Statistics for even money chances part 6

Statistics for even money chances part 6

In our previous articles about statistics of the even money chances Black / Red, Even / Odd and Low / High we have discussed the appearance of singles and series in great detail.
Here we will have a closer look at patterns or appearances formed by the even money chances.

THE LAW OF THE SERIES.
If a roulette permanence is checked not only for the frequency and distribution of chances like BLACK and RED, DOZENS and COLUMNS, LINES etc., but in respect to its structure, we can see a regularity in the seemingly rule-less back and forth. The roulette researcher Alyett developed the patterns named after him in the classic roulette-research for the game on even money chances.

By summarizing in each case four spins, 16 possible patterns do emerge:



The patterns the lower row are the mirror images from the upper row.

Both the French mathematician Thédor d`Alost as well as Alyett came to the following conclusion: these patterns are subject to the same laws that govern the appearance of the even money chances.
They also develop TENDENCY, DEVIATIONS and BALANCE.
All patterns have the same probability. The appearance B-B-B-B has exactly the same probability as R-B-R-B or R-R-B-B etc. . This is valid for every possible appearance of the even money chances. A series of ten BLACK spins has the same probability as for example a series of ten singles!

APPEARANCES OF SAME SIZE HAVE THE SAME PROBABILITY!



Around 1920 the French roulette-researcher Henry Chateau analysed the relationship of singles and series for the even money chances in 56,534 ideal-spins and came to following results:



Chateau did not consider the appearance of 1,536 zeroes in this analysis. If you look careful at the above table, you can easily see that
1. the number of singles is double the number of series of 2
2. the number of series of 2 is double the number of series of 3
3. the number of series of 3 is double the number of series of 4 and so on.
The sum of the singles is approx. 25% of all spins.

Based on this analysis Chateau constructed a pyramid.
In this pyramid you can find the frequency of series:
- the columns in the table show the length of the series,
- the black numbers on the outer left show the numbers of appearances,
- the black numbers on the outer right show the number of spins needed to form the appearances.
The pink highlighted column shows for example, that 1 series of 6 is based on average on the appearance of 2 series of 5,
4 series of 4, 8 series of 3, 16 series of 2 and 32 singles.
128 spins are neccesary for the development of a series of 5.



With this pyramid you can check how many spins are necessary for series up to 11.
Another example:
a series of 9 needs on average 1024 spins and
- 2 series of 8
- 4 series of 7
- 8 series of 6
- 16 series of 5
- 32 series of 4
- 64 series of 3
- 128 series of 2 and 256 singles.