Roulette is one of the world's most popular casino games.The game is pretty straight forward - a ball is spun in a

rotating wheel with 38 possible numbers or chance opportu-nities and when the ball lands to rest on a number, a wager eitherwins or looses. In 2005, a progressive surveillance team conducted an inquiry to find out if roulette was in fact truly asstraight forward and simple as it appears.

The inquiry's topic was roulette biases, regarded as apotential bias of the equipment of the game, an issue we allshould realize can exist. An equipment bias is defined as anirregularity in gaming equipment that causes a change, pref-erence or a “prejudice” in the results of the game. Proactivesurveillance departments include audits that should have adefined purpose for being conducted. A key question to askis, “What is the audit accomplishing?” Roulette audits are per-formed for numerous reasons such as the round times perhour, game efficiency, procedure adherence, etc. None ofthese stated audits purge deeper into the game, which wasthe goal of this inquiry.

This roulette inquiry analyzed 20,000 roulette spins and theirresults. A large number is a necessary ingredient for any analyzes because on any particular day anything can happen ina game of chance and to verify the proper cause of a problemwith quick assumptions can prove careless and potentiallyharm employees or the casino operation. For instance, this study,after 1,000 spins, immediately provided statistical data infor-mation showing casino dealers were performing target location spins, meaning the dealers were able to select droppoints in the wheel head that produced an advantage for players and created possibilities for high level scams and liability issues. The recorded details of the 1,000 spins provideddata with evidential and undeniable proof dealers were cheat-ing, but was this really the issue?

Incorporating common sense into the equation, this datamade very little sense. To successfully perform a target loca-tion spin, three elements would need to be virtually perfect eachtime: The dealer's release of the ball and spin, the speed of thewheel head, and the bounce of the ball would all need to beequal and consistent each and every time. There may be someprofessional cheats or even one or two industry professionalscapable of target location spinning, but to have four dealerscapable of such feats in one casino did not provide an amplejustification that made any sense.

Muscle memory was suggested as a potential cause for theproblem. Muscle memory regarding a roulette dealer wouldrefer to the dealer's ball spin having an automatic signature combined with an equally consistent wheel spin with no realcognitive effort being involved. The theory of muscle

memory would discredit dealers intentionally preparing tocheat the casino while creating a need to procedurally alter thedealers' normal routine. Still those three important factorsremained for the theory to be influential: the dealer's spin, alongwith the speed of the wheel and the bounce of the ball wouldneed to be perfectly equal every single time, making the muscle memory theory equally hard to justify.

Roulette wheels are designed with parts such as canoes, frets,the cone, and the turret, made specifically to reduce anychances of target location spins and muscle memory issues.While the theories of target location spins and muscle memory are intriguing, common sense made the theories hardto digest as predominating factors or issues. Further analysesbecame a necessity to unveil the real issue being represented.

At this juncture the scope of the inquiry was expanded,adding the data from the 1,000 spin audits of the same wheeltogether and at 10,000 spins, patterns began to be revealed.Select numbers from the wheel began to appear prejudice orbiased. Tracking of the select numbers became the focal pointof the inquiry. These numbers were tracked and recorded; keeping a ledger of the win and loss percentages for these specific numbers utilizing a table limit minimum of $1 and amaximum of $25 as straight up wager benchmarks.

The 20,000 spin mark of the inquiry produced astonishingresults. If a player wagered the three numbers that were notedas biased, the player would win $5,304 wagering $1 and$132,600 wagering $25 on each of the three biased numbers.The inquiry's mathematical breakdown is structured as follows:Out of the 20,504 recorded spins and dividing the number ofstraight up wager opportunities (38), each number should onaverage “hit” or become the point 539.6 times. Applying thisaverage number of hits in comparison with the three biasednumber is the next step. By taking the actual number of hitsfor a winning number and multiplying it by 35, the win for thathit will be established. The loss still needs to be accounted andthis is done by subtracting the remaining non-winning hits fromthe total spins. The number remaining is the actual win or profitfrom the number. Outlined below is the potential financial profitachieved from playing the biased numbers of this particular wheel:

40 Indian Gaming July 2007

Roulette Bias Exposed

SURVEILLANCE

by Jeff Murphy

Number (times hit)

#0 (628)

#25 (621)

#29 (607)

Minimum Bet

$1

$1

$1

Amount Won

$2,104

$1,852

$1,348

MaximumBet

$25

$25

$25

AmountWon

$52,600

$46,300

$33,700

Total $5,304 Total $132,600

42 Indian Gaming July 2007

SURVEILLANCE

The duration of time the roulette inquiry took, to reach20,504 spins was approximately 48 days. The roulette table wasopened approximately 12 hours a day, with steady play estimatedat around 8 hours each day. This means at a large resort, witha wheel opened 24 hours and a larger time span of active play,the results from this 20,000 spins inquiry could be achieved inapproximately two weeks. Two weeks worth of efforts by anadvantage player potentially could turn a $132,600 profit.Imagine the returns from this advantage play investment if thesetwo weeks became one full year?

The following circular graph is an example detailing the wheelhit results of the 20,504 spin, roulette inquiry and provides avisual aide to the wheel problem. The green line indicates a trueaverage for the amount of times a number should hit on aver-age. The red line indicates the actual hit patterns of this wheel.(Note the spikes regarding the numbers 0, 25 and 29)

The study of a roulette wheel bias includes two standardsof statistical analyses: standard deviation and chi-square.

Standard Deviation is a statistic used as a measure of disper-sion. Chi-square is a statistic used in testing a hypothesis concerning the discrepancy between the observed and theexpected results. The following graphs detail the chi-squareresults of an unbiased wheel, a wheel considered biased by industry standards, and the bias results for wheel of the inquiry.

Below left is a figured example showing the normal disper-sion of the numbers on a normal unbiased wheel. The 38 numbers are being represented by blue boxes. The bottom number of the chart indicates the Standard Deviation. The sidenumber indicates the percentile.

Below shows the actual disbursement of the numbers (blueboxes) compared to the expected disbursement (red line) witha chi square total of 55, which is the industry standard for a biaswheel (a 98% probability of a bias). Charted is an actual example of a chi square total of 55.43 taken from the inquiry'ssecond sample of 10,252 spins. Note the closer the wheelbecomes to biased, the pyramid shape of the blue boxes beginsto spread out.

Below is the actual disbursement of the inquiry's extremewheel bias at chi square total of 94.59, the full 20,504 spin sample. 10.5% of the numbers fall into the lower bias range(below -1.96 SD). 7.9% of the numbers fall into the higher biasrange (above 1.96 SD). The blue boxes are spread even farther

Chi Square Total of 35

Normal unbiased wheel

Chi Square Total of 55.43

55 is the industry standard for a bias wheel

Chi Square Total of 94.59

Extreme bias wheel

July 2007 Indian Gaming 43

apart and no longer resemble the pyramid shape of a normalunbiased wheel.

An unbalanced wheel issue was eliminated from the list ofpossibilities as those results would have provided a biasedgrouping or section of numbers, leading to the inquiry's educated hypothesis: this particular wheel possesses a rotarybias, meaning the bias is caused by thecomponents that create the wheel's spinning capabilities. Although the performed roulette inquiry did not produce a defining single reason forthe wheel's bias, it did provide some possible areas of potential cause for thebiased wheel such as: a manufacturer'sissue pertaining to imperfections of thecone's panels, the casino's wheel maintenance staff replacing the lateralbearings of the wheel with lateral bearings not purchased from the manufacture, and small scratches andslight grooves on the steel casing thatsurrounds the cylinder or “wheel head.”

Roulette wheel biases can be causedmany ways. A bias can be temporary (a small foreign object influence likewax build up or tape) or a bias can belasting (a wheel structure deficiency).Finding a single reason for a wheel biasmay be virtually impossible, but thenumbers and patterns created by abiased wheel provide casinos with theopportunity to locate a potential prob-lem or liability. Throughout the rouletteinquiry detailed in this article, certainfactors (the numbers) remained consis-tently troubled and lead to a concludedbiased wheel.

Casinos will need to find a methodthat can address issues that can beproven though the numbers for allgames, without issuing a blind eye to thetopic, for advantage play is not limitedto the counting of cards or the game ofblackjack. ¨

Inquiry and graphic efforts provided in thisarticle were performed by John Holcomb,Melanie Pedersen, Chris Hudgeon and theSurveillance Department Branch of theCow Creek Gaming & Regulatory Commission.

Jeff Murphy is Director of Table Games Operations at SevenFeathers Hotel & Casino Resort in Canyonville, Oregon. He can be reached by calling (541) 839-1171 or email jmurphy@sevenfeathers.com