The law of independent trials is fundamental principle that allows the casino gaming industry to accumulate mass amounts of wealth from unsuspecting customers. Every game in the casino has the perception of being completely random in nature. This means there is no predictability of the outcome of an upcoming event. What the casinos rely on is the overall advantage that their games have that favor the casino. This reliance assumes a static wager by the player as well as all of the variables remains constant. There is a branch of probability mathematics that challenges this idea and it is the Chaos Theory of Mathematics.

The simplest way to illustrate Chaos Theory is through a fractal geometry image. In its simplest form Chaos Theory asserts that a seemingly random line along a geometric plane, when viewed in a larger context (or zoomed out view on a geometric plane), displays a discernable pattern. Another key concept is that the small changes within a closed system leads to drastic changes downstream from that event. The classic example is that a butterfly flaps its wings in the jungle and causes a car crash in New York.

The mathematical derivation of these assertions is pretty complex and well beyond the understanding of most recreational and pro gamblers. This article will strictly focus on how gamblers can benefit from even a basic understanding of how it can be applied.

## BLACKJACK CHAOS THEORY

Every game has a set of rules that dictate the overall advantage the live casino enjoys. Blackjack rules can vary by whether you can double after the split of if the dealer stands or hits on a soft 17. To determine what the house edge is billions of computer simulations are utilized to find a convergence of a loss per dollar using an optimal strategy and a flat bet for each event. Blackjack is used the first example because its system is a dependent one not based on the law of independent trials. For instance, when an Ace is played then there is one less Ace in the deck available for a Blackjack. But it is a good lead into evaluating games that are more accepted as adhering to the law of independent trials.

Blackjack is a dynamic game and what cards are played in prior hands directly affect what hands will be played in the future. Each card played either adds to or subtracts from the houses initial advantage. ANs when enough of the right cards are dealt the advantage swings to the player’s advantage. The players then up their bets and can gain the advantage over the house. Other games offered by casinos are also susceptible to this type of attack. The dynamics are much more subtle but they are there. And as stated before a defining characteristic of Chaos Theory is that small changes cause drastic down-stream results. Roulette is the most common application of this.

## ROULETTE CHAOS THEORY

American Roulette wheels have 38 spaces; 1-36 and a 0 and 00 slot. In a perfect statistical world, the ball would land in each basket an average of 1 time in 38. This would indicate that the conditions that the ball was initially spun in remain the same for every spin. This is not the case. The wheel inevitably experiences wear and tear. The humidity in the casino changes over time. The temperature of the wheel will change depending how many people are in the casino. All of these differences may seem unimportant to the recreational player, but as Chaos Theory teaches us small changes leads to drastic shifts in the end results.

Now that it is clear what the small changes are that can lead to a shift the question becomes what is the end result and how can we determine the end result and the most important question how can a knowledgeable player take advantage of the information for financial gain.

The first question is what is the end result?  The clear result is that some numbers will come up more frequently than others, creating a number bias. So how is it that a player can determine what the bias is. Unfortunately, there is no short way to determine this. The only way is to collect data; more precisely a whole lot of data. For roulette, no less than 50,000 spins on a given roulette wheel should be evaluated. A roulette wheel spins approximately 20 times per hour. It is very time-consuming to get the initial data set. This begs the question what is the best approach for data collection?

Because not every wheel will have a biased it is best to record data for several wheels at one time. The data should be put into a spreadsheet and evaluated to see what the frequency of each number is. A one time in 36 frequency yields a positive game and any frequency greater than 1 time 36 is a positive expectation game. Any time you can find at least 2 bias wheels in 10 is a great find. There are both good and bad aspects of this methodology.

First, the bad, the obvious downs side is it takes a very long time to collect the data, several months in fact. Once the data is collected it takes several more months to utilize the system and realize the positive expectation. It is perfectly reasonable that a negative downswing can be experienced during the first few weeks, thus leading to an emotional turmoil. Another thing to consider is that a casino can change out the wheel at any time rendering all your data collection useless.

Now the good, the financial value of this approach is fantastic if you find a wheel with frequencies occurring any more frequent than 1 time in 25. Betting numbers on the inside, as well as ranges and red and black all, can be utilized in this approach. Once you know what the long-term outcome will be you can take full advantage of this information for an exceptional profit.

## CHAOS THEORY IN ONLINE CASINOS

In the online realm, data can also be collected to determine if there is any bias in the random number generators. There is almost always a slight bias in all RNG’s, however, the bias can only be determined after 100 of thousands of events. The chaos theory application can be applied to online Baccarat through this approach. However, it cannot be used on traditional table games because the casinos only use the Baccarat cards one time before they are no longer used.

The Chaos Theory is all about taking advantage of small unnoticeable changes in a system. It is a tedious process but when applied correctly it is a very profitable approach to casino gaming.