is to capture them when they already show or are present.
That way you have a indication that the bias or imbalance has stop growing stronger.

This is what i call tendency play.
We can also see it as regression towards the mean or correction.

It is the best existing trending method for even money bets.
Based upon pure math and probability.

The key to solve the final solution is how you define a march to capture does events with money management.
Measuring and find bias is the easy part.

This is how it looks like with the example i mention above.
Singles contra larger series.

2 x
1 x
2 x
1
1
1
1
2 x
1 x
2 x
1 x
2 x
1 x
2 x
1
1
2 x
1 x Statistical Ecart around 2.5
2
2
2 Stop growing stronger and getting weaker.
1
2
2
2
2
2 Larger series
1
2
1
2
2
2
2
2
2 Larger series
1
2
2
2
2
2
2 Larger series
1
2

[ego]

Before i start referring to playing models from the book i want to mention this quote.

"IS EVERY ROULETTE SPIN NEW?"
Marigny de Grilleau
translated from "The gain of one unit on the even money chances at Roulette and Trente et Quarante"


One can hear that question in every casino everyday.
The word "new" means according to the definition "which one yet did not see".
In this sense each day is a new day.
It is quite obvious that people asking this question do not realy mean "new" to express this natural truth.
Their questions is badly formulated and surely they mean "new" in the sense of independent.
Thus they wanted to ask whether each spin is independent of the others, the previous or following spins.
The above question should be asked as follows: " Are all appearances and are all spins independent?" In this formulation no wordplay and no wrong interpretations are possible.

Grilleau does not hesitate with a clear answer: "No, neither the appearances nor the spins can be independent, because everyone of them is a part of the whole. This whole is arranged and limited in all its movements and is subject to precise laws."

Each spin, while the ball turns in the wheel, carries in itself a certain quantity of independence and a certain quantity of dependence.

The independence results from the following:
every time the dealer rolls the ball, it is faced with 18 red and 18 black, 18 even and 18 odd as well as 18 high and 18 low pockets. Therefore the ball has the same chance to fall in one of the 36 pockets (we do not consider zero or doublezero this time) since each pocket indicates Red or Black, Even or Odd, High or Low at the same time.

The dependence results from
1. the Law of Deviation (Ecart),
2. the Law of Balance (Equilibrium)and
3. the law of the distribution of appearances into different accumulations or clusters and isolated units

Thus the mathematical truth of the independence of the spins is constantly in conflict with the statistic truth of the dependence of the spins.

If between two equivalent appearances none, or only a very small deviation exists, the independence of the two appearances remains retained in their fight against each other.
But if the statistic deviation reaches a certain size, the size of this deviation more or less limits the independece of these appearances and spins.
In this instant the dependence of the appearances on the laws of nature demands again its right, by limiting its freedom for deviation within the statistic average values, of which these never can free itself.

In our opinion neither a single spin nor an appearance can be independ in a roulette permanence of a certain length, for example within 1024 spins.
The dependence of the spins which are affected by chance due to exactly defined laws, is a fact, which the usual gambler does not understand without difficulty. And because of this difficulty the gamblers and also the mathematicians believe in the independence of roulette spins.
In reality each spin and each appearance has its necessary and mandatory function in the whole of a roulette permanence.
Chance does not exist there, because all effects have their visible or hidden causes.


The dependence of the spins on the laws of nature becomes obvious, if we analyze a roulette permanence and classify the developed appearances.
However we do not succeed in each case in determining this dependence, which must be present for all spins, if only small deviations occur, which do not exceed the average statistical Ecart of 1.
We only succeed then, if we determine the partial return to equilibrium after very strong deviations greater than a statistical Ecart of 3.
The roulette ball cannot extract itself from the laws of nature.
These laws force it into the pocket, into which it must fall, so that it can perform the necessary function, which it has to, in the statistic harmony of the whole permanence - like a note in a score.
Chance can let many obvious, strange features develop before our eyes. But nevertheless, statistically seen, chance can not repeat these individual strange things too frequently, like for example a series of 25, which needs approximately 34 million spins to develop once.
Modify message

[ego]

Here is an simple chart that I did a long time ago with some values that you can use as reference.



The french word for STD is Ecart

First you have to get the Absolute Ecart when you calculate.
So lets assume you have an sequence with 14 series alternating with two singles present.

Then you take 14 - 2 = 12

Now we want to get the statistical ecart so we continue with...

14 + 2 = 16

Now we take the sqr of 16 = 4

And finally we divide the absolute ecart whit the sqr

12 sqr 4 = 3,00

The Statistical Ecart 3,00

[ego]

In the old days i did many hundred thousands simulations and will end this topic about algorithms or march with money management.
Here i will go deep into how you can measuring the random flow or distribution.
Its based upon taking advantage of the law of series in all existing aspects.

This is the values and existing playing models based upon pure math and probability.
This is how you find you windows of bias or overrepresented events.

Series contra Singles.
Series has the value of 1 and Singles has the value of 1.
There is as many singles as existing series no matter length.

Singles contra series.
Singles has the value of 1 and Series has the value of 1.
there's is as many singles as existing series no matter length.

Singles contra larger series.
Singles has the value of 1
Series of two has the value of 0
Series of three has the value of 1
Series of four has the value of 2
Series of five has the value of 3
Series of six has the value of 4
And so it continues

Series of two contra larger series.
Singles has the value of 0 (you just skip them as none existing)
Series of two has the value of 1
Series of three has the value of 0
Series of four has the value of 1
Series of five has the value of 2
Series of six has the value of 3
Series of seven has the value of 4
And so it continues ...

Series of three contra larger series
Singles has the value of 0 (you just skip them as none existing)
Series of two has the value of 0 (you just skip them as none existing)
Series of three has the value of 1
Series of four has the value of 0
Series of five has the value of 1
Series of six has the value of 2
Series of seven has the value of 3
Series of eight has the value of 4
And so it continues.

Now to the underlying dimension.
You can divide singles only into singles of singles and series of singles.
And you can divide singles series versus series of series.
With the same math and probability measuring the random flow.

[ego]

Singels contra series - March 1

This is flat betting with a total of four attempts.

1) Rule number one is to wait for two series to chop, the formation of two series look like this RRRBBB and after that formation appears you attack twice and gain +1 unit.

If you don´t get a straight hit with three series in a row like this RRRBBRR you will have the following formation RRRBBR and aim for it to hovering with your secound bet RRRBBRBBBB if at zero you just follow the betting behavior, the march, until +1 or -2 being your first attack.

2) If you don't get two series to chop as I mention above you make your first attack when a state of hovering appears and it looks like this RRRBRRR and play that next formation will be followed with a serie like this RRRBRRRBB if not you will have the following formation RRRBRRRBRRRR and would play it will continue to hovering and ride it out until +1 or -2 being your first attack.

3) If first attack fail you would repeat the betting signals above for one more attack with the difference that you don't aim to win +1 and now aim to break even because that would give you one less formation of correction to appers more (variance)  regulary then an longer correction to end up with +1 and this is a way to make the play more stabel with good results.

Result:

+1 +1 +0 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +0 +1 +1 +0 +1 -4 +1 +1 +1 +0 +1 +1 +1 +1 +0 +1 +1 +1 +1 +1 +1 +1

31 won
4 loss
27 total gain

Clarification:

You wait until two series chop after each other, then you play that the third will show.

R
R
B
B
B
R
R W

Now if you lose this first bet, then you bet you will win the second bet.

R
R
B
B
B
R
B L
B W

Now lets assume none of the bet wins then the STD start to grow again with out drop point after stop growing stronger.
So now you have to wait for this two betting signals again.
Two series to chop or the hovering state.

R
R
B
B
B

or

B
B
R
B
B

After 3.0 or strong imbalance and this two state start to show as drop point or indication that the bias stop growing stronger - then this two states start to chop or clustering in waves where you end up +1 unit or break even at +0.

If you follow the march above you should get similar results.
+1 +1 +0 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +0 +1 +1 +0 +1 -4 +1 +1 +1 +0 +1 +1 +1 +1 +0 +1 +1 +1 +1 +1 +1 +1
If i remember it correct i once reach 3.0 STD flat betting this way or was it another march, not sure ...

What you will see after 3.0 STD if it stop growing and go into the other direction is the two following states.

R
R
B
B
R
R
R

There will be many events that will become at least three series that chop after each other.
Tiny drop point and larger drop points.

The other common one is the hovering state follow by hovering state or series that chop.

R
R
B
R
R
B
B

Or

R
R
B
R
R
R
B
R
R
R
R

This creates two kinds of Loses and Winnings ...
Direct wins or break even W or LW chops.
When there is no correction you only end up with two loses LL.

I will show that how the regression towards the mean look like.
You can get very long strings of winnings before reaching a loss limit ...

LWWLWLWLWWLWWWWLWLWLWLL LWWLWLWLWWLWLWWLWWLWWLWLL LWLWWLL
All does are series that chop or hovering with out the STD to start growing again.
So if not flat betting, then i would suggest D'alambert as staking plan.

This is the kind or similiear LW-Registry Bayes gets ( if i assume ) and others get with there methods when the use tendency play.
This is the real thing.

[ego]

Here is a simulation software 1.1 Ecart - It has both Singles contra series and Series contra singles (pick your own settings).
I also test this simulation software and it works great.
See attach file.

You run the software and load your spin file.
I prefer running 10.000 trails from random org.

Click on the next button and the software will find you a window of 3.0 STD.
After that you can click on the spin button and see how the drop point behave.

[ego]

.i have question, is there any sign to know how big regression is going to be..because sometimes even chance reaches say std 4  and breaks back but it does not even very much...but sometimes even chance go to say lower std 3 and breaks back very nice...thanks

Sometimes it does not have to have a drop point or even out.
You win if it just stop growing stronger and stay at same level without getting stronger or weaker.
This is what i call or name the hovering state and i define it being part of the drop point or correction as it is present change.

I have simulation software where you can observe the values.
You can run 10.000 trails and look how the imbalance behave ( The ECART )

By this observations you can build a working march.
You can see what happens after 3 4 5 6 STD windows.

The software show the values on a rolling basis.
This way you can make statistical relevant observation of hundred thousand simulations.

It check R/B H/L O/E and measuring the ECART.
I attach the simulation software ecart and result file of one simulation.

You run the simulation software and load a spin file.
Then the software will convert the file into Ecart values.

This is also a good simulation software for deeper understanding of waves or Ecart play.
The simulation software indicate at right side when it reach 3.0 STD ...

B-0.94    E 1.57    H 1.00
B-0.94    E 1.57    H 1.50
B-0.94    E 1.57    L 1.50
B-0.94    O 1.57    H 1.21
B-0.94    E 1.37    L 1.00
R-0.94    O 1.18    H-0.85
R 1.00    O 1.33    H 0.94
R 1.00    O 1.33    H 0.94
B 1.00    O 1.33    H 0.94
B 1.15    E 1.33    H 0.94
R 1.15    E 1.48    L 0.94
B 0.97    E 1.48    H 0.69
B 1.12    O 1.48    L-0.73
B 1.12    O 1.62    L 0.65
B 1.12    O 1.62    H 0.65
B 1.12    E 1.62    L-1.00
R 1.12    E 1.76    L-1.00
R 1.26    E 1.76    L-1.00
B 1.26    E 1.76    L-1.00
B 1.41    O 1.76    L-1.00
B 1.41    E 1.58    H-1.00
B 1.41    E 1.72    L-1.21
R 1.41    O 1.72    H-1.50
B 1.23    O 1.85    H-1.21
R 1.07    O 1.85    L-1.21
B 0.90    E 1.85    H-1.50
B 1.04    E 1.98    L-1.70
B 1.04    O 1.98    L-1.41
R 1.04    O 2.11    H-1.41
B 1.00    E 2.11    L-1.61
R-0.73    E 2.24    L-1.34
B-0.90    O 2.24    L-1.34
R-1.06    O 2.50    H-1.34
B-1.22    O 2.50    L-1.53
R-1.50    E 2.50    H-1.71
B-1.70    E 2.67    H-1.46
B-1.50    O 2.67    H-1.46
R-1.50    E 2.36    H-1.46
B-2.00    O 2.14    L-1.46
R-2.18    O 2.26    H-1.63
B-3.00    E 2.26    H-1.40  */25
R-3.15    O 2.00    L-1.40  */25
R-2.83    O 2.18    H-1.57
B-2.83    O 2.18    H-1.35
R-2.98    E 2.18    H-1.35
B-3.13    E 2.36    L-1.35  */27
R-3.27    E 2.36    H-1.51  */28
B-3.41    E 2.36    L-1.67  */29
R-3.54    O 2.36    L-1.46  */30
B-3.67    E 2.06    L-1.46  */30
B-3.40    E 2.24    L-1.46  */30
R-3.40    O 2.24    L-1.46  */30
R-3.14    E 1.98    H-1.46  */30
R-3.14    O 1.73    L-1.62  */31
R-3.14    E 1.51    H-1.77  */32
B-3.14    E 1.67    H-1.57  */33
R-3.27    O 1.67    L-1.57  */33
B-3.40    E 1.46    L-1.37  */34
B-3.16    O 1.26    H-1.37  */34
B-3.16    E-1.21    L-1.52  */35
R-3.16    O-1.50    H-1.67  */36
B-3.29    E-1.70    H-1.48  */37
B-3.05    E-1.41    H-1.48  */37
R-3.05    O-1.41    H-1.48  */37
R-2.83    E-1.61    H-1.48
R-2.83    E-1.50    H-1.48
B-2.83    E-1.50    H-1.48
R-2.96    E-1.50    L-1.48
R-2.74    E-1.50    H-1.62
R-2.74    O-1.50    H-1.44
R-2.74    O-1.50    L-1.44
R-2.74    O-1.50    L-1.26
R-2.74    O-1.50    L-1.26
R-2.74    O-1.50    H-1.26
B-2.74    E-1.50    H-1.09
B-2.54    O-1.70    L-1.09
B-2.54    E-1.89    H-1.23
R-2.54    E-1.61    L-1.37
B-2.67    O-1.61    L-1.21
B-2.47    O-1.34    L-1.21
B-2.47    O-1.34    L-1.21
R-2.47    O-1.34    L-1.21
B-2.60    O-1.34    L-1.21
R-2.72    O-1.34    H-1.21
B-2.85    E-1.34    H-1.04
B-2.65    E-1.09    L-1.04
B-2.65    E-1.09    H-1.18
B-2.65    O-1.09    H-1.02
B-2.65    E-1.28    H-1.02
B-2.65    O-1.46    L-1.02
R-2.65    O-1.22    H-1.15
R-2.47    E-1.22    L-1.29
R-2.47    O-1.40    L-1.13
R-2.47    O-1.18    H-1.13
B-2.47    E-1.18    H-0.87
B-2.29    E 1.00    L-0.87

[ego]

Alternative March - Development ...

One other famous way is to only attack after +1 when using a march or algorithm.
Lets assume you would play singles contra larger series and your march is to attack after three in a row.
Then if it fails attack after a series of two show and if it fails again attack after a series of two show.

Then you would not attack until one of them show a positive result or +1.
Same with March 1 above if you prefer to be more careful.

Cheers

[ego]

The Ecart windows strength.

We deal with independent random flow where singles and series come in any combination.
As you can see with the simulation software above so does the Ecart grow and getting weaker in waves.
The nature of the game is chaos with tiny, medium and large waves of imbalance or some times even out.

Lets assume you would play this for real with real money.
Then you should know some rules that effect the strength behind the bias window of events.

Say that you search for 3.0 Ecart windows before you are ready to attack.
Then the minim window is 16 events or trails.

Then you have to set a limit that the 3.0 STD should appear during 16 to 30 events and not more or less.
Maybe you set your limit to 16 to 25 events / trails.

This is because if you have a stretch window with 50 events and a Ecart of 3.0.
Then parts of the events during this window is underrepresented events / trails.
That makes the weaker stretch of the window.

Then the likelihood with equilibrium to have some events / trails already been showed - can effect the future drop point to become weaker or with same weak stretch over length as the window with 50 events.
That makes it harder to catch.

So with other words so does the probability window being small give a more rapid drop point overall.
As none of the underrepresented events / trails had a show during the Ecart window.

This is about the length and how much you stretch the bias and limit with your Ecart window - that in the end effect what kind or regression towards the mean you can expect.