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.