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START HERE PART 1 START HERE PART 2 A PROOF OF STRING
On a 38 pocket Roulette wheel, at the third in a series of three random trials, with a dealer’s r andom release of the ball, predict the 5 adjacent pockets on the physically direct opposite side of the wheel from the pocket of the first trial. This is the basic gravi ty bet. Only the third trial is predicted o r bet. A dealer's random release of a Roulette ba ll is distinguished from the European or Asian Regulated release which requires a deeper finesse. The Regulated release, and the Quadrant and Selective releases, are described and explor ed in CRACKING PI CRACKING RANDOM.
THEORY: PI AND
MECHANICS q
Let the first random ball land in any pocket. Let it be, for convenience of this explanation, the pocket “0” .
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AUTHOR BUFFON NEEDLE PROBLEM q CENTER OF ROTATION q CRACKING ROULETTE q CROP CIRCLE OF PI q DECONSTRUCTING PI q q
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DIGITS OF 1/2 PI
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DIGITS OF 1/4 PI
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DIGITS OF 1/6 PI
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DIGITS OF PI
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FROM LOVERS TO
The geometric player waits another turn, letting the second ball land anywhere. It is assumed to be the game or wheel or field's Center of Rotation (COR). This second event is ignored. It is a "default" event about which the player does nothing. The third ball is predicted to land in 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.
TERRORISTS AND BEYOND q
GETTING STARTED WITH
THE GEOMETRIC FINESSE q
GETTING STARTED WITH
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GETTING STARTED WITH
GEOMETRIC PROBABILITY q
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 . That is: 1/6 pi.
GETTING STARTED WITH
MONTE CARLO METHODOLOGY q
The five relative opposing pockets on a 38 pocket wheel are a relative dimensional pole. In geometry, it is calle d a “pi-angle” pole. This is the gravity gravity bet.
GETTING STARTED WITH
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. This is the reason only five pockets comprise the relative pi-angle pole of a 38 pocket wheel.
PERCEPTION q
GETTING STARTED WITH
RANDOM NUMBER GENERATORS q
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RANDOMNESS q
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RELATIVITY q
GETTING STARTED WITH
SPOOKY ACTION AT A
DISTANCE q
GETTING STARTED WITH
THE GRAVITY BET q
QUANTIFYING
BEGINNERS LUCK q TAKING DOWN THE STOCK MARKET q
THE PARADOX OF A
FOUR POCKET ROULETTE WHEEL
The value of .16666 is the .33333 geometric probability of one of three rotating diameter poles factored by the algebraic possibility of two directions. The gravity bet is easily and best played with short sessions at several different wheels. The geometric player will tend to averagely win half of the sessions and lose half of the sessions. In the long run, the geometric player will tend to mathematically mathematically enjoy a .16666 flat-bet geometric advantage, less the standard house percentage of: .05263...! That net advantage is: .16666 - .05263 = .11403.... . ***GEOMETRIC PLAYERS NEED TO CAREFULLY NOTE THAT THE CASINO INDUSTRY IS KNOWLEDGEABLE OF THE GEOMETRIC FINESSE. THERE IS A HIGH PROBABILITY THAT REGULAR AND CONSISTENT USE OF A ROULETTE DEALER'S RANDOM RELEASE OF THE BALL IS GENERALLY A THING OF THE PAST. IT SHOULD ALSO BE NOTED A CONTROLLED RELEASE IS EASILY DISGUISED AS BEING "RANDOM" WHEN IN FACT IT IS NOT. PLAYERS WISHING TO USE THE GRAVITY BET AT ROULETTE WILL FIND IT MORE APPLICABLE WITH DEALERS USING A
REGULATED RELEASE. THIS REQUIRES A DEEPER FINESSE AND IS DISCUSSED IN CRACKING PI CRACKING RANDOM. IT SHOULD ALSO BE NOTED THAT ON ONE WHEEL, THE GEOMETRIC G EOMETRIC AVERAGES MAY TAKE A COUPLE OF THOUSAND TRIALS TO RELIABLY AVERAGE***
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WHEELS HAVE NO
MEMORY BUT DIAMETERS
Two extensive Roulette studies, using the random release, taken 25 years apart, were compared using the gravity bet.
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The “Pi-odds Roulette Study” was taken in the late 1990's. It is the statistical heart of CRACKING PI CRACKING RANDOM and appears in the Appendix. It is a study of 21 Roulette wheels from both Las Vegas and Indian Casinos. The only criterion was whether the dealer was releasing the ball randomly.
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The earlier study was published in 1979, in a two volume set, “Roulette Statistiks.” 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 casinos 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 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 at takes approximately one minute, each column represents approximately 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 co lumn of each day of the first volume, gives the geo metric advantage. It comes with near predicted precision: .16666! Early in the study, after the author of CRACKING PI CRACKING RANDOM wrestled, over hundreds of hours, to understand this unusual phenomenon, the only possible explanati on seemed to be there was extra supervision of the dealer during those periods. Statistically, it appears that at other times the dealer was not throwing randomly! This seems reasonable because, durin g daytime periods when there are inevitably 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 “ga mes” with a release of the ball that was other than random. 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 o f 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, but not explored extensively, in a book of Roulette by Thomas Bass: "Eudaemonic Pie," Houghten Mifflin, 1985.] If this was the case, 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? 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 “No ...my husband did!” He was then retired but had been 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, for 30 days, without the geometric finesse, is 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 is not significant from a practical standpoint but 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 .0350877 the result is: .0350877 (.16666) = .0058479.... . When .0058479 is subtracted from .16666 the answer is: .1608187.... . This is the expected flat-bet advantage from predicting or betting the 5 pockets comprising a relative piangle pole on a 38 pocket Roulette wheel with a dealer's random rel ease 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 i n 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, for a geometric advantage of .16666 pockets: .114035.... . When 5 pockets are bet, the net expected advantage after the house advantage is accounted is: .1608187 - .0526315 = .1081872.... . The Pi-odds Roulette study delivered a net flat bet advantage of: .10018.... . The net flat bet advantage for Roulette Statistiks was: .10117.... . GETTING FORCEFUL There are two forces that are 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 with the relative pi-angle pole predicted, at the third trial, as a .33333 geometric probability. This 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). Since the middl e pole is the COR which is finessed through, the product delivers the random value of Centrifugal force on a randomly measured diameter, measured with "action at a distance." 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 ball's 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 curve. To a person standing beside the wheel, the same ball would appear to roll in a straight line. The Coriolis force does not statistically appear in older Roulette wheels with a steep slope to the rotor (the part of a Roulette wheel that spins). This is because the ball drops so quickly and for only a short a distance. However, the Coriolis dramatically appears with the newer "low profile" wheels that were introduced in the late 1970's and early 80's. They are designed to allow the ball more time to bounce around. In low profile wheels, the Coriolis averagely "moves" the dead center pi-angle pocket of the pi-angle pole to one side by the distance of precisely one pocket. Predicting the Centrifugal and Coriolis forces delivers another unique phenomenon. Since only one particular pocket is targeted by the additional straight line of Centrifugal force, the house effectively enjoys the advantage of an additional pocket as each house pocket averagely appears in turn. That is 3/38 = .07894.... ! In the Pi-Odds Roulette Study, the Centrifugal force appeared with a true flat bet advantage of .27603.... . Allowing for a house advantage of .07894 , that delivered a net advanta ge of: .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 of: .26666 and a net advantage of: .18276 .... ! The results tested in Roulette Statistiks, VOL II, indicate a geometric variation in which a flat bet advantage of .16178.... was found, at the thir d trial, at the pole/pocket of the relative d iameter base! This may be explained by the fact that Las Vegas attracts ambitious 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 STATISTKS, VOL II, is in a relatively obscure off-strip La s Vegas location. It has never been gene rally successful and has passed through a succession of owners and bankruptcies. It may also have, by intent or not, been part an American training experience for foreign dealers. 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. From an analytical perspective, that release appears to be regulated over the opposing pocket (relative pi-angle pole) from each previous outcome (diameter-base). 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 fi nesse 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 of: .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 were probably following a consistent release protocol that would shift the pi-angle focus by a pocket (such as a requirement that a dealer spin the wheel and carefully release the ball with his fingers in a certain position relative to the release pocket). A book titled “Roulette System Tester” was published in 1995. It contains 15,000 trials from a variety of wheels, generally from several 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 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, 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 al most 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 (see below) delivered a flat bet advantage of: .34196... ! Similar results, with near precision, of .08333 and .16666 (depending on how the software program factored direction) have been obtained from books that publish “Roulette” trials but are actually from random number generators. Additionally, all of these 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 (the first of a series) delivering a flat-bet .08333 advantage is the result of the diameter base being pa rt of the diameter, but not yet relative (the relati vity 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 is clearly 1/12 of the wheel and 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 po ssibilities of the 3
pockets-- that meet traditional expectations. The diameter base still contains its own geometric probability of .08333 . That geometric probability of the non relative diameter base appears to be have of the mathematical explanation of "beginner's luck" (side link: QUANTIFYING BEGINNER'S LUCK).
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