|(the table is for illustration purposes only – doesn’t mean anything)|
It is often said that “roulette is a game of independent evens, therefore no information can be obtained by previous outcomes.“
In a physical sense, roulette spins are independent. The previous spin has no physical effect on the trajectory of the next spin. We are right to assume that Black has 18/37 probability to appear in the next spin.
However, roulette spins are related in a statistical sense.
And we are right to assume that Black coming 100 times in a row is an unlikely outcome.
The answer to the dilemma, if roulette spins are related or not, is “it depends” (no pun intended). Studied separately, each and every spin is an independent physical event.
Studied as a group they are statistically related. (I prefer the word related to the word dependent)
Spins sometimes should be considered independent and sometimes related to each other. Like light, which sometimes should be considered particle and sometimes wave.
Here is an example how things can be related and independent at the same time:
Consider a nation that has to have a specific income from taxes each year. It sets its tax policies according to this income target. The tax each taxpayer pay is independent from the tax the previous taxpayer payed. However they are related in the greater scheme of things, because if for example the other taxpayers pay high tax, you have to pay less and vice versa.
This way of thinking, based on “statistical necessity”, is often the basis of various interesting roulette methods.