Mathematical Certainty for a Game of Chance? Better Odds for Winning at Roulette

Most roulette players will be honest when they tell you that the chances of winning on a roulette spin depend on the odds. There are different types of bets but, for instance, if you bet on a single number on a European wheel (36 pockets) you have a one in thirty-six chance of winning. It’s that easy.

Or is it?

A duo of chaos theorists examined that premise more closely from the standpoint of Chaos Theory. They tried to determine whether that theory stands up when online casino roulette players and land-based casino gamers play for roulette wins and no deposit casino bonus giveaways.

Chaos Theory

Chaos Theory deals with the “science of surprises.” In mathematical terms, it focuses on the unpredictable and the nonlinear. While most traditional science deals with supposedly predictable phenomena (i.e. chemical reactions, electricity, gravity, etc) Chaos Theory teaches us to expect the unexpected.

Chaos Theory examines events that are impossible to effectively predict or control (the stock market, weather, turbulence, etc). Mathematicians use fractal mathematics to describe these phenomena as they capture the infinite complexity of nature.

Natural objects like clouds, trees, human organs, rivers, and other elements exhibit fractal properties. Such properties are also used to describe some of the systems in which we live which exhibit chaotic and complex behavior. By understanding the chaotic, fractal nature of our world we can gain new power, wisdom, and insights into our surroundings. Maybe, we can even learn to control those elements to some degree.

In short, if we’re able to understand how our economic systems, our social systems, and our ecosystems are interconnected we can take action to ensure positive outcomes.

Chaos Theory in Action

As mentioned, Chaos Theory deals with complex phenomena. It’s an integral part of how physics explains our Laws of Nature. Chaos Theory can also be put into play in small ways. If a balloon pilot can understand the chaotic dynamics of the atmosphere, he can “steer” a balloon to the desired location.

Similarly, if a roulette player knows how to combine his gaming and his betting with properly-understood Chaos theory, will he be able to experience a higher-than-average win rate?

That was the question that Michael Small and Chi Kong Tse wanted to examine when they looked at the question of whether Chaos Theory could help roulette players exploit the deterministic nature of the game of roulette for profit.

In their article abstract, Small and Tse noted that “through its history, the inherent determinism in the game of roulette has attracted the attention of many luminaries of chaos theory.” Their paper set out to determine “to what extent that determinism can really be exploited for profit.”

Small and Tse modeled the motion of the ball and the wheel. They then were able to confirm their predictions, both in simulation and by activating an actual roulette wheel. Small said "Knowing the initial conditions allows you to beat the odds. In some cases, you can beat them quite significantly."

The Experiment

The researchers provided a very simple model for the motion of a roulette ball and wheel. Their goal was to demonstrate that knowledge of initial velocity, acceleration and position would be sufficient to predict the outcome with adequate certainty which would then result in a positive expected return.

Two physically realizable systems were used both incognito and in situ to obtain this knowledge with a standard casino-grade European roulette wheel.  The first system relied on a mechanical count of the rotation of the wheel and ball to measure the relevant parameters. Using these techniques Small and Tse demonstrated an expected return of at least 18% which is significantly higher than the −2.7% expected of a random bet.

A second, though more intrusive system involved mounting a digital camera above the wheel. In that system, the researchers were able to demonstrate a range of statistically significant, systematic biases which could be exploited increase the percentage of a correct guess on the outcome of the spin.

The analysis of the experiment demonstrated that even a very slight slant in the roulette table leads to a significant bias. This bias could be further exploited to enhance returns.

Application

Casinos don’t encourage their patrons to undertake computer simulations and precise measurements of their roulette balls and wheels on the gaming floor. The researchers developed a simple method that would allow them to more accurately predict the outcome of a roulette game without the need to visit a Las Vegas casino venue.

Step One involves noting the time it takes for the ball to pass a fixed point. This gives the player a rough approximation of the velocity of the ball.

Step Two takes those simple measurements and applies them to the equations presented in the paper.

By activating these two steps on a laboratory ball and wheel, the researchers could predict, approximately 59% of the time, in which half of the roulette wheel the ball would end up falling. When the researchers bet on those predictions they got an 18% return on their gambling. That compares to a -2.7% return when compared to normal roulette odds.

The researchers say that some casino practices could deliver even better returns. In a press release to introduce his paper “Predicting the Outcome of Roulette” to the public, Small stated that  "If you wish to beat the house, look for a wheel for which the ball drops only from one side of the rim – that is, a crooked table. Prediction becomes substantially simpler and more reliable."

Small added "even if the odds are in your favor, there is still a probability of losing, and losing big. In the long run you would come out ahead but you may first need very deep pockets."