"You can't calculate probabilities with just algebra. The geometry must be taken into account."
Comte George Buffon, Essay on Moral Arithmetic
CRACKING ROULETTE WITH A DEALER'S RANDOM RELEASE OF THE BALL
This is as close as it can get to the near perfect application of "action at a distance" in gaming. It only requires a dealer's random release of the ball.
Since it is sometimes difficult to find a wheel with a dealer using a random release, experimenters may easily prove these matters with dice or an RNG (see: What's Cracking).
Cracking roulette with true random number generators is discussed in WHATS CRACKING. Let it be noted that RNGs cannot duplicate the geometric probability of another object, including roulette wheels. RNGs have only their own specific geometric probability found through the algorithm that defines them.
These are averages of geometric probability. The Pi-odds Roulette study included just under sixteen hundred trials on 21 different wheels. That was an average of just under 75 trials per session. Half the sessions were successful with a flat bet advantage. Considering the total of all trials, winning and losing, the flat bet advantage overall delivered close to the expected .16666.... .
Until the full scope of geometric probability is uncovered, experimenters should look for and expect similar results with a selection of several sessions on several different wheels. Always first making certain by close inspection that the dealer is releasing the ball randomly.
These are matters of geometric probability. On a 38 pocket roulette wheel, at the third in a series of three random trials with a dealer’s random release of the ball, predict or bet the 5 adjacent pockets on the physically direct opposite side of the wheel from the pocket of the first trial. The five pockets at the third trial are the opposite pole relative to the first trial. This holds the heart of true relativity. It is gravitational and dimensional in nature. This is the basic gravity bet. On a roulette wheel with a dealer's random release, only the third trial is predicted or bet.
This methodology is also the heart of Quantum Mechanics in predicting random particle spin.
The gravity bet has little to do with previous "numbers." In the first instance of randomness, it is not "numbers" on a circle that are gravitationally occurring. The "numbers" on a wheel or game are only reference points that, without relativity, are meaningless by themselves. The truth of randomness is not found in the algebra of a circle or game. It is found only in the relative geometric positions of the circle or game's diameter. It is found only with the methodology of "action at a distance."
Action at a distance is a geometric finesse in which the middle event(s) or measurement(s) are allowed to happen but not predicted or"bet." Geometrically, it is the elimination of the field or object or game's Center of Rotation (COR).
The gravity bet and its prediction concern only relative geometric positions and values that are only found with "action at a distance." This is the "actio in distans" that was suppressed by the Vatican four centuries ago. Action at a distance holds the methodology that was first organized by Isaac Newton in predicting the orbits of comets. This is the "action at a distance" that was the subject of the Laplace/Boskovic debate. This the "action at a distance" that motivated Simon Laplace to instigate the Terror so as to bury it. This is the "action at a distance" that Albert Einstein called "spooky." This is the "action at a distance" that drives Quantum Mechanics and Bell's Theorem.
A dealer's random release of a roulette ball is distinguished from the European or Asian regulated release. The regulated release requires a deeper finesse. The regulated release, and the quadrant and selective releases, are described and explored herein but the heart of these matters are in a dealer's random release.
Let the first random ball land in any pocket. Let it be, for convenience of this explanation, the pocket: “0.” The key to success of these matters --the "action at a distance" in the gravity bet-- is to geometrically structure the prediction or bet to match the geometric structure of gravity's straight line pull on the diameter of that which is being predicted or bet. On an American 38 pocket wheel, the physical "number" or pi-angle pole relative to "0" is "00." The pocket "00" is the "other end" of the straight line across the wheel from pocket "0." Relative to pocket "0", pocket "00" is the relative pi-angle pole.
That which is being randomly measured or bet is the diameter or "pi-angle" of a circle or field or game. All such diameters have three poles: one end, the Center of Rotation (COR), the "other end." It is the "other end" that is predicted or bet. This is the relative pi-angle pole. It is the pole and/or pockets directly opposite the first random event.
The gravity bet succeeds because gravitationally, all that is rotating and being randomly measured in the first instance of randomness, is the single dimension of a diameter (or "pi-angle").
Gravity only pulls in one direction: straight down. When "action at a distance" is used, the gravitational structure is the same in all series of random events. Regardless of the apparent "shape" of the field, game object or game, the geometric nature of gravity's random pull is identical in all instances. It is a straight line pull along the game or game object's diameter or "pi-angle." It is only found with the geometric finesse of "action at a distance." It is only found statistically.
After any random trial, the geometric player waits another turn, letting the second ball land anywhere. Within the concept of "action at a distance," the second event is assumed to reflect the game or wheel or field's COR. This second event must be allowed to physically happen ...but is statistically ignored and not predicted or "bet." It is a default event about which the player does nothing. Eliminating the second measurement is the geometric finesse. This is the methodology at the heart of "action at a distance." This is also the driving gear of Quantum Mechanics and Bell's Theorem.
The third ball is predicted to land in the .16666.... of the wheel that represents the relative "pi-angle" pole. On a 38 pocket wheel, that would be one of the five pockets directly and physically across the wheel from the pocket of the first ball. In this example, and on all 38 pocket American roulette wheels, the pockets directly opposite “0” are: 13, 1, 00, 27, and 10.
It is that simple!
Celebrate! The geometric player has just enacted Quantum Mechanics in a game room!
The five relative opposing pockets on a 38 pocket wheel are a relative dimensional pole. In geometry, it is called a “pi-angle” pole. In the gravity bet, it is also a pi-angle pole/pocket. The five relative pockets most closely represent an even spread of one sixth of the wheel’s 38 pockets. That is: .16666.... of the wheel. It must be noted that 6.33333.... pockets cannot be evenly bet on a 38 pocket wheel. So too, it must be noted that 7 pockets necessarily include a geometrically losing proposition.
The value of .16666.... is the .33333.... geometric probability of one of three rotating diameter poles, factored by the algebraic possibility of two directions, with the geometric certainty of one direction. Without factoring the geometric certainty of one direction, the algebraic possibilities of two directions would be meaningless in this study of geometric probability.
The gravity bet is easily and best played with short sessions at several different wheels. It is absolutely critical that the dealer use a random release. The geometric player will tend to averagely win half of the sessions and lose half of the sessions. In the long run, the player will mathematically enjoy a .16666.... flat bet geometric advantage, less the standard house percentage: .05263.... !
It must be noted that dealers can easily conceal a non-random release so that it appears random.
The "half win/half lose" scenario strongly suggests a natural and automatic "seed" circumstance. The "seed" is not like the "seed" of a Pseudo RNG but rather appears to be an average alternating start between a diameter base ...and a Center of Rotation. If with a "seed" that is a natural diameter base, it would tend to be a flat bet winning scenario. If with a "seed" that is a COR, it would tend to be a series subject to traditional random odds.
The overall net advantage (that is: the .16666.... flat bet geometric advantage less the house percentage): .16666.... - .05263.... = .11403.... .
***GEOMETRIC PLAYERS NEED TO CAREFULLY NOTE THAT KEY PEOPLE IN THE GAMING INDUSTRY ARE KNOWLEDGEABLE OF THE GEOMETRIC FINESSE. REGULAR AND CONSISTENT USE OF A ROULETTE DEALER'S RANDOM RELEASE OF THE BALL MAY SOON BE PAST. IT SHOULD ALSO BE NOTED THAT A CONTROLLED RELEASE IS EASILY DISGUISED AS BEING "RANDOM" WHEN IN FACT IT IS NOT. PLAYERS WISHING TO USE aA VARIATION OF THE GRAVITY BET AT ROULETTE MAY FIND IT MORE APPLICABLE WITH DEALERS USING A REGULATED RELEASE. THIS REQUIRES A DEEPER FINESSE AND IS DISCUSSED BELOW. IT SHOULD ALSO BE NOTED THAT WITH 38 POCKET WHEELS AND LONG TERM PLAY, THE GEOMETRIC AVERAGES MAY TAKE A COUPLE OF THOUSAND TRIALS TO RELIABLY AVERAGE. THESE ARE AVERAGES OF AVERAGES AND ARE FOUND BY AVERAGING THE RESULTS OF SEVERAL SESSIONS ***
Two extensive Roulette studies, using the random release, taken 25 years apart, were compared using the gravity bet.
The “Pi-odds Roulette Study” was taken in the late 1990's. It is the statistical heart of CRACKING PI CRACKING RANDOM. It is a study of 21 roulette wheels from major Las Vegas casinos and one major Indian casino. In Vegas, only major Strip casinos were used. The single critical criterion was whether the dealer was releasing the ball randomly. Each dealer's release was carefully studied for several minutes before being accepted into the study.
The earlier study, “Roulette Statistiks,” was published in two volumes in 1979 and 1980. Each volume contains the trials and outcomes from one wheel, eight hours a day, from morning to late afternoon, for one month. Each volume was recorded in a different casino. The two casinos involved had agreed to provide a dealer whether there were money players at the table or not. The publisher hired a young man to sit and record (he was replaced soon after starting when he was found taking an unscheduled break). The format of each book arranges the outcomes in vertical columns. The columns stretch across each double page. The number of trials and columns for each day varied depending on whether there were money players ...which would slow the play. As well, the number of trials would vary by the differing individual speeds and styles of the various dealers. Each column contains 53 trials. Since each Roulette trial takes approximately one minute, each column roughly approximates one hour of play.
Analysis of "Roulette Statistiks" gives the following unusual results. Using the geometric finesse, only the first column of the first day of the first volume, and the second column of the first day of the first volume, and thereafter, only the second column of each day of the first volume, gives the geometric advantage where it is expected: at the relative pi-angle pole. It comes with near predicted precision to the expected: .16666....!
Unusually, the second column of each day of the second volume delivered a near precise .16666 flat bet advantage at the relative diameter base ...which is that to which the relative pi-angle pole is relative. This would appear to indicate the dealer was releasing the ball directly opposite the last successful pocket.
Early in the study, after this author wrestled hundreds of hours to understand this unusual phenomenon, the only possible explanation in the first volume --that throughout the book only the second column (and the first column of the first day) delivered the expected flat bet advantage-- seemed to be the good possibility there was extra supervision of the dealer during those particular periods. That extra supervision would tend to "keep the dealer honest" and ensure he was releasing randomly. Statistically, it appears that at other times the dealer was not throwing randomly!
This seems reasonable since, during daytime periods when there were fewer players than at night, there would be frequent periods when there would be no players ...and the casino would have no reason to supervise the table. In those circumstances, a dealer could play his own “games” with a release of the ball that was other than random.
When there were no money players at the table, dealers could also have been responsive to the natural question that virtually anyone would opportunely ask when alone with an unsupervised roulette dealer and there was no money at stake: "could the dealer hit a particular number or group of numbers or areas of the wheel?"
It is worth noting that a dealer's ability to successfully hit specific parts of the wheel is reported in a book of roulette by Thomas Bass, "Eudaemonic Pie," Houghten Mifflin, 1985. If this was also the case in "Roulette Statistiks" --wherein the dealer was "playing games" with himself when there were no money players and therefore less supervision-- where did the extra supervision come from during only the second hour of each day if the casino did not provide it or need to provide it since there were likely few or no players during the day, particularly in mid morning?
The mystery was solved with a call to the publisher of "Roulette Statistiks." When asked if she went to the casino during the second hour of each day, stayed around for an hour to supervise, then left, she responded (this was the critical initial breakthrough in this entire study) “No ...my husband did!” He was then recently retired as a senior employee of the casino.
Without this explanation, the probability of the second hour of each day delivering a predictable and near precise .16666.... random flat bet geometric advantage, complete with formula, for 30 days, without the geometric finesse, would be nothing short of giga-astronomical under any theory of randomness!
A true .16666.... flat bet geometric advantage was predicted in both studies, modified by the fact that only 5 pockets were bet rather than 6.33333.... pockets.
The difference may be statistically accounted for.
The difference between 6.33333.... pockets and 5 pockets is: 1.33333.... pockets.
When 1.33333.... pockets are divided by 38 pockets, the quotient is: 1.33333.... / 38 = .0350877.... .
When .16666.... is factored by .03508...., the result is: .03508.... (.16666....) = .00584.... .
When .00584.... is subtracted from .16666.... the answer is: .16081.... . This is the expected flat bet advantage from predicting or betting the 5 pockets comprising a relative pi-angle pole on a 38 pocket Roulette wheel with a dealer's random release of the ball.
The studies delivered a true (paying off at true odds without the house advantage) flat bet advantage of: .16130.... in the Pi-odds study.
The true flat bet advantage in Roulette Statistiks Vol I was: .16235.... .
When the payoff is accounted for with the house advantage of: 2/38 = .0526315...., the expected net results are, from a theoretical .16666 advantage, a geometric advantage: .114035.... .
When 5 pockets are bet, the net expected advantage after the house advantage is accounted: .16081.... - .05263.... = .10818.... .
The Pi-odds Roulette study delivered a net flat bet advantage of: .10018.... .
The net flat bet advantage for Roulette Statistiks was: .10117.... .
CRACKING ROULETTE WITH A DEALER'S REGULATED NON RANDOM RELEASE OF THE BALL
With a non random regulated release, the flat bet advantage is looked for at the fifth random trial at the diameter base. That is, the pole/pocket of the first trial. The most common release other than random is the regulated release. It is widely used throughout Europe and Asia. By law, regulation or custom, this generally requires the dealer to release the ball over the last successful pocket. Since the average "distance" between one random measurement and the next is 1/4 of the circle or wheel (the original Needle's length of relative 1/4 pi) the effect of consistently releasing over the last pocket is similar in effect to retarding the distributor advance of an internal combustion engine by 1/4 of the circle of points. At the fifth retardation, the effect on what would otherwise be random is to return the matter to the beginning point.
TAKE A SAMPLE AND USE A REGRESSION
The most effective way to find the advantage for a particular release protocol is to take several samples of approximately 50 to 100 trials for a particular wheel and track where the advantage is appearing on that wheel. Since these are matters of averages, the process should be repeated on several different wheels. Keep in mind that the Coriolis forces may tend to deposit the ball in a particular relative pocket depending on the manufactured shape of the wheel and frets.
In casino gaming, there are two forces that are generally unique to roulette: Centrifugal and Coriolis.
When randomly and geometrically looked for, Centrifugal force adds a .11111.... flat bet advantage to the basic universal advantage of .16666.... . That is: .16666.... + .11111.... = .27777.... .
The additional .11111.... advantage is the geometric probability of the straight line of a diameter of three poles factored by the algebraic possibility of the three poles squared. This appears to be the tendency towards geometric certainty after three series of three random events, each with the relative pi-angle pole predicted, at the third trial, as a .33333.... geometric probability. It completes the product of 1/3 (that is: the geometric probability of a relative diameter base) and 1/3 (that is: the geometric probability of a relative pi-angle pole).
The middle pole is the COR which is finessed through with the "action at a distance" of the gravity bet.
The product delivers the relative random value of Centrifugal force. That is: 1/3 X 1/3 = 1/9 = .11111 .
The centrifugal advantage is over and above the .16666.... universal flat bet advantage.
The Coriolis force modifies the Centrifugal direction. The Coriolis is not actually a "force" but is rather a factor of rotation, orientation and perception. To a person sitting smack in the middle of a rotating wheel, a ball rolling straight out from the COR would appear to roll in a curve. To a person standing beside the wheel, the same ball would appear to roll straight.
The Coriolis force does not statistically appear in older roulette wheels. This is due to the steep slope of the rotor (the part of a roulette wheel that spins) wherein the ball drops quickly and for only a short a distance. In other words, there isn't much bounce and/or time to bounce before the ball hits a pocket and stops.
However, the Coriolis dramatically appears with the newer "low profile" wheels that were introduced in the late 1970's. With the sides of the rotor almost flat with only a casual slope, they are designed with an intent to allow the ball more time and room to bounce around. This is, in theory, to give more "randomness" to the occasion.
From the statistics herein, using "action at a distance" on a low profile wheel, it is apparent the Coriolis tends to averagely "move" the measurement of a dead center pi-angle pocket of a relative pi-angle pole to one side by the distance of: ...precisely one pocket!
Playing the Centrifugal and Coriolis forces delivers another unique phenomenon. It effectively gives the house an additional pocket. Since only one individual pocket is targeted by the additional straight line of Centrifugal force, and since a house number will tend to averagely appear with the same frequency as any other number, the house effectively enjoys the advantage of an additional pocket as the house pocket enjoys the success of geometric probability as well as its algebraic possibility. That is: 3/38 = .07894.... !
In the Pi-Odds Roulette Study, recorded from new low profile wheels, the Centrifugal force appeared with a true flat bet advantage: .27603.... . Allowing for a house advantage: .07894, that theoretically delivers a net flat bet advantage: .19866.... !
In Roulette Statistiks, recorded from older high profile wheels whereon the Coriolis was limited, the Centrifugal advantage appeared as expected: in the dead center pocket of the relative pi-angle pole. It appeared with a true flat bet advantage: .26666.... . That gives a net advantage: .18276.... !
The results tested in Roulette Statistiks, VOL II, indicate a geometric variation in which a flat bet advantage: .16178.... was found, at the third trial, at the pole/pocket of the relative diameter base! This may possibly be explained by the fact that Las Vegas attracts dealers from all over the world, most of whom are already trained to use a Regulated release of the ball (as is common in Europe and Asia) or a precise geometric version thereof.
The particular casino recorded in "Roulette Statistiks, Vol II," was in a relatively obscure off-strip Las Vegas location. As a working casino, it was never successful and passed through a succession of owners and bankruptcies. It may also have been part of a system that was training foreign dealers for American casinos.
Since virtually all foreign roulette dealers are trained in some version of a Regulated release, the statistical phenomenon in "Roulette Statistiks, Vol II," appears to be from a foreign dealer using a unique geometric variation of a Regulated release. Statistically, from an analytical perspective, that release appears to be a release over the direct opposing pocket (relative pi-angle pocket) from each previous outcome. This would be a variation of the Quadrant release and would perhaps explain why the advantage was .08333.... rather than .16666.... . Since the release protocol is unknown, only future experimentation will show the truth.
Another study of roulette trials of one wheel for one month was published in 1971, “Roulette for the Millions” (O’Neil-Dunne). It contains 20,000 trials and was recorded in Macao. The study used a team of people playing 24/7. The only break was for 15 minutes each morning when the wheel was balanced. A random selection of over ten thousand trials was analyzed using the geometric finesse. The selected trials were the first ten days of the month and the remaining Fridays and Saturdays.
Since, in Macao, a dealer’s release is regulated to be over the last successful number, a deeper finesse is necessary, with a rotational variation to the relative diameter base. This is described in CRACKING PI CRACKING RANDOM. It is carefully noted that O’Neil Dunne reported the wheel was not reversed with each spin. The results gave a flat bet advantage: .09673.... .
Since the relative pi-angle pole is, with near expected precision, to be twice that of the diameter base, it is apparent the various dealers may have been following a consistent release protocol that would shift the pi-angle focus by a pocket. For example, the casino protocol may require the dealer to release the ball with his fingers in a certain position that could cause the randomness of the release to be geometrically shifted by a pocket. This may have shifted the expected results by a pocket.
A book titled “Roulette System Tester” was published in 1995. It contains 15,000 trials from a variety of wheels in several minor off-strip Las Vegas casinos.
With such a wide variety of dealers, there would have been a variety of releases, some Random, some Regulated, some by Quadrants, some by dealer’s Selection. The first edition of “Roulette System Tester” contains numerous errors in which parts of various columns of numbers are erroneously repeated. The publisher has reportedly corrected these errors in a subsequent edition but it is not known if they reflect the original recordings or are patches from a random number generator (which would somewhat skew a geometric finesse unless the patch was known as such and adjusted for). Using the geometric finesse, and allowing for the publishing errors in the first addition (to avoid statistical distortion if the "corrections" in the subsequent edition in fact came from an RNG as generally appears) the results of all 15,000 trials (less the publishing errors) delivers a flat bet advantage of .08623.... directly on the center pocket of the pi-angle pole.
This is remarkably close to the precision (.08333....) of Bell’s Theorem and the Quantum sciences ...which use the same geometric finesse to predict random particle spin.
A study of two wheels, for one day at Casino Baden Baden, also gave predicted geometric results. Like the protocol in “Roulette for the Millions,” the dealer’s release of the ball is Regulated. However, in Baden Baden, the direction of the wheel’s spin is reversed with each trial. The results of almost 400 trials, with the deeper finesse that is required with a regulated release, delivered a flat bet advantage of .15025... ! A variation of the bet, predicting the Coriolis and Centrifugal forces delivered a flat bet advantage of: .34196... ! This huge advantage would almost certainly come down to .16666.... with more trials.
Similar results, with near precision, of .08333.... and .16666.... (depending on how the software program factored direction) have been obtained from some books that publish “Roulette” trials but are actually from random number generators.
Additionally, many studies revealed another unusual geometric phenomenon. A flat bet advantage is nearly always found at both ends of the field or game’s diameter ...but the pi-angle pole tends to be precisely double that of the diameter-base!
The phenomenon of the diameter base (any random outcome) as the first of a series, revisited for prediction with a deeper finesse and delivering a flat bet .08333 advantage, is the result of the diameter base being part of the diameter, but not yet being relative (the relativity of "action at a distance" over three random trials). This give a diameter base a .33333 geometric probability as a diameter pole as well as an algebraic possibility of .25 on the circle.
That is: a diameter-base that is not relative has a mathematical possibility of 1/12 of the circle. That is: 1/3 (1/4) = 1/12.
Since 1/12 of a 38 pocket wheel is just over 3 pockets, that is what delivers the flat bet advantage. At first blush, there is no apparent advantage since 3 pockets are clearly proximate to 1/12 of the wheel. The traditional payoff matches the bet. But the non relative diameter base also contains the geometric probability of the algebraic possibilities of the COR. It is this --the algebraic possibilities of 3 pockets over 4 trials-- that meets the expectations of traditional random theory. However, the diameter base still contains its own geometric probability: .08333.... .
The geometric probability of the non relative diameter base appears also to be the mathematical explanation of "beginner's luck."
Beginner's luck is discussed separately, but in general, it is the natural and automatic geometric probability that is in every series of random outcomes ...but is impossible to find after the third trial without "action at a distance." That is: it is impossible to find without a geometric finesse. The player who arbitrarily and randomly enters a game, is automatically enjoying the effectiveness of a geometric finesse?!
Without "action at a distance," the fourth bet automatically puts the roulette player into an algebraic system of circles, cardinal poles and quadrature. That is, into traditional random theory in which there is no flat bet advantage.
Action at a distance keeps the roulette player in the world of geometric probability and pi-angles ...and able to enjoy a very distinct flat bet geometric advantage.
INTRODUCTION USING A RANDOM NUMBER GENERATOR
With RNG's, the randomness is first filtered through the decimal system defining the algorithm. That's enough to retard the natural advance of randomness. The randomness of an RNG is only "random" relative to our mathematical perceptions. It is not relative to gravity in the first instance.
Since not everyone has ready access to a roulette wheel, the dynamic results of the gravity bet may be seen using a random number generator. There are two basic types of RNGs: true and pseudo. Foremost, and the subject of this study, are "true" random number generators. The true RNG's can derive their numbers from several different random sources, from atmospheric noise to radioactive decay to the grey scales of a photograph and other such random sources. The depth of finesse appears to depends on the algorithm. See: What's Cracking.
Pseudo RNGs derive their numbers from a programmed algorithm that starts with a selected seed. The numbers from a pseudo are therefore not actually random. For most practical superficial purposes, they initially appear statistically similar to numbers from a true RNG. However, when the algorithm starts to repeat itself the apparent "randomness" is lost. Since pseudo RNG's are not truly random, they are not part of this study.