The distribution of even money figures in isolated units and different accumulations
In the preceding three articles about the statistics of even money chances we could see that a roulette-wheel produces figures on the even money chances, which we have called series and singles. We have discussed the appearance and the frequency of the developing series and singles in roulette-permanencies.
In the analysis of permanencies we can state that each figure of a certain category sometimes will appear isolated between two figures belonging to higher categories (the figures of a lower category is never to be considered), which statistically seen is their hostile equivalent, sometimes in different accumulations or clusters :
| figure | hostile eqivalent |
| single | series |
| series of 2 | series > 2 |
| series of 3 | series > 3 |
| series of 4 | series > 4 |
| series of 5 | and so forth......: the sum of all singles in a roulette permanence is equal to the sum of all series. The sum of the series of 2 is equal to the sum of all series greater than 2. etc.etc. |
| isolated single | cluster of singles |
| cluster of 2 singles | cluster > 2 singles |
| cluster of 3 singles | cluster > 3 singles |
| cluster of 4 singles | cluster > 4 singles |
| cluster of 5 singles | and so forth......: the sum of all isolated singles in a roulette permanence is equal to the sum of all clusters of singles. The sum of clusters of 2 is equal to the sum of all clusters greater than 2. etc. etc. |
| isolated series | cluster of series |
| cluster of 2 series | cluster > 2 series |
| cluster of 3 series | cluster > 3 series |
| cluster of 4 series | cluster > 4 series |
| cluster of 5 series | and so forth...... the sum of all isolated series in a roulette permanence is equal to the sum of all clusters of series. The sum of clusters of 2 series is equal to the sum of all clusters greater than 2. etc. etc. |
| isolated series of 2 | cluster of series of 2 |
| cluster of 2 series of 2 | cluster > 2 series of 2 |
| cluster of 3 series of 2 | cluster > 3 series of 2 |
| cluster of 4 series of 2 | cluster > 4 series of 2 |
| cluster of 5 series of 2 | and so forth...... the sum of all isolated series of 2 in a roulette permanence is equal to the sum of all clusters of series of 2. The sum of clusters of two series of 2 is equal to the sum of all clusters greater than 2. etc. etc. |
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The precise laws of nature - namely the law of the distribution of figures into different accumulations or clusters and isolated units - rule these different appearances.
The knowledge of these laws clarifies the marvelous order and harmony, which governs in the apparent disorder of a permanence. The law of the distribution of figures, which may not be mistaken above all with the law of the appearance of figures, can be divided in two categories:
- the law of the simple distribution of the figures
- the law of the special distribution of the individual manifestations of individual figures
Seemingly, most roulette-players are aware of the fact that each cluster of the same figure is terminated by the appearance of the equivalent hostile-figure whose periodicity is the same. Many also know that the sum of each figure is equal to the sum of the higher figures. But most ignore the above stated solid facts!
It is quite useful to know these strange equivalences in the distribution of the manifestations of the figures. However these will become clear only through a long and careful analysis of a roulette-permanence or a certain number of shoes at Baccarat or Trente et Quarante.
The following four tables represent:
the law of the distribution of figures into different accumulations / clusters and single units
Table 1. distribution of singles on a single chance (BLACK),
Table 2. distribution of singles on a double chance (BLACK / RED),
Table 3. distribution of singles on all three double even money chances together and
Table 4. distribution of isolated series and clusters of series on a double chance (BLACK / RED)
Table 1: Law of distribution of singles in 1024 spins without zero on a single even money chance:
BLACK: 512 SPINS
Table 2: Law of distribution of singles in 1024 spins without zero on a double even money chance:
BLACK / RED: 1024 SPINS
The table of the law of the appearance of the singles and series (table 2 of statistics for even money chances, part 1)determined that the singles claim 256 spins of a permanence of 1024 spins. We now see from the above table that of 256 singles 64 of these did appear isolated and 192 singles did appeare in 64 clusters of different length.
Further becomes clear from this distribution-table that in 1024 spins a classified cluster of 7 singles and one of 8 or more - that therefore is not classified - originates (for this unclassified cluster the statistical natural law intends 9 spins, since 9 is the average-value between a cluster of 8 and a possible higher cluster). Also we can see that the clusters of singles consist in the average of three spins as also the straight series are formed on average from three spins. The clusters of singles are nothing other than series, that are broken off or terminated after each spin. Finally became clear that just as many isolated singles like clusters of singles, just as many clusters of 2 singles like cluster of 3 or more, just as many clusters of 3 singles like clusters of 4 or more and so on, do appear.
The appearance of singles is governed by the same law as the series. Each single or cluster of singles in opposition to the sum of the higher clusters on the same chance.
Table 3: Law of distribution of singles in 1024 spins without zero on all three double even money chances:
BLACK / RED EVEN / ODD HIGH / LOW: 1024 SPINS
Table 4: Law of distribution of isolated series and clusters of series in 1024 spins without zero on a double even money chance:
BLACK / RED: 1024 SPINS
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