The common belief in the gambling world is related to the roulette wheel bias. Many kokodrilos (big–time gamblers) swear by the wheel in the sky that they make millions by exploiting the roulette wheel bias. There are plenty of legends. The wheels must have been terribly worn out.
I do have some problems and some remarks regarding the bias of the roulette wheel. I have done the most thorough research in this field. My tool of choice is computer software. My roulette software is not only unique, but founded on solid mathematics. I have analyzed both real–life casino roulette spins and random–generated spins. The reports are very much the same. Nobody will ever be able to tell which one is the real spin report and which one is the report on computer–generated roulette spins. The number frequencies are the same. I apply a key parameter in my analysis: the SKIP. The skip represents the number of spins between two hits of the same roulette numbers. Again, the skips are the same for both real–life spins and randomly generated roulette spins. The statistical parameters are in accordance to theory of probability. You will see a statistical report on this page, and another one on a different page.
Wheel bias might occur sometimes. It's hard and costly to check very often every roulette wheel in a casino. Later on this page you will see an event of possible wheel bias I witnessed in a real casino. The data sample was not very large, however.
• The second statistical report I told you about is very interesting. If there is roulette wheel bias, then each roulette number must be followed preponderantly by certain numbers. I call this feature number pairing. It is a common feature that occurs in lottery as well. The pairing is also a feature in computer-generated roulette spins. The roulette pairing is not the result of mechanical bias. It is the result of probability theory, IF the results are compatible with the normal probability rule.
I analyzed 1968 real roulette spins recorded at the Hamburg, Germany casino, February 1 – 6, 2000. File name: HAMB00.DAT freeware from my FTP download site.
The results are categorized by the following parameters, in order:
Table or Wheel (Tisch) – Day (Tag) – Month (Monat) – Year (Jahr).
I downloaded the spins at one roulette table or wheel (#1) for the entire month of January 2006. File name: HAMB0106.WH1; 7990 lines (draws or spins) in text format; the last draw of 31 January 2006 is at the very top of the file (line #1). The file contains roulette numbers (spins) only, one number per line. The casino results files have also other data, such as frequency and various statistics. The files also have dashed lines (----) which probably represent dealer changes at the roulette table.
HAMB0106.WH1 represents the best recording format for roulette: table by table. Do not mix the spins from different roulette wheels in the same file.
I remarked that same-number repeats are far less frequent than different-number pairing. One roulette number is followed by itself slightly less than once in 1000 spins (on average). But the same number is immediately followed by a different number (best pairing) 3 or 4 times in 1000 spins.
One issue concerns the reaction of casinos to this roulette system and strategy. You may be asked not to use pencil and paper at the roulette table. I stress here that the casinos have NO right to prohibit the use of pencil and paper on the premises. Such an act would represent a form of discrimination. Don't let yourself be intimidated. We all have rights under the law. The courts of law are wide open, including to class action suits.
Finally, I advise against the use of these roulette systems in a cyber casino (online). Internet gambling is prone to very serious fraud. Read the Gambling Odds, House Edge, Integrity, Fraud page for details based on observation and logic. Among other types of fraud: The higher your bet, the higher the probability you will lose it!
Roulette Frequency and Skip Chart Number of Spins Simulated: 1000 Roulette Number: 0 • Hits: 29 times • Skips: 48 64 48 19 8 22 49 67 63 14 11 11 * Median Skip: 19 Roulette Number: 1 • Hits: 27 times • Skips: 51 18 0 18 29 36 10 39 91 19 21 83 85 14 48 15 * Median Skip: 29 Roulette Number: 2 • Hits: 28 times • Skips: 86 1 33 0 34 30 35 24 16 76 32 13 1 25 36 1 73 * Median Skip: 32 .... etc. Roulette Number: 37 (00 = double-zero) • Hits: 38 times • Skips: 59 9 17 23 3 13 26 75 10 85 65 14 3 * Median Skip: 15 etc.
In most cases, Handy Brandy wins two times in a row without any of the last four roulette numbers repeating. He goes immediately to another table. He knows that the long run "kills" the casino roulette player more than anything else. After winning at the second table too, Handy Brandy usually cashes out. He runs out of the casino. Sometimes he might try doing the same things at the third table, but never more than winning at three roulette tables. The player will do the same thing the next day at a different casino and again at another casino... Here is illustrative data from the Hamburg casino. The following figures do NOT represent roulette numbers, but SKIPS. The skips, as in the frequency reports above, represent the number of roulette spins between hits.
9 5 57 17 30 18 0 3 13 25 6 0 4 17 2 24 0 4 3 15 13 8 21 2 23 2 6 7 7 10 3 3 17 10 15 11 1 15 3 1 24 11 10 2 3 13 6 12 3 3 24 6 10 21 4 8 9 8 0 20 7 21 7 18 6 0 17 4 13 5 2 6 16 0 2 4 0 7 0 7 1 8
A figure such as 57 represents the skip of a particular roulette number. That particular roulette number (the 3rd most recent in our database) hit after 57 spins. That is, if we look at index 57+3 in our database, we'll find the same number again. Zero in the string above does not represent the 'green 0' (roulette number 0). It means that a particular number hit two spins in row, or hit in two consecutive spins. It couldn't be clearer now. This page has been written by addition, rather than from the ground up. I added instead of editing and rewriting the material from top to bottom. The page also shows my growing in my linguistic English shoes! It is also clear that a force inside fights me from being too clear! No gambler has ever been more generous with his/her secrets than me!
The casino roulette software program SPINS.EXE (also SuperRoulette.EXE) offers the best graphical representation of this free system. Page-down to the end of the frequency report. The system of interest is named Play all roulette numbers except for the last 5 spins. The report also recommends playing immediately following two consecutive misses (indicated by the – sign).
You only play at the points marked 0 (zero). That's when the last number is a repeat from the previous 5 roulette spins. You will play as above the next 3 points where the skip is zero. In many cases, it's after the third win in a row when you can encounter a string like 0 0. When that happens, you will lose 34 * 2 = 68 units. You improve your chances further when you leave after you won at three roulette tables. You should expect to lose once a week.
The maximum gain comes when playing 38 roulette numbers in one spin: 36.3%. Obviously, it makes no sense to play that way because of the house advantage. On the other hand, a so-called wise gambler is more than happy to play one number at a time. What he does is simply losing slowly! Not only that, but losing slowly is accompanied by losing more. That cautious type of gambling is like a placebo. A roulette system such as the Free Roulette System #1 scares most roulette gamblers. "Play 34 or 33 numbers in one shot? I'll have a heart attack!" In reality, the Free Roulette System #1 offers a 28.8% advantage over playing singular numbers in long sessions. In fact, the gain is higher since the bets are placed at optimal moments. That's mathematics, and there is no heart to worry about.
• • Relation of the Birthday Paradox to roulette
The connection between the Birthday Paradox and the game of roulette is extraordinarily appealing to some gamblers. Unfortunately, the appeal has a thin mathematical foundation. The roulette game draws one and only one number at a time. The birthday paradox requires at least two elements. At least two persons in a room..., etc.
If the roulette would draw 10 numbers at a time, the probability would be 72.7% that at least two of the numbers would be equal to one another (i.e. duplicates). But even if the roulette game would consist of 10 spins at a time, the birthday paradox would have nothing to do with predicting the numbers. Some gamblers make the following illogical connection. If I consider 10 roulette spins at a time, in 72.7% of the cases, at least two of the roulette numbers will be repeaters. So, if I play the last 10 numbers, the chance is very good (almost 3 out of 4 cases) that one of the numbers will repeat next! Wow! That would bankrupt every casino on the planet in a few days! If the roulette strategy would hold true, the probability would rise to 99.8% that the next spin will repeat a number from the last 20 roulette spins! Virtually, play the last 20 numbers and win every time. The cost is 20 units, the payout is 36 units, and therefore that roulette player would make a profit of 16 units in every play!
The cold truth is that the famous and appealing Birthday Paradox merely shows the percentage of sets with duplicate elements in the total elements of an exponential set. That's all. So, unsuspecting roulette enthusiasts do NOT rely on the birthday paradox when playing roulette with real money. If you do, don't ask me for a refund later! Mathematically, it is correct to expect that one of the numbers in the last 26 spins will repeat next with a better than 50-50 chance. It is the median skip calculated by the Fundamental Formula of Gambling. Real life roulette spins and randomly generated roulette numbers validate this law — always.
The SuperRoulette.EXE gambling software adds kind of a new system to the Free Roulette System #1. The program adds two more columns to the report. Instead of tracking only the last 5 spins, Roulette.exe tracks also the last 15 spins as displayed on the roulette marquee.
The relation to the Free Roulette System #1. What is the probability that two randomly drawn roulette numbers (spins) will be the same in a group of 5 roulette numbers? It is a Birthday Paradox with 38 birthdays. Instead of 5 persons, we deal with 5 randomly drawn roulette numbers. The probability of at least two collisions (coincidences, or repeats) is: 24%. It's scary for the players of the Free Roulette System #1. Fortunately, the roulette wheel does not draw 5 numbers at a time. The reports of SPINS.EXE show you a more optimistic story. The reports are validated by real-life roulette spins, in a real-life casino. Actually, the analysis of roulette repeats must go much deeper! The roulette probability here refers to chunks of N numbers; e.g. 5 unique roulette numbers versus 5-number groups with at least one repeater...
Months after I published the mathematics of roulette related to the Birthday Paradox, I received negative reports from roulette players around the world. Quite a few casinos decided to turn off the electronic displays (marquees) at the roulette tables. Gamblers say that the decision of casino executives depends on how roulette players stare at the marquees and if the players take notes of the roulette numbers... and especially if they bet big and win big!
I also discovered wide piracy of my mathematical analysis of the Birthday Paradox as a potential roulette system. Even weeks after I published my roulette analysis, there were absolutely no other references on the Internet. Now, there is thousands of roulette systems derived from the Birthday Paradox as I presented it! Beware of other acts of piracy! You can find further information in the roulette resources section of this page.
The Free Roulette System #2 is presented on Web page: James Bond Roulette System in the Taliban Desert.
By the way, if your bankroll is smaller, you can apply this system in 50-spin sessions.
One more tip. It is possible for a two-dozen (two-column) group to hit more than seven times in a row; or, more than seven out of 10 times. If that happens, you rode a very favorable standard deviation tide. Cash out immediately and move to another table!
My message and the system were provoked by an alleged casino top executive.
"I am currently the Chairman of the MGM Grand, and I was advised of this site by way of a memo sent to me."
In a way, the alleged executive's message is an endorsement of my gambling systems. If the systems were not valid, why bother to risk being rear-end kicked by an understandably angered author? I want to stress again that the casinos have no legal grounds for banning record keeping by the players. Record keeping is also a requirement of tax laws. The rules of private entities do not take precedence over the national laws.
That's how the free system #1 came to life as well. I am aware of such tendency now and I believe I have it under control. It will give the player and edge, without a doubt. I have checked for thousands of spins, broken down in 100-spin sessions. There are clearly two situations.
One, the roulette player wins 65 or FEWER spins; it is a losing session. The player counts 100 spins. The player started with 100 chip-units. At the end of the roulette table session, the player counts 61 units. The result was under the standard deviation. Remember to increase the bet the next session.
Two, the player wins 66 or MORE roulette spins; it is a winning session. The player counts 100 spins. The player started with 100 chip-units. At the end of the session, the player counts 69 units. The result was above the standard deviation (calculated for roulette probabilities). Remember to decrease the bet the next session.
The fluctuations in the roulette systems are mathematical, considering the game is totally fair. In an online casino, for instance, the fluctuations go mostly in the favor of the house. The house has to win above the standard deviation — always! Or especially when player's bet is high! That's anything but fairness! This roulette system does not even require strict record keeping. The player can just put aside a chip for each session played, and for each 10-spin roulette groups.
In all honesty, I don't see anything out there that offers better ways to winning at gambling or roulette. I wish there was something easier and more efficient than my approach. Nothing, honestly. IF my casino gambling methodology doesn't win the — there is absolutely nothing to accomplish such daunting tasks. Never will be, if my research has been futile. In the end, it's all about streaks and skips, no matter what the phenomenon is. The skips (misses) are shorter and the streaks are longer if the probability is higher; and vice versa.
The rest of the roulette gambling theory is nothing more than static progression betting and/or clocking the speed of the roulette wheel.
Static progression betting has virtually NO mathematical validity. The number of roulette skips (misses between wins) can be staggering. The winning/losing streaks are dynamic; they flow. It is random, but FFG discerns with various degrees of certainty DC how the streaks move.
Clocking the speed of the roulette wheel is an illusion the myths are made of. NASA sophisticated instruments may be able to measure precisely the speed of the roulette wheel. But NO instrument can predict the landing position of the spinning ball on the roulette wheel. The wheel deflectors randomize the movement regardless of the speed. Of course, it is absolutely impossible for any roulette player to clock the roulette wheel speed precisely, even if the casinos allowed the use of any instruments or computers on the premises.
Not to mention the thorough tests conducted by the manufacturers of roulette wheels. They certainly perform tests regarding the wheel speed and the landing of the spinning roulette ball. They probably run the roulette wheel at exactly the speed v (rotations per minute) for a number of runs R. They note that the roulette ball is landing randomly; i.e. in various positions on the wheel. They change the wheel speed and run another batch of tests. They notice the randomness of the ball landing. It is a strong fact regarding the roulette wheel. The same speed of the roulette wheel leads to highly random landing positions (roulette numbers).
The next number should be FFG-equally distributed between the two wheel hemispheres. That is, the roulette insiders and roulette outsiders should be FFG-equally distributed. I tracked the spins at a roulette table in Atlantic City. To my (belated) dismay, the ratio was 80% to 20% biased towards the outer hemisphere! Actually, two roulette dealers — a woman and a man — shifted at the table during that continuous run! So, it was not a so-called roulette dealer's signature! It was a malfunctioning of the roulette wheel. It is likely that the casinos have no knowledge of such phenomenon. But tracking the landing in the roulette inner hemisphere and the outer hemisphere is pretty hard to accomplish when actually playing roulette in a casino.
Later on, I decided to release free roulette software that works with the roulette wheel sectors and the birthday paradox. Program name: RouletteHemis.EXE; software category 5.5.
Right now, in all honesty, I cannot see any casino roulette gambling system better than mine. That's the only way, like my gambling theory and software do: Track the winning and the losing streaks and their corresponding skips (misses). Apply the Fundamental Formula of Gambling (FFG). There are some no playing moments (or play the minimum bet); other situations demand a higher roulette bet. It is hard work, but nothing else works better. It might not be attractive to the faint at heart or the illusion drinker.
Read Ion Saliu's first book in print: Probability Theory, Live!
~ Founded on valuable mathematical discoveries with a wide range of scientific applications, including probability theory applied to roulette gambling, software, real winning systems.