One question is as old as the game of roulette itself: "Are the spin results independent of each other?" The math guys will answer that question with a clear "yes of course, if the wheel is unbiased". They will not hesitate to proof their statement with formulas for single zero wheels like p = 1/37 = 0,027, which is the probability of a single number to appear. Or for the even chances like red and black p = 18/37 = 0,487, which is the probability of red or black to appear. And of course this is true even after a series of 24 consecutive red numbers having been spun.

Many players would be tempted to bet on black after that many reds. Wouldn't you too? Or would you laugh about the poor fellows at the table and call them victims of gambler's fallacy?

But how is it after 30 consecutive reds? Or 50? Or 1000 consecutive reds? That's not going to happen you say? Aha, and you are right. But why if every spin is independent and everything can happen and the wheel does not care about past spins? There need to be other forces in the game that influence the sequence of spin results.

Marigny de Grilleau, a French mathematician and gambler studied roulette extensively and published his findings in a book he named "The gain of one unit on the even money chances at Roulette and Trente et Quarante". He was convinced that neither the appearances nor the spins can be independent, because every one of them is a part of the whole. This whole is arranged and limited in all its movements and is subject to precise laws.

Each spin is determined by a certain quantity of independence and a certain quantity of dependence. The independence derives from the fact that every time the dealer rolls the ball, it is faced with 18 red and 18 black, 18 even and 18 odd as well as 18 high and 18 low pockets. Therefore the ball has the same chance to fall in one of the 37 pockets.

The dependence derives from the **Law of Deviation** (Ecart), the **Law of Balance** (Equilibrium) and the **Law of Distribution** of appearances into different clusters and isolated results. Thus the mathematical truth of the independence of the spins is constantly in conflict with the statistic truth of the dependence of the spins.

The conclusion is that the deviation limits the independence of possible appearances of spin results. In his book "The scientific winnings of one unit" Marigny de Grilleau described how to bet for balance after observing rare and extreme deviations at the even chances in roulette. The same he did for the appearances of even chances as singles and series of 2 and higher.