Real money roulette is one of the world’s most popular casino games. It is pretty straight forward: A ball is spun on a rotating wheel with 38 possible numbers or chance opportunities; when the ball comes to rest on a number, a wager either wins or loses. In 2005, a progressive surveillance team conducted an inquiry to find out if Roulette is, in fact, truly as simple as it appears. Roulette audits are usually performed for numerous reasons, such as rounds per hour, game efficiency, procedure adherence, etc., but none of these audits delve deeper into the game, which was the goal of this particular inquiry.
The inquiry’s topic was Roulette biases. By definition, a bias is a prejudice. The gaming industry automatically has a predetermined bias; we call it the house advantage because the odds are favorable to the casino. Naturally “house advantage” is the preferred term, as bias has a negative overtone. The term “bias” was not utilized in the Roulette inquiry to prove the house had an advantage — we all already knew that. Instead, the inquiry regarded a potential bias of the equipment of the game — an issue we all should realize can exist. An equipment bias is defined as an irregularity in gaming equipment that causes a change, preference or prejudice in the results of the game.
This Roulette inquiry analyzed 20,000 Roulette spins and their results. A large number is a necessary ingredient for any analysis because, on any particular day, anything can happen in a game of chance. Also, quick assumptions about the cause of a problem can prove careless and potentially harm employees or the casino operation. For example, after 1,000 spins, this study provided statistical data that showed casino dealers were performing target location spins, meaning the dealers were able to select drop points in the wheel head that produced an advantage for players and created possibilities for high-level scams and liability issues. The recorded details of those 1,000 spins provided data that could evidentially and undeniably “prove” that dealers were cheating, but was this really the issue?
Incorporating common sense into the equation, that conclusion made very little sense. To successfully perform a target location spin, three elements would need to be virtually perfect, equal and consistent each and every time: the dealer’s release of the ball and spin, the speed of the wheel head, and the bounce of the ball. There may be some professional cheats or even one or two industry professionals capable of target location spinning, but to have four dealers capable of such feats in one casino did not make any sense no matter what the data showed.
Muscle memory was suggested as a potential cause for the problem. “Muscle memory” is a term used to describe the phenomenon of skeletal muscle activity that is learned and becomes automatic with practice. For example, walking is automatic and takes no real cognitive effort. In this case, muscle memory would apply to a dealer’s ball spin having an automatic signature and an equally consistent wheel spin with no real cognitive effort involved. The theory of muscle memory would discredit the idea that dealers were intentionally preparing to cheat the casino and create a need to procedurally alter dealers’ normal routines. But the dealer’s spin, the speed of the wheel and the bounce of the ball would still need to be perfectly uniform every single spin, making the muscle memory theory a bit of a stretch.
Roulette wheels are designed with canoes, frets, cones and turrets made specifically to reduce any chances of target location spins and muscle memory issues. While the theories of target location spins and muscle memory are intriguing, common sense made them hard to digest as predominating factors.
Further analysis became a necessity to unveil the real issue, so the scope of the inquiry was expanded. When the data from the 1,000-spin audit of the wheel was added to 10,000 more spins, patterns began to be revealed. Select numbers from the wheel (#0, #25 and #29) began to appear biased. Tracking of those numbers became the focal point of the inquiry. A ledger was kept of the win and loss percentages utilizing a table limit minimum of $1 and a maximum of $25 as straight up wager benchmarks.
At the 20,000-spin mark, the inquiry produced astonishing results. If a player bet on each of the three numbers that were noted as biased, he or she would win $5,304 wagering $1 and $132,600 wagering $25 (see Chart 1).
The inquiry’s mathematical breakdown is structured as follows: With 20,504 recorded spins and 38 straight up wager opportunities, each number on the wheel should, on average, “hit” 539.6 times. Comparing this average number of hits to the three biased numbers is the next step. By taking the actual number of hits for a winning number and multiplying it by 35, the win for that hit will be established. The loss still needs to be accounted for, and this is done by subtracting the remaining non-winning hits from the total spins. The number remaining is the actual win, or profit, from the number. Chart 1 outlines the potential financial profit achieved from playing the biased numbers of this particular wheel.
It took the Roulette inquiry 48 days to reach 20,504 spins. The Roulette table was open approximately 12 hours per day, with steady play estimated at about eight hours each day. This means that at a large resort with a wheel open 24 hours and a longer time span of active play, the results from this 20,000-spin inquiry could be achieved in approximately two weeks. Two weeks of effort by an advantage player could potentially turn a $132,600 profit, providing an excellent income-to-work-performed ratio and an equitably sound investment by most people’s standards. Just imagine the returns from this advantage play investment if those two weeks became one full year.
Graph 1 details the wheel hit results of the 20,504-spin Roulette inquiry and provides a visual aide to the wheel problem. The green line indicates a true average for the amount of times a number should hit on average. The red line indicates the actual hit patterns of this wheel. (Note the spikes regarding #0, #25
Standard Deviation and
The study of a Roulette wheel bias includes two standards of statistical analysis: standard deviation and chi-square. Standard deviation is used as a measure of dispersion. Chi-square is used to test a hypothesis concerning the discrepancy between observed and expected results. Graphs 2, 3 and 4 detail the chi-square results of an unbiased wheel, a wheel considered biased by industry standards, and the results of the 20,000-spin inquiry, respectively.
Graph 2 shows the normal dispersion of the numbers on an unbiased wheel. The 38 numbers are represented by tan boxes and the red line shows the expected disbursement. The x-axis indicates the standard deviation, and the y-axis indicates the percentile.
Graph 3 shows the actual disbursement of the numbers compared to the expected disbursement with a chi-square total of 55, which is the industry standard for a biased wheel (a 98 percent probability of a bias). Charted is an actual example of a chi-square total of 55.43 taken from the inquiry’s second sample of 10,252 spins. Note that as the wheel becomes closer to biased, the pyramid shape of the blue boxes spreads out.
Graph 4 shows the actual disbursement of the inquiry’s extreme wheel bias at chi-square total of 94.59, the full 20,504-spin sample. Ten and one-half percent of the numbers fall into the lower bias range (below -1.96 SD). Seven and nine-tenths percent of the numbers fall into the higher bias range (above 1.96 SD). The blue boxes are spread even farther apart and no longer resemble the pyramid shape of a normal unbiased wheel’s chi-square.
Biased, Not Unbalanced
This particular wheel possessed a bias. It was not simply unbalanced, as an unbalanced wheel would have provided a biased grouping or section, not individual numbers. The type of bias identified is referred to as a rotary bias, meaning the bias is caused by the components that create the wheel’s spinning capabilities. Although the Roulette inquiry did not produce a single defining reason for the wheel’s bias, it did provide some possible areas of potential cause, such as a manufacturer’s issue pertaining to imperfections of the cone’s panels; the casino’s wheel maintenance staff replacing the lateral bearings of the wheel with lateral bearings not purchased from the manufacturer; or small scratches and slight grooves on the steel casing that surrounds the cylinder or wheel head.
Roulette wheel biases can be caused many ways. A bias can be temporary (influence from a small foreign object like wax build up or tape) or lasting (a wheel structure deficiency). Finding a single reason for a wheel bias may be virtually impossible, but the numbers and patterns created by a biased wheel provide casinos with the opportunity to locate a potential problem or liability. Throughout the Roulette inquiry detailed in this article, certain factors — the numbers — remained consistently troubled, ultimately leading to a concluded wheel bias. Casinos need to find a method that can address numbers issues for all games without issuing a blind eye to the topic — advantage play is not limited to counting cards or the game of Blackjack.