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Henri-Bernard de Grilleau, (aka Marigny de Grilleau) is a famous French roulette scholar of the past. Born on 1 August 1855 in Pau, he died on 25 February 1942 in Beausoleil.

His most important work was:

" *Le gain scientifique d'une seule unité sur toute attack d'une figure seléctionnée à la
roulette ou au trente et quarante assuré par des probabilités convergentes bases sur les lois du hasard ou le rythmes de la fatality periodic.
(1926)"*

We certainly do not have the presumption of wanting to summarize Marigny de Grilleau's work in a few lines but, taking it to the extreme, we can say that the author expects a high gap to then make a partial compensation for it.

Let's quantify what has been said.

Let's start from the principle that a gap can almost never reach a value equal to 5 times the square root of the shots taken into consideration.

In practice, out of 100 shots,
the maximum possible deviation should not exceed 5 multiplied by the square root of the shots taken into consideration (10), i.e. 10x5=50. In simple terms, at most we could have 75 reds and 25 blacks (or vice
versa). *However, this gap can be overcome, but these are truly rare events.*

If we wanted to wait for a gap equal to 5 times the square root, we would embark on very long waits: we will almost never witness such an event: for this very reason the scholar suggests starting the attack after gaps of 3 times the square root. The attack will not focus on classic simple chances, but on their distribution methods, according to a logic of probability convergence.

THE CONVERGENCE OF PROBABILITIES at roulette according to Marigny de Grilleau

The method looks for a "probability convergence" .

LET'S EXAMINE SOME "RULES":

1) The classic simple chances will not be used. Instead, we will consider Groups (of any size) and Intermittences as opposing chances.

We will also consider opposing possibilities, in the context of both Groups and Intermittences (obviously independently of each other), their occurrence as a Single, or in the form of an Agglomeration (of any entity).

Example:

1 R

2 R

3 R

4 ... No

5 R

6 R

7 ... No

8 ... No

9 R

10 ... No

11 R

12 ... No

13 R

14 R

a) The numbers 1 2 3 form a G

b) The number 4 forms an I

c) The numbers 5 6 form a G

d) The numbers 7 8 form a G

e) The number 9 forms an I

f) The number 10 forms an I

g) The number 11 forms an I

h) The number 12 forms an I

i) The numbers 13 14 form a G

We therefore have, in relation to G and I, 9 ballots, of which 4 produced G and 5 produced I

*But in practice, what is meant by "Aim I" or "Aim
A"?*

Let's admit for a moment that, having reached the 14th shot, the system suggests we play for I (obviously this is an example). How do we bring I into play?

We wait for the Red G to stop with the appearance of Black; at this point we will play Red (in this way the previously played Black would be I).

Likewise if, on the 14th shot the system suggests we play for A. How do we play this "chance"?

We wait for Red's G to stop with the appearance of Black, and we play Black again (in the event of a win the two Blacks would form a G).

Still regarding the example above, regarding S and A, we find the following situation.

At letter a) we have Single shot (regarding G)

At letter b) we have Single shot (regarding I)

At letters c), d) we have an Agglomeration (regarding G)

At letters e), f), g), h) we have an Agglomeration (regarding I)

We cannot yet give any classification to letter g). If an Intermittent were formed in subsequent numbers, g) would be a Single hit (relative to G); otherwise it would be an Agglomeration.

2) Use deviations of at least 3 times the square root of runoffs

( note: *by ballot we mean the appearances of I and G or of
S and A; for example, a series of 10 Rs will not be considered as 10 ballots, but as a single one, in fact, it constitutes a G)* .

3) Use gaps that form in a number of ballots between 20 and 40 , as the scholar believed that they have a greater compensating force.

4) The attack is suspended as soon as the profit of a piece is registered. In any case, if the profit is not obtained, on the 5th shot played, the attack is interrupted regardless of the cash situation.

EXAMPLE

Let's assume that out of 25 ballots (the number that satisfies the 3rd condition) we find 20 G and 5 I. The difference is equal to: 20-5=15. The square root of 25=5; 5x3=15. Therefore our difference is equal to 3 times the rq of the observed ballots. The 2nd condition is observed.

ATTACK CONDITION

It is necessary that the sorts (5, in the example) of the deficient mode (I in the example) all appear as S. In the example in question therefore the Intermittences must all be Single, without forming any Agglomeration.

Therefore, under respected conditions, we have the convergence of 2 deviations:

Gap between I and G

Difference between S and A

Once the condition has been found, it is necessary to wait in vain, for a degree 2 or 3 Agglomeration of the deficient chance (I in the example). If the grade of A is higher than 3, it is not worth playing).

Note: By degree of an Agglomeration we mean the number of chances from which it is formed. For example RRRNNRR is a 3rd degree Agglomeration (of Groups), as it is made up of 3 groups.

As soon as one or more Groups returns, we wait in vain for a new I. At this point we will play for the formation of an Intermittency Agglomeration, we will therefore play for the formation of I.

If we win, we consider the attack to be over and look for new gaming opportunities either in the same roulette or in other roulettes.

In case of loss we wait in vain for a new I to play for the formation of a Group of Is, that is, we will play Is again. We proceed in this way until we have a profit of 1 piece or at the end of 5 rounds of play

Note: *if while waiting for an A of Intermittents, several Single Is occur, the system may become
invalid. It will only come into play if, when the
trigger appears (by trigger we mean the Agglomeration of 2 or 3 Intermittents that we were talking about before), without considering the trigger itself, G and I still fall within the discard
parameters (difference equal to 3 times the Rq of the number of ballots)* .