The only reason I will be in a casino will be for the roulette wheel. Maybe it is the numbers, the probabilities or just the rush of the game. As a barely regular roulette player myself, I am constantly plotting new systems for calculating the optimal bet.
After a little search, one may find many betting systems advertised in the web promising huge money earnings. On the other hand others will say that no betting system exists for roulette playing. Well, once again the truth lies somewhere in the middle. Einstein once said that the only way to beat the roulette can happen only when the croupier is not looking you. Indeed, mathematically speaking, if roulette numbers are drawn from a uniform distribution, you have no chance of beating the house. But roulettes are mechanical systems. Croupiers that spin the roulette and keep the game going, can also be thought as physical systems. And any system can be analyzed or studied.
The roulette can be modeled as consisting of four major parts : the rotor, the stator, the deflectors and the pockets. Any slight deficiency in one of these parts can be responsible for making a roulette biased. An elementary analysis on a tilted roulette can prove that creates a forbidden region of the wheel in which the ball is sure not to land. This is tilt can be as small as 0.1-0.3 angle degrees.
On the other hand, many theories are popular about the way croupiers spin the wheel. The most common one attributes a kind of signature to every roulette croupier: The speed he spins the wheel, the speed he launches the ball and the way he disturbs the results. This is certainly true. Croupiers are regular people working sometimes for 12 hours in a row, and depending on the schedule sometimes overnight. Under these conditions, croupiers can act somewhat mechanically by spinning both the wheel and ball the same way for several game turns. Experienced players can identify such circumstances and have profitable bets at the right time. But casinos also have their counter measures. When a croupier understands that he becomes predictable he changes the style of his play by varying the speed or initial position of the system.
However, such kind of croupier behavior, if analyzed, can exhibit in turn more interesting patterns. One striking example happened just yesterday. The croupier was playing on the numbers near 0 (voisins du zero). This soon became obvious even to amateur players. After a huge house loss, the croupier obviously disturbed the play by moving the ball to the other side (5 and 10 neighborhood) or in roulette slang, by spinning opposites. In regular playing the croupier was moving in the neighborhood and when the croupier decided to disturb the results, he moved the outcomes to the opposite roulette side of the current play.
However, there are no magical systems for the roulette. It is certain that the house has the edge and the most important challenge is proper money management. Psychology is a crucial factor and it is certain that the casino retains huge earnings because players become anxious, neurotic or maniac making silly and meaningless bets.
Mathematically, the game has been studied by the Blackjack-Buster, the mathematician Edward Thorp who invented the card counting technique in blackjack that created a whole new generation of professional blackjack players. Together with Claude Shannon they tried to study the game and the physics involved. While there are exist many stories about making huge earnings, I think most of them are total nonsense. Thorp himself in the Mathematics for Gambling does not report any relevant interesting result. After analysis both in terms of playing and in terms of counter measures, he concludes by saying : "...Then for the reasons explained above, the result will be perfectly random." However, the personal wearable computer is said to have come from the roulette studies of Thorp and Shannon.
Mathematical theory in roulette analysis can also be assisted by using the Kelly criterion. Kelly was a researcher in AT&T when he published a paper about communicating information over noisy lines. His analysis provides equations that point to the optimal bets (in terms of % of your bank roll) for maximizing your capital. In an unbiased roulette the Kelly criterion cannot be applied but this is not true for roulettes we believe exhibit some patterns in the results.
To sum up, roulette is an exciting game which involves heavy mathematical theory spanning from probabilities to information theory. In later posts, I will try to give my own perspective about the game. Till then, stay cool and bet low.