8. Wheel Tracking Systems
In the winter of 1873 an English engineer and mechanic left the damp and dreary British Isles for the warmer clime of Monte Carlo. In his business of manufacturing spindles for cotton mills, he had become intrigued with roulette wheels, which are theoretically perfectly balanced and therefore produce purely random results. He had a theory that the wheels might not be as perfectly balanced as they were alleged to be and he had a plan to discover and exploit any imperfections in the wheels.
After viewing the renowned casino, the Englishman, Joseph Jaggers, hired six clerks to sit all day long at the six tables in the Beaux-Arts Monte Carlo Casino and record every number shown on every spin on every roulette wheel.
The next week Jaggers spent holed up in his hotel room, analyzing the increasing pages of numbers his clerks were providing.
Finally he emerged, satisfied that he was now ready to battle the LIVE dealer online casinos.
Jaggers entered the casino and calmly began to play on the sixth roulette wheel. He started with small wagers and as he won, he gradually increased his wagers. By the time his winnings exceeded $10,000 he was under the scrutiny of casino personnel, and when his winnings broke $50,000, fully three casino inspectors were nervously watching this casino novice. By the end of the day, Jaggers had won $70,000!
On the following day, Jaggers returned and began wagering on the same wheel. He continued to win. The inspectors believed that he must be cheating, but they finally discovered a pattern to his betting. Even though he disguised his play by wagering other numbers, he consistently bet 7-8-9-17-18-19-22-28-29. Of these numbers, all except 8-17-18 are adjacent on the wheel.
By the fourth day, Jaggers had won an incredible $300,000!
Finally, an inspector noticed that Jaggers always played at the same wheel. After the casino closed for the evening, casino employees moved all six of the roulette wheels.
When Jaggers sat down to play the next day, he began gambling heavily at the sixth table – which unknown to him was not his favorite – and proceeded to lose $200,000. Finally he realized something was wrong and having an excellent memory, he recalled a scratch on the side of the original wheel. He found it, in spot number one.
Playing conservatively, he accumulated $350,000 in the next three weeks. The casino was in a state of panic. At this point, not only was Jaggers cleaning up, but a large crowd of other players had begun making the same wagers, so that the casino was losing much more than just Jaggers' wins.
The casino dispatched a courier to the wheel manufacturer in Paris. The manufacturer discerned that the problem with the sixth wheel was due to the frets (the metal walls separating the pockets on the wheel). The courier returned to Monte Carlo with a whole new set of frets and the casino changed the frets in all the wheels in the wee hours of the morning when the casino was closed.
This, of course, was kept secret from Jaggers and the casino fervently hoped that Jaggers would not notice the change and would be kind enough to lose all of their money back.
Jaggers resumed playing as usual. Within two days, he had lost $75,000. Realizing that the casino had finally prevailed against him, he calmly picked up his sizable winnings, which now totaled $325,000, bade farewell to Monte Carlo, and returned to England.
He never returned to Monte Carlo.
The size of Jaggers' winnings are simply staggering when we consider that this sum would be worth over three million dollars today.
His method is perfectly legal, is still practiced, and by some estimates has won over $6,000,000 in the well published ventures. How much has been won in unreported successes, by gamblers who keep their mouths closed, no one knows. But the amount is sizable.
What Jaggers and others have done is to clock roulette wheels to determine if the wheel is biased enough to allow the player to exploit this bias.
As there is no such thing as a physically perfect roulette wheel, the biased wheel player seeks to detect defects by writing down the roulette numbers as they occur to determine whether certain numbers are coming up with greater than expected regularity.
While casinos use and discard cards and dice daily, roulette wheels cost as much as an automobile and so are used for long periods of time. Over time, a minority of wheels will exhibit enough wear and tear such that they no longer produce random results, but rather become biased in favor of certain numbers or groups of numbers. By clocking enough numbers this bias can be detected, and if the bias is strong enough, a player, by wagering the number or numbers with greater probability of occurring, can win substantial amounts of money.
How much of an advantage can be gained by finding a biased wheel? The table below shows the frequency of a given number and the mathematical advantage possible on a biased wheel.
Players Percent Advantage
This table shows the player's percent advantage on a biased wheel, whether American or French, with a payoff of 35 to 1.
Using the table, we can see that on an ordinary double-zero American wheel with no bias a number will show on an average frequency of every 38 spins, and with the payoff of 35 to 1 (which is the same as 36 for 1), the casino advantage over the player is 5.26%.
On the unbiased French wheel with 37 numbers, the house edge is 2.70%. If we could remove the zeros from both wheels, then our expected frequency of a single number would be 36 and the house would have no advantage.
Now, the object of finding a biased wheel is to gain an advantage over the casino. The table shows the percentage advantage attainable dependent upon the frequency of a number showing. If a number shows on the average every 34 spins, then we have gained a 5.88% edge over the casino. If the frequency is once every 30 spins, our advantage increases to a whooping 20.00%.
And if we are fortunate enough to ever find a situation where a number shows with a frequency of once every 20 spins, our advantage in playing this number is 80.00%.
There have been a number of players who have found and exploited roulette wheels. We recall Joseph Jaggers' success in 1873. In the period from 1969 to 1971 Dr. Richard W. Jarecki won about $1,280,000 playing at San Remo and Monte Carlo using biased wheel play.
The Billy Walters syndicate during different periods from 1986 to 1989 won over $4,400,000 in Atlantic City and $400,000 in Las Vegas!
Obviously, the rewards of finding and exploiting a balanced wheel can be rather extraordinary. But how difficult is it to find such a wheel?
The only tried and proven legal way of accomplishing this is to clock, that is, record the numbers of a roulette wheel as they are spun and analyze them, much as Jaggers did in 1873.
Obviously a hand held computer would be very helpful, but such devices are banned in most casinos, and use of a computer or similar device in a casino in Nevada may even earn you jail time. So the only practical way of identifying a potentially biased wheel is to record and analyze the results of spins.
A significant amount of mathematical analysis has been done in determining the minimum number of spins which should be tallied in order to determine if a wheel is truly biased. To be reasonably sure that a wheel is biased you should record a minimum of 800 spins. In the United States, with an average number of spins of 100 an hour this would take eight hours. At the slower European rate of 40 an hour, accumulating a sample of 800 spins would take twenty hours.
After the sample has been made, you will look for a number with a statistically significant number of occurrences. Based on sound theories propagated by the Belgian gambler and mathematician Pierre Basieux (Roulette, Die Zahmung des Zufalls, Munich, 1992), the expected frequency of a number, if it is truly random, in 800 spins is 33. If the number occurs more than 33 times, the wheel may be biased. The higher the number of occurrences, the greater the potential bias.
If we clock a sample of 800 spins and find that number 6 shows up 34 times, number 13 occurs 35 times and number 16 shows 38 times, we obviously have a much better case for 16 being a biased number than for either 6 or 13. In this situation, the best play would be to start wagering on all three numbers, while continuing to record the spins as they occur. Since each of these numbers has exceeded our target of 33 occurrences in 800 sample, each number should be considered a candidate for occurring more often than randomly.
How easy is it to apply this wheel clocking approach? We have noted that there have been some celebrated successes in using wheel clocking to identify biased wheels.
Allan N. Wilson, in The Casino Gambler's Guide (New York, 1970), recounted his adventure as a young man in trying to beat the wheel. Wilson and a companion, Robert Bowers, sought to emulate other well-publicized successes in wheel clocking. In June, 1948, they descended on Harold's Club in Reno to try this approach.
After playing a wheel for 80,000 spins (a month of continuous play) they increased their bankroll from $50 to only $350. At this point, they decided to switch wheels and after a week's play or 20,000 spins, they had lost back $100 of their $300 profit.
The first wheel they picked because they liked its location; the second wheel they picked because the wheel was severely worn and seemed to be a likely candidate for producing biased numbers.
On a later trip to Reno in 1951, the two young men found a wheel which showed considerable promise, and they felt confident that they could win a substantial amount of money. They were enjoying a moderate success wagering on number three when the casino interrupted the game.
Wilson describes what happened in his own words: "At this point the pit boss unexpectedly sent a mechanic in to test the wheel. First he laid a carpenter's level across the rim. The bubble didn't show a true horizontal, so he cranked up the feet of the table until he was better satisfied.
Actually, we didn't care a hoot about that because we didn't believe that a slight tilt could affect the success of any number very much. But then he began feeling the metal slots between the numbers. When he came to [our hot] number 3, he got very excited, and went running off to tell his boss.
"Meanwhile, we commenced playing at $4 per spin instead of the quarters we had played previously. . . We played for about an hour with the new stakes, rocking up and down, when suddenly the owner himself appeared on the scene. He stopped the action immediately. Then he picked up the ivory ball and conducted his own little test on the wheel. He held the ball against the metal slots, spun the wheel very fast, and listened to the noise that the ball made upon the slots as it went around, ‘Klunk-klunkklunk-ping–klunk-klunk-klunk-ping.’ That was enough for him, and he growled that the mechanic who was responsible for that wheel should be fired. He ordered a new wheel!
"Everybody was stunned, for this was the first time in the history of Harold's Club that the management had ever changed a wheel on any roulette player. It was supposed to be the biggest and most generous club in Nevada…
Everyone was astonished: the players, the spectators, the dealers, and even the pit bosses. We were utterly crushed, of course, for all our data-taking became useless."
Because of the casino's tactics, Wilson and Bowers won only about $125 on the biased wheel in twenty four hours of straight play!
These young men spent a considerable amount of time and energy to come away with very meager winnings. Just how realistic is wheel clocking for the average player? Is there a way to benefit from this knowledge without undergoing the ordeal of Wilson and Bowers? Surprisingly, there is different approach relying on normally occurring variations in the results of roulette spins which will give you a greater advantage than wheel tracking and is much easier to use.