Beating the Wheel
One topic that has received a bunch of discussion amongst various sources that I have not yet broached is the notion that Roulette can be a beatable game. There has been some discussion pertaining to the efficacy of a concept known as, 'Visual Ballistics,' which is really just a fancy way of saying, 'Knowing where the ball is or is not likely to go.'
While the game of Roulette has declined somewhat in America, and perhaps in other places, it remains a very solid staple that can be found in virtually any casino in which the game is actually legal. California, for instance, would not have any Roulette wheels in their commercial, 'Card rooms,' because all of the games in such locations must have their results adjudicated with playing cards. It is for that reason that, 'Card Craps,' is a somewhat popular game in certain California card rooms. Aside from jurisdictions that specifically prohibit the game, however, Roulette can be expected to be found in virtually any major casino.
There are very few side bets that have been developed for Roulette, and none of the ones that have been have really taken off in any serious way. However, that does not mean the game is without variations. In American Roulette, for instance, there is both a zero and a double-zero on the wheel, yet the pays are the same as they would be on a single-zero wheel, which results in a house edge of 5.26% which is a return-to-player of 94.74%.
If one wanted to beat American Roulette straight up, then the simplest way to do it would be to eliminate a few numbers as possibilities with respect to where the ball would land, and that is what visual ballisticians as well as computer programmers have attempted to do. For example, if one could absolutely conclude that just three numbers on an American Roulette wheel would not hit on a particular spin, and then had the time to bet just one unit on each of the other thirty-five numbers, then the end result would be that person winning one unit every single time.
Of course, even those practitioners of visual ballistics would not claim such unerring accuracy, and furthermore, they would not even claim it was that simple. While such people believe that small sections of numbers can be eliminated as possibilities given certain parameters surrounding a given spin, they do not unanimously believe that this sort of thing occurs with each and every individual spin.
Of course, American Roulette is a variation, if anything can be called that, of the game of European Roulette, alternatively simply called, 'Single-Zero,' Roulette. That game has a house edge of 2.70%, which translates to 97.3% return-to-player, and the game only has one zero on the wheel compared to two. Simply put, any player that could exclude just two numbers from being possibilities would have an advantage on this game.
Atlantic City rules work basically the same as American Roulette rules for most bets, however, Atlantic City rules essentially follows something similar to European rules as relates even-money bets. Any player who loses to a zero or double-zero on an even money bet will only lose half of the total amount wagered, however, this variation would really have no practical effect from the standpoint of visual ballistics which often calls for a series of single-number bets to be made. With respect to single-number bets, Atlantic City rules and American rules are one and the same.
With French rules, a player will play on a single-zero wheel and will only lose half of the bet if the ball lands in zero. The player also has the option of having the bet, 'Imprisoned,' but the decision just to lose half will either be as good or better in every possible set of Roulette rules.
The ultimate result of these different rules is that, if Roulette is somehow beatable via computer tracking or visual ballistics, which is essentially the human attempt at tracking, then the lower the house edge, the more beatable the game will be. One less zero on the wheel is simply one less number the player has to worry about having not hit.
There are a number of sites out there that purport to be able to teach people the concept of, 'Visual ballistics,' but there is a very good chance that they exist primarily to get people to purchase private lessons or other materials. I can certainly say that, if I had visual ballistics down well-enough to make me a long-term winner at Roulette, I wouldn't be publicly disseminating information about the subject at all...much less teaching it to complete strangers.
Other sites and articles have described computers that can measure the deceleration of the ball by recording, three times, when the ball has reached a certain point. Of course, this relies on a person hitting a button each time the ball reaches or passes that point, and even if such were theoretically possible, it would have to be done with a high degree of accuracy in order to result in the player being able to beat the game. Furthermore, someone watching the computer and receiving the results would have to somehow communicate what numbers to bet to the player, who would then, in turn, have to get the bets down before the croupier called, 'No more bets.'
In Las Vegas as well as most, if not all, gambling destinations in the United States, the use of such a computer would be construed as cheating. In fact, the communication of the likely results could also be argued as being tantamount to wire fraud as well as cheating with an electronic device. Even if such a computer were available, and could be employed successfully, and potential windfall would hardly be worth it if the player was caught with one.
For such an allegedly effective device, there has been little published about its uses, and the same goes with visual ballistics.
Another thing that one should consider when musing over whether or not Roulette is a beatable game in this regard is that the casino takes little to no action (when it would be very easy) to prevent a player from gaining an advantage in this manner. While it would certainly bring the number of spins-per-hour down at the Roulette table, if any casinos were truly concerned about people being able to tilt the odds in their favor in this way, then why wouldn't they just require all bets to be placed prior to the croupier spinning the ball?
The answer to that question is very simple: The casinos are simply not that concerned. The holds on Roulette continue to be consistent enough that the casinos believe that they have little to nothing to worry about in that regard. Furthermore, casinos are much more concerned with other forms of cheating such as bet capping or attempting to pull bets back while the croupier is distracted.
Back in 2004, The Guardian reported on a trio that allegedly used a computer device to take The Ritz for 1.3 million pounds at the Roulette table:
The trio allegedly used a computer as well as a laser scanner to analyze the decaying orbit of the ball and, when such information was transmitted, the proper numbers to bet (i.e. the most likely sector of numbers to hit) were relayed back to the person doing the betting who then had only a few seconds to get the bets down. The trio left the casino with a substantial sum of cash and had received the rest of their winnings by check, but surveillance had determined the trio had cheated.
News Scientist later spoke with Norman Packard, then a physicist at at Santa Fe Institute in New Mexico:
Who not only reported that such a device in a cell phone was possible, but furthermore, that a program in the cell phone itself could solve the equation and reveal the most likely quadrant for the ball to land in. Packard then went on to claim that he had developed a similar device in the 1970's which operated via toe-tapping each time the ball reached a certain point. Laws that prohibited the use of such devices would go on to be passed, which prevented Packard from continuing to use the devices in the casinos, though he claimed to have been winning when he finally stopped.
The way that this device worked involved no communication between the two people, just communication between the device and the wearer. What the wearer of the device would do is tap his big toe each time the ball hit a certain point on the Roulette wheel, and after the third tap, the computer would then send an electronic signal that would cause vibrations in another device, hidden underneath the shirt, which essentially told the wearer in what octant to place the next bet, or alternatively, the computer would tell the wearer not to place a bet if the computer couldn't discern anything from the data.
Eventually, Norman Packard and his partner decided that it would be easier for one of the men to signal the computer the visual information while the other man would simply await the signal and decide where to bet.
Furthermore, a study by Michael Small of The University of Western Australia's School of Mathematics and Statistics and Chi Kong Tse representing the Department of Electronic and Information Engineering of Hong Kong Polytechnic University:
Concluded that an expected return, in favor of the player, of no less than 18% of all monies bet could be achieved using a non-optimal betting strategy combined with computer information. The research goes on to describe a number of historical occurrences in which certain roulette wheels were beatable due to imbalances or irregularities in either the wheel or the table itself.
Of course, in the majority of casinos, the statistics of a Roulette wheel are kept on a computer and if there are any tendencies that seem to defy expectation, or even come close to doing so, the wheel is inspected and potentially recalibrated to behave as it is intended. While there may be some small casinos in which a fundamental wheel bias could be exploited, that has little to do with computer tracking or visual ballistics, though it can be combined with either of those things, theoretically.
Computerized wheel tracking should theoretically be able to provide information that will result in advantageous bets on even a standard and perfectly balanced, at least to such extent as one can be, 'Perfectly balanced,' Roulette wheel. The methods of computer tracking that have been proposed, in fact, might benefit from a wheel that behaves in as close to the physically expected manner as possible. While the computer can also be programmed to check for bias, as well as calculate the effects of that bias and incorporate same into its modelling, it is much easier for the computer to be dealing with a balanced Roulette wheel as a mostly balanced wheel is the, 'Starting point,' that the computer is basing the expected results it releases on.
For those of you with an interest and understanding of trigonometry, in other words those of you who are not me (I learned just enough to get through the college course and promptly forgot exactly all of it) you might be interested in some of the formulas and theories presented in the research paper. While I got the gist of what they were saying, because they were kind enough to also use, 'Plain English,' rather than only, 'Plane English,' (get it?) the formulas themselves meant exactly nothing to me and, in fact, I am not ashamed to admit that I don't even necessarily recognize all of the symbols being used.
The research goes on to demonstrate that the 18% advantage that they claim to have is based on recording the speed and anticipating the result based on the deceleration of the ball and wheel based on ball position alone as it hits certain points, and they stated that they guessed the half of the wheel upon which the ball would land on thirteen of twenty-two trials as well as guessing the specific slot on three trials.
While guessing the specific stopping number for the ball is hardly trivial, guessing the half of the wheel the ball would land on certainly is. That would be equivalent, on an American Roulette wheel, to betting eighteen units on either red or black and hedging one of the zeroes with one unit while winning thirteen out of twenty-two bets. In other words, something that probably happens all of the time. Guessing the correct specific number on three out of twenty-two attempts is a bit less trivial, given that a single-zero wheel was being used for the experiment, a binomial distribution based on guessing right at least three out of twenty-two times with a probability of 1/37 puts the success rate at 2.07%.
How many times have you walked up to a Roulette tracking board and noticed that the same number appears three or more times while the board usually only tracks fifteen or twenty numbers? I haven't played live Roulette in a few years, and only played it rarely when I did enjoy it, but I've noticed a certain number hitting a lot many times just in passing. Granted, they did have to guess the number right, but when a random guesser has a 2.07% chance of performing the same feat, or better, I have no choice but to determine that the particular set of results is statistically insignificant due to limited sample size.
Using a more intricate means involving a camera placed over the wheel (impractical in a casino) and a much larger sample size (700 spins) the duo found that that the wheel could be clocked in a manner as to offer, outside of the 99% confidence interval, the ability for the computer to be correct with respect to whatever pocket it considered the, 'Target.' Furthermore, the first few numbers prior to the target pocket, which the group explained would require the ball to bounce backwards to hit, that occurred with a statistically significant lesser frequency than did the target pocket or pockets immediately after the target pocket on the wheel. Finally, the group concluded, the first few pockets immediately after the target pocket seemed more likely with only a marginal significance.
Keep in mind that such doesn't mean that the computer selected the target pocket and was correct 99% of the time, it simply means that it was correct outside of the 99% confidence interval. Looking at the Binomial Distribution once again, that simply means that the computer selected the correct number thirty-one or more times out of seven-hundred spins. While a confidence interval of greater than 99% is certainly impressive, even given only 700 samples, I'll leave it for you, the reader, to discuss in the comments whether or not that sample size is statistically significant.
Before I do that, though, it is worth mentioning that such predictive capabilities, assuming a bet of one unit per spin, would result in winnings of 1,085 units (or more) against losses of 669 units (or less) for a total of at least 416 units gained, roughly .5943 units per spin.
Again, though, this method would be difficult, if not completely impossible to actually execute in a live casino to the same degree of predictability, even assuming that the sample size is meaningful. Interestingly, the method of doing this that actually is feasible and the one that The Guardian reported that trio to be using, or at least some version thereof, had a sample size that was definitely not at all meaningful in the study.
The research concluded that the trajectory of the ball and ultimate resting place could be determined in a meaningful way provided conditions remain constant enough, however, it also indicated that minor changes to the wheel, or the croupier releasing the ball in varying manners would also suffice to largely protect the casino from the implementation of these computers. In other words, by following what the procedures already are in most casinos, croupiers will be able to protect the game from those seeking to gain an advantage via computer.
While not necessarily offering any suggestions as to what sort of computer modelling would work, the research paper closes out by stating that more sophisticated methods could result in greater advantages by way of more inherent predictability. In other words, the paper cited that it was lacking somewhat due to the fact that their modelling systems did not take all possibilities into consideration, rather focusing on base implements. If they are correct, and I would tend to agree, from reading the, 'Plain English,' version of their study that more sophisticated modelling methods are possible, then one can readily conclude that Roulette is a beatable game via a player being added by a computer device.
Furthermore, the research paper also concluded that Packer's computer, which essentially operated in the same fashion and made the same general predictions that the duo conducting the research did in their first model, would have been possible at the time that Packer claimed to have implemented it.
All of this brings us back to the concept of visual ballistics, and the goal of visual ballistics is to essentially accomplish all of this by the naked eyeball. First of all, it should be noted that there is a difference between visual ballistics and finding a biased wheel, though the two can also operate dependently on one another, at least in theory, on a imbalanced wheel.
However, finding an imbalanced wheel alone simply means that a player has determined that the results of a particular Roulette wheel generally favor one section as opposed to another. This is usually accomplished by, 'Tracking,' the results of the wheel over a substantial period of time, but is either impractical or impossible for a few different reasons including, but certainly not limited to:
A.) The quality of the equipment is simply too good now. The casinos use expensive Roulette wheels and should theoretically also be using sophisticated devices that exist for no other purpose to check the balance on the Roulette wheel. While many people operate under the flawed assumption that casinos will cheat in any way they can, they have no way of knowing how individual people are going to bet, and given that an imbalanced wheel could theoretically be exploited by someone, the optimal decision for the casinos is to play the game with as fair and balanced a wheel as possible.
B.) The number of spins it would take to absolutely conclude that a wheel is imbalanced is nothing short of ridiculous. Interestingly enough, the greater the amount of numbers for which you are trying to determine bias, the more trials it takes to get outside of that 99% confidence interval that you have found bias. In other words, a great amount of time will be spent studying the Roulette wheel, logging the results and then doing the math just to find that there is no bias (because of A) and now you must move on to a different wheel.
C.) Because of both A and B, many casinos actually have computers that are doing what the players are manually trying to do in B. There is hardware that essentially determines the final resting place of the ball and delivers that information to a computer which has the job of determining the likelihood, for each individual number as well as any combination of numbers and/or sections that could ever be imagined, that the wheel is fair. If the wheel is somehow imbalanced, the computer will generally suspect such to be the case before the player ever does and the wheel will either be repaired and adjusted or replaced.
The only way that, 'Simply,' finding an imbalanced wheel is going to work is to go to some casino in God-knows-where that has an older wheel and lacks either the ability or concern required to determine whether or not the results are truly random, or if there is some degree of predictability. While I would certainly assume there is at least one such wheel in existence somewhere, I wish whoever wants to find it good luck. I also hope, for their sake, that they do not find themselves in the sort of place where the mere act of consistently winning might result in them being arrested or having adverse physical action taken against them.
That brings us back around to visual ballistics alone which, in a nutshell, seeks to accomplish what the Roulette computers are trying to do by way of the naked eyeball. The methodology is simple, the person purportedly performing visual ballistics tracks the rotation of the ball around the wheel and attempts to use the trajectory to determine a likely stopping point which, generally, will consist of some arbitrary section of numbers (in terms of the amount of numbers around the guessed stopping point) that they will bet.
At least, that is the way that visual ballistics is explained on the vast majority of nearly unreadable websites I have found on the subject. I don't believe that there have been any visual ballisticians that have conclusively proven that the game is Roulette is beatable with simple eyesight, and once again, even if it were, they would likely keep the information to themselves. To that point, visual ballistics only works in the theoretical sense and is not, and cannot be, the equivalent of a computer doing it. An interesting question is, 'Could it ever be good enough to result in a player winning?'
Again, that remains unknown, but much like the alleged dice influencer/controller that bets the Pass Line and/or Odds, if not bets with an even greater house edge against him, I find myself confused at visual ballisticians who don't make the process easier on themselves! The Don't Pass has a fundamentally lower house edge than the Pass Line bet, even though the difference is very small, yet I still find myself confused by the fact that a so-called dice influencer wouldn't try to learn how to roll sevens! Rather than relying on what they term a low, 'Sevens-to-Rolls,' ratio which might even include hitting other numbers (such as crap numbers and elevens after the come out) that don't help them at all, why would it not make more sense to just focus on one number?
If I may be blunt for just a second, it would absolutely make more sense just to focus on rolling more sevens that expected and then attempting to find an empty craps table from which the alleged dice influencer could shoot by himself, but the answer is that they don't do that because they are all full of shit. There is no way to beat the dice, other than using crooked dice or a wide variety of other cheating methods that would usually result in a player getting caught, there never has been a way to beat the dice (other than by cheating) and there never will be a way to beat the dice. Clearly, the earlier statements in this paragraph do not include any legitimate promotions or disportionate awarding of points and/or other offers that make the game fundamentally advantageous for the player.
The same thing can be said for visual ballistics, which largely purports to be able to track a particular section of the wheel in which the ball is likely to end up. What would be easier, at least from my perspective, (if possible) would be to determine where the ball will absolutely not end up if the bets can be placed deftly enough upon making that determination. As I mentioned before, if just three numbers could be ruled out on a double-zero Roulette wheel, or just two numbers could be absolutely ruled out on a single-zero Roulette wheel, the a player betting all of the other numbers would be guaranteed to have a profitable result.
While there may be a few successful visual ballisticians lurking around out there, and I doubt even that, the simple fact of the matter is that these people are largely full of shit. What is actually quite likely is that they focus on the winning sessions rather than the losing ones, or alternatively, have placed so few actual bets that simple Variance would have some of them ahead rather than behind. In other words, I can appreciate that there are several potential sets of circumstances that would cause many of these visual ballisticians to legitimately believe that they are playing with an advantage, but in reality, that is almost certainly not the case.
Any recorded attempt to prove the efficacy of visual ballistics, at least what few recorded attempts there are, have been plagued by limited sample sizes. Quite frankly, an individual would probably have to make at least one bet, per trial, over thousands of trials to prove that his results were outside of the 99% confidence interval, and it is doubtful that many people out there have either the time or inclination to either attempt to do that or to watch it happen.
Therefore, manual visual ballistics remains nothing more than a theory. However, computer-aided visual ballistics, at least from my perspective, seems rooted in fact.
What we learned from all the information we gathered as well as the research paper cited above is that Roulette is quite likely to be a fundamentally beatable game given that a player is using a computer aide of some kind. However, the degree of beatability is largely predicated upon how much information can be gathered and the gathering of sufficient information to result in a proven advantage based upon trials of a sample size that could be arguably called significant is also not practicable. To wit, no casino is going to enable a player to set up a high-speed camera directly over the Roulette wheel.
However, it remains believable that a computer device that is less capable of acquiring such specific information might gather and analyze enough information in an expedient enough manner as to result in the player having some sort of advantage, as Packer claimed having done with, 'The Eudaemons.' Furthermore, Packer's story is also believable because it was essentially repeated in that research paper, and although they did not seem to care to assure a meaningful sample size of that experiment for the purposes of the paper, it can be argued that Packer was also dealing with less sophisticated Roulette games at the time. For one thing, there may have been less specifics in the way of croupier procedures with respect to the delivery of the spin of the ball. In other words, the game may have simply been more predictable at that time.
BBC News later reported that the trio mentioned earlier:
Would be allowed to keep their winnings from The Ritz and no charges would be filed as nothing illegal had occurred.
While Roulette computers are absolutely illegal in Nevada as well as most, if not all, commercial gambling jurisdictions in the United States, they are not specifically illegal in many European countries and were made illegal in Britain, at one time, and then were made legal with the casinos left to police themselves, and I am not entirely sure of their status now.
My recommendation, if you really wanted to use a Roulette computer, is to make darn sure that you are aware of the laws of the jurisdiction in which you intend to use said computer because, at least to me, no amount of money is worth risking arrest. If you determine that the jurisdiction in question has no problem with computer implements to help you cheat the Roulette table, at least not in a criminal sense, remember that any attempt to use such a device will likely be frowned upon by the casino likely resulting in you being asked to leave...if not worse.
There are also a number of websites that sell such devices, but I am not going to recommend any of them because I have neither the desire nor inclination to purchase one and try it for myself. If you have tried to use any such devices, feel free to report your results in the, 'Comments,' section below. For my part, I suppose the only aspects of the devices I would be really interested in hearing about are detectability and ease of use.
One other thing to keep in mind is that, even if you purchase such a device, even if it can legally used in your jurisdiction, and even if the casino doesn't catch you; you're still going to have to worry about using the device properly if it is one that requires manual input of any kind. If you do not use the device correctly, then my understanding is that you will either receive no prediction at all, or alternatively, the prediction will be wrong.
Personally, I do not have a lot of faith in the efficacy of these devices at all simply due to how little information on them is available out there (at least from reputable sources) as well as the fact that many casinos have done nothing to change their dealing procedures to thwart the use of such devices and/or visual ballistics. If nothing else, the croupier's procedure of allowing the ball to go around the wheel for multiple revolutions, rather than requiring all bets to be made before the ball even enters the wheel, lends itself to my theory that the casino wants some players to think that they are practicing visual ballistics when, in reality, they're just betting a bunch of random numbers on a random result.
Besides that, if there is anyone out there that can both legitimately and legally beat the game of Roulette in brick-and-mortar casinos, I doubt if he would have anything to publicly say about it.