"You can't calculate probabilities with just algebra. The geometry must be taken into account."
Comte George Buffon, Essay on Moral Arithmetic
* PI See: "Exploring Random."
* BEGINNER'S LUCK See below.
* ORIGINAL BUFFON NEEDLE PROBLEM See: "Exploring Random."
* ACTION AT A DISTANCE See: "Exploring Random."
* ROULETTE See: "Exploring Random."
* RELATIVITY See below.
* DICE See below.
* CARDS See below.
* RANDOM NUMBER GENERATORS See below.
* RANDOM PSYCHOLOGY See below.
* RANDOM STOCK MARKET See below.
NOTE: THERE IS AN ALGORITHM FOR INPUTTING ANYTHING RANDOM
Beginner's luck occurs automatically within the first three predictions or "bets" of a random entry into a random series. It is the natural outcome of a player naturally and necessarily (however unwittingly) placing initial bets on one of three diameter (or "pi-angle") poles.
As discussed throughout, all that is "rotating" in any random series of anything are the three poles of a diameter. Therefore, the third pole will necessarily tend to be a .33333.... geometric probability within the first three trials. Whenever the third pole occurs (which it must) in the first three random trials, predictions or "bets" ...traditional random theory expects and pays off as though it was a quadrant pole with a .25 possibility.
Beginner's luck ends if a fourth bet (and each successive bet) is made without the geometric finesse.
Gravity only pulls on one dimension: the straight line diameter of any randomly measured field, object or game. Dimensionally, relative to gravity, the three poles of a diameter are all that is rotating with any random series of anything. Therefore, the relative third pole of a diameter must be --and is-- a .33333.... geometric probability.
That percentage is lost and replaced with traditional random theory if the fourth bet and successive bets are not made with the finesse methodology of "action at a distance." This is so since, in any random series without the geometric finesse, the middle pole statistically appears once for each appearance of an end pole. Therefore, without the finesse methodology, each end pole is a .25 algebraic possibility. This is quadrature.
The "gravity bet" is what this site is all about. It is a prediction or "bet" that is made with a geometric finesse ...over and over and over and over and over, etc.. This is what delivers the flat bet advantage.
The gravity bet is simply an organized form of beginner's luck ...over and over and over and over and over, etc..
Relativity refers to a random event being connected to, or the result of, another or prior event when it appears there should be no such connection. The random, gravitational, geometric truth of relativity is only found with the geometric finesse of "action at a distance."
The mathematical truth that supports the geometric probability is found with the original Needle Problem.
Relativity, along with "action at a distance" and the original Buffon Needle Problem, were all lost in the French Revolution.
Albert Einstein didn't believe in "action at a distance." He called it "spooky action at a distance." More and more physicists are coming to realize that, gravitationally, randomly and geometrically, in the face of "action at a distance," Einstein's theory of relativity is only algebra that is geometrically meaningless relative to random gravity. It only has meaning in a context of life's perceptions.
Modernly, true relativity is only found with quantum theory (and the pi-odds of Cracking Pi Cracking Random). It is demonstrated and proven with Bell's Theorem. Priorly, it was only found with Newton's use of the geometric finesse to predict the random orbit of comets. As well, with Rudjer Boskovic's use of the same work by Newton to predict the random orbits of comets.
True relativity is geometric in nature and always and only found on or along a randomly measured field, object or game's diameter. Every series of random events or measurements are always on the diameter of the field or object or game. Every diameter has three poles. The relativity connection is found with a series of random measurements using a geometric finesse to eliminate the middle pole from statistical consideration. The disregard of the Center of Rotation (the middle pole) allows the third pole to be found relative to the first randomly measured pole. The middle --or second-- pole must be allowed to happen, but is then disregarded from statistical consideration.
The confusion over the statistical truth of relativity is the result of human perception. Or "mis-perception" as the case may be. The eternal confusion is with the appearance of a randomly measured 3 pole diameter statistically appearing as a 4 pole circle or "game" when it is measured with Monte Carlo methodology without the geometric finesse.
Monte Carlo methodology was introduced by the original Needle when it introduced relativity with its first random proof of pi. Simply put, Monte Carlo methodology takes and considers every measurement or event in a series of random measurements or events. With traditional Monte Carlo, there is no geometric finesse. The results of Monte Carlo without the geometric finesse always delivers traditional random theory. There is no meaningful relativity in traditional random theory. Everything is, Like Einstein's theory, equally relative.
Gravitationally, every random event is on the diameter of every field object or game. every diameter has three poles: one end, the Center of Rotation, the "other end." However, using Monte Carlo without the geometric finesse leaves every series of random events on a 3 pole diameter always statistically appearing as though on a circle of 4 poles (as described elsewhere in this site).
Monte Carlo methodology without the geometric finesse of "action at a distance" makes geometric relativity statistically impossible.
Relativity is finding the random statistical connection between the end poles of a 3 pole diameter. That relativity connection is the third pole (the "other end") appearing as a .33333.... geometric probability relative to the first pole.
It is the middle pole --the Center of Rotation (COR)-- that causes the mathematical confusion.
The Center of Rotation is the "game." The game is a circle. Since a circle is only the end points of radii extending from the Center of Rotation, the Center of Rotation is also the circle of the "game." Since a circle is pi, therefore the COR is also pi. This is a deduction from the original Needle.
The lock on the door to relativity is the original Buffon Needle Problem's universal random average: 1/4 C.
By the deductive and inferential proof of the original Needle, the average distance around a circle between one random event and the next is 1/4 of the rotating or randomly measured circle. That is, 1/4 C. That is a quadrant. However, that is also just algebra since it is just a mathematical average. Since an average is just a perception ...it may fairly be said that, relative to the geometric randomness of gravity, we and our perceptions and measurements and statistics are also just relative pi in rotation.
Any ascribed activity of a random event on a circle or game is, relative to the random geometry of the circle or game ...meaningless in regards to its relativity. It is already part of the circle or game.
Here come the home fires of relativity.... .
Matters start with the original Needle. All true random relativity is in a world of pi that was stoked by the original Needle.
The average of 1/4 C is meaningless relative to the circle. However, it takes on a meaningful context of relativity when it is mathematically understood as also relative 1/4 pi, relative to the circle's diameter. This was the proof of the original Needle. This is the mathematical foundation of true relativity. It is an average --identified on the circle of our perceptions that is randomly described by gravity as relative to gravity's straight line pull along the diameter of a field or object or circle or game.
The original Needle proves 1/4 C is also 1/4 pi. While 1/4 pi is also the mathematical average distance around a circle between one random measurement and the next, it is also a percentage of the diameter. Since it is on the circle ...but is a percentage of the unseen diameter ...it may be identified as relative to the diameter. It may fairly be said that the original Needle was also the first mathematical proof of relativity.
Algebraically, a random average is just a mathematical perception of 1/4 C as the average distance between one random measurement and the next on a circle ("C"). This fits our perceptions as well as traditional random theory.
However, geometrically, relative to a diameter through relative 1/4 pi, the average distance between random events is a radius of the diameter.
The confusion of traditional random theory and its apparent lock on randomness is found and bound with the COR. The key to relativity and the flat bet advantage is uncovered with how the COR is treated. It must be eliminated from consideration since it is just a mathematical perception. It is our common perception. Eliminating the COR is effectively eliminating ourselves and our perceptions from s series of random measurements ...and that is exactly what science wants.
Relative to the circle, the COR of the diameter randomly appears once for every random appearance of an end pole.
The "end poles" hold the random geometry of the diameter. Geometrically, one end pole s a diameter base. Geometrically, the other end pole is the relative pi-angle pole. Between the two end poles is the COR. The COR is and holds the algebra of the "game."
The geometric values of relativity cannot statistically appear when Monte Carlo methodology is used without the geometric finesse inherent in "action at a distance."
Let the end poles be called North and South. Let it be given that, gravitationally, every series of random events is on a 3 pole diameter. It is completely irrelevant how many possibilities define the game. Let there be any number of "pockets" on a roulette wheel ...its diameter still has only three poles.
There is only one diameter from wherever it is randomly measured. Every random event of any kind whatsoever is on a diameter.
Let the first of a random series land in South.
If Monte Carlo methodology is used without the geometric finesse of "action at a distance," the averages tend to look like this: S, COR, N, COR, S, COR, N, COR, S, COR, N, COR, etc.. .
Each end pole has a statistical appearance of .25 . This is quadrature. This is traditional random theory. This may be demonstrated and proven by predicting or betting one unit each time for each random event.
The geometric finesse of "action at a distance" eliminates the COR from statistical consideration. It does this by allowing, but not predicting or "betting," the second of three measurements or events. This changes a long series of algebraically equal averages into several shorter series of geometric probabilities of three events each on a diameter of three poles. The geometric finesse eliminates the COR from consideration. With the geometric finesse, the geometric averages tend to statistically look like this: S, COR, N; S, COR, N; S, COR, N; S, COR, N; etc..
With the geometric finesse, the relative end pole North (the relative "other end") appears as a .33333.... geometric probability. This is automatically factored by the possibility of one of two random directions. This is true relativity. It statistically appears when, by all appearances and traditional expectations ...it shouldn't.
The appearance of a relative end pole is always at the position of relative 1/2 pi. As discussed elsewhere in this site, the end pole and its flat bet advantage is also statistically evident as 1/6 pi.
This is the relativity resulting from "action at a distance." The geometric probability of the third diameter pole appearing as the third diameter pole comes from the geometric finesse of "action at a distance." Otherwise, without the geometric finesse, the 3rd pole will statistically appears as the fourth quadrant pole on a circle. With the geometric finesse, there is a statistical connection when, by our perceptions and traditional random theory ...there should be none. This geometric appearance of the third pole on a diameter statistically appearing as the third pole on a diameter ...is true relativity.
By all appearances and traditional expectations, the third pole of a diameter should appear as a the 4th pole of a circle. As the fourth poles on a circle, there is no meaningful relativity since the 4th pole of a circle is already part of a circle of four poles.
True relativity takes form as the unexpected 3rd pole on a diameter is delivered as a .33333... geometric probability ...but is expected and "pays off" under traditional random expectations and theory as a .25 algebraic possibility!
The result is a .08333.... flat bet advantage. This is the methodology and flat bet advantage of Quantum Mechanics in predicting random particle spin. This is geometric probability. The geometry is factored by the algebra of the random possibility of two directions.
That unexpected statistical appearance of 1/2 pi (or 1/6 pi) is the demonstration of true relativity.
As discussed in Deconstructing Pi, relativity and the flat bet advantage are also found --with predictable precision-- between the relative digits of 1/4 pi and 1/2 pi (as well as between 1/4 pi and 1/6 pi).
That unexpected geometric connection defines true relativity.
Dice cubes are the easiest physical objects readily at hand to demonstrate the .16666.... flat bet advantage and the relativity of 1/2 pi.
This is not an effort to play or beat "craps." For the purposes of this study, only the outcomes of each single cube is considered. When testing, it is convenient to throw two or three cubes at a time in order build a data base. Each cube should be with different color or identification mark. The results of each cube should be recorded separately. The bottom line results should then be statistically averaged together.
If ordinary game cubes are used, it may be assumed they are unbalanced with one radius/facet of each delivering a decided preference. For this reason, at least half a dozen such common dice (each identifiably different) should be used. Ordinary game cubes will almost certainly not deliver the full .16666.... advantage. However, there should still be a lesser but significant advantage.
Casino quality cubes are obviously the best preference. If casino cubes are not readily available, they can be ordered online.
A good home throwing pit can be organized with stacks of books forming a "U" or "Y" shape. For most people, it is not difficult to handle and throw three cubes at a time.
Two protocols are critical: 1) handling the cubes 2) throwing the cubes.
1) HANDLING THE CUBE(s). Between each throw, the cubes should be picked up exactly as they landed and not turned or tumbled in any manner whatsoever. This is because the cube doesn't know if it is being tumbled randomly for the record or just accidentally. Any kind of turning or tumbling between throws destroys the continuity of geometric probability for that series and for which the entire effort is straining.
2) THROWING THE CUBE(s). They should be thrown randomly, with force, with intent to hit at least two of the uneven sides of the pit. This assurance of randomness is double the criteria of a casino which only requires their cubes to hit one uneven surface.
The .16666.... flat bet advantage is found at the relative pi-angle pole at each 13th (thirteenth) trial.That is, throw the cube, record the number and count that as the first throw. Then throw 12 more times. The last throw will be the 13th. It will tend to be the opposite side of the cube from the first throw.
This succeeds since, with the extended foundation finesse of "action at a distance, only the geometry of a diameter of three poles is being thrown each time. The middle pole remains the COR. The intermediate throws represent the cubical structure of the COR. On a cube, the structure of the object is in three dimensions while the "game" remains in two dimensions (a roulette wheel of two dimensions and six pockets would give the same algebraic results). The additional cross diameter through the COR, with the additional random factor of tumble, delivers the relative pi-angle pole at the 12th relative throw after the first.
The multiple throws are necessary to eliminate the complex structure of the COR from consideration. That is: six facets factored by two tumbles each ...or ...four cross diameter end poles factored by the tumble of three dimensions.
The factor of non replacement leads to an algebraic discussion outside this study. It is enough that the fifth card off the top of a well shuffled single deck will tend to be predictable as one of two cards as follows. If the first card is an ace, the fifth card will tend to be predictable as either a 4 or J. If the first card is a 2, the fifth card will tend to be predictable as a 5 or Q. If the first card is a 3, the fifth card will tend to be predictable as a 6 or K, etc..
The A - 4,J (and 2 - 5,Q, and 3 - 6,K, etc.) relationship will also tend to not appear at each 9th trial.
There are, of course, other geometric advantages with cards.
RANDOM NUMBER GENERATORS
There are two fundamentally different types of random number generators (RNGs). Each is driven by an algorithm through which the input/output is filtered.
True RNGs may receive their input from a variety of sources. Two popular sources are random radio waves from outer space and random radioactive decay from earth materials. The quantum RNG tested herein fires light photons at a semi transparent mirror. Half go through, half are reflected. From the random "1/0" results, random numbers are obtained.
Pseudo RNGs receive their input from a non random "seed" number around which the subsequent numbers occur. Pseudo RNGs are not random. There is a reason they are called pseudo. They have an initial appearance of randomness which is then lost as the algorithm repeats itself over and over. This is study is not concerned with pseudo randomness.
This True RNG uses light photons. It is advertised as a Quantum Random Number Generator and promoted as one of the most secure and reliable RNGs. The field used was a random series of thirty-six numbers (0 - 35). There were two sets of 16 sessions each. Each session consisted of 108 original one time numbers from the quantum RNG. Each session flat bet 108 trials with a geometric finesse. There were a total of 3,456 trials.
One predictable point of relativity delivered a flat bet advantage: .06875.... . This is closely proximate to the .08333.... flat bet advantage of Quantum Mechanics.
Another another point delivered a flat bet advantage: .29452.... . This is closely proximate to the .27777.... flat bet advantage of the gravity bet plus the additional flat bet advantage (.11111....) of centrifugal force (of the light photons).
A third point delivered a flat bet advantage: .24005.... .
Each point of geometric probability was flat bet separately over the 3,456 trials. That was an effective total over 10,000 trials.
There are other points of probability and flat bet advantage. These are enough for an introduction.
Details to follow soon
Two separate studies of psychology have each delivered fascinating results. The first concerns anti social behavior. The second concerns the stock market.
ANTI SOCIAL BEHAVIOR:
There is a stretch of highway that is properly signed "DAYLIGHT HEADLIGHTS ON." For many years it was never enforced. It was mainly used by commuters from a nearby town and everyone knew the LIGHTS ON requirement was never enforced. Over a two week period tests were done up and down a ten mile stretch during fairly busy hours. A note was made of whether each approaching car had its headlights on or off. The question was simple. What percentage of people did not follow the social contract without the pressure of enforcement?
The answer was riveting. The percentage was very close to 1 - pi!!! More specifically, 1 - 3.19!!
This simple result appears to follow the simple fundamental nature of the human family. That is, regardless of youthful tendencies, people (parents) tend to be more conservative as they age while their two (+) average children tend to separately follow conservatism by one and rebellion by the other. That is: 1 - 3 (+).
It is worth noting about two years after the study, when the state decided to enforce the "DAYLIGHT HEADLIGHTS ON" requirement, there was a front page notice to that effect in the local paper.
Several years ago, a five week study of the stock market undertook to theoretically buy and sell the "12 Most Active Stocks" featured daily in the Wall Street Journal. The market was fairly steady at the time. They were bought or sold as frequently as possible at a specific time and day relative to a previous specific time and day. The intrinsic value of each stock was not considered. The geometric finesse of "action at a distance" was used. The simple question was whether the stock would go up or down. A .16666.... flat bet advantage was looked for. A .145.... flat bet advantage was found.
There is an algorithm to computerize. It is mentioned here as an example of mass psychology.
A few years ago, there was some evidence that this study had been hacked by a major Wall Street Firm. There is also some evidence that the fall of the Greek market on Black Monday, 2011, was perhaps the result of a reckless effort to apply the gravity bet on a large scale.
When all players are informed with an even chance, using the gravity bet on the stock market is going to level the playing field.
It is worth noting (again and again) that a computer simulation of the stock market only reflects the quadrature of the computer's algorithm. It will also reflect the algebra and quadrature of the stock market. A computer cannot duplicate the geometric probability of the stock market. A computer can only process the data put into it. If the computer isn't programmed to properly use the geometric finesse, the output will only be more algebra.
Recently, Wall St. investment firms are looking to quantum computers for their incredible speed in transmitting data. The use of the light photon quantum experiment is being experimented with and considered. It is mind numbing that these major companies are completely missing what quantum science is all about in the first instance: a flat bet advantage!
As discussed above, the light photon random number number generator has been cracked with the geometric probability of a .27777.... flat bet advantage. As noted again this is only applicable to the algorithm of the RNG.
The stock market has its own geometric probability and flat bet advantage regardless of what RNG is used to analyze it.
It is ironic that Wall Street is looking at quantum science methodology for speedily getting data almost as fast as light ...while completely missing the far more salient fact that the quantum methodology holds the means of delivering far more meaningful data (complete with a flat bet advantage) faster than light and without the slowing intermediary of the quantum experiment itself.
"You can't calculate probabilities with just algebra. The geometry must be taken into account."
Comte George Buffon, Essay on Moral Arithmetic
INTRODUCTION TO CRACKING PI CRACKING RANDOM
Here is a grail to predict the outcome of any random series of anything. It appears with the solution of five deeply interconnected mysteries spread over 4 centuries: Pi, randomness, "action at a distance", the French Revolution's Terror, and the "hidden variables" of Quantum Mechanics. Recovered as well is the original Buffon Needle Problem.
It may be fairly said the world's technology is four centuries behind in development.
The mystery of the Terror is now exposed as a ruthless mass slaughter that was intended to effectively conceal the original Buffon Needle Problem and its proof of pi. Buried as well was the original Needle's natural extension: "action at a distance."
The Vatican must take responsibility for initiating the problem four centuries ago by suppressing the concept of "action at a distance" (actio in distans).
Simon Laplace, who falsely and knowingly bragged himself as the "greatest mathematician in France," must be assigned responsibility for effectively continuing the Vatican's suppression, although for his own reasons. Laplace was a mathematical fraud who initiated the Terror with the motive of protecting his undeserved reputation. He did so with tactics that ultimately and specifically inspired Adolph Hitler and the Nazi regime.
This grail is a flat bet (same amount or measurement taken each time) .16666.... advantage over traditional theories of random expectation. Many applications may be fine tuned with an additional .11111.... from centrifugal force. Relative to traditional random theory, the advantage only makes mathematical sense in the world of pi.
The advantage is found as a geometric probability that dramatically contrasts with the algebraic possibilities of traditional random theory. It appears with the unification of two long lost geometries: the original Buffon Needle Problem and "action at a distance."
These matters solidly belong in the actuarial sciences. There has been exhaustive testing, with 100% success, with gaming and random number generators. Other subjects have been lightly tested, with the partial coin exception noted below, with 100% success. The subjects range from the stock market to psychology to biological and geological distributions. Anyone may easily find and prove the advantage at home with dice, cards or a true random number generator (see: What's Cracking).
Waiting in the wings are studies in the dynamic applications to such varied random matters as weather, terrorism, relationships, inventory controls, and sports.
No word in the world's languages is more misused than "probability." Modernly, true "probability" only exists in the quantum sciences. It is only found with the use of the geometric finesse within "action at a distance." In a series of random measurements, the "finesse" is an omission of the middle measurement(s) from statistical consideration. The finesse is through the object, field or game's Center of Rotation (COR). This is the methodology of Quantum Mechanics.
Relative to the geometric randomness of gravity, all other applications of the word "probability" are actually the algebra of possibility. Traditional random expectations and theory are based only on the algebra of possibilities. Relative to gravity, the algebra of traditional random theory is only the equal possibility of one of two directions.
The difference is between the randomness of geometric probability that gravity always delivers on one dimension ...and life's inherent perception of randomness delivered on two or more dimensions.
Within the "possibilities" found on two or more dimensions, such as a circle or any other shape, is the randomness of our common perceptions and traditional random theory.
By the proof of the original Needle, everything that is not geometric probability or the randomness of two directions is --paradoxically including two possible directions-- just pi.
Geometric probabilities are what gravity delivers in the single dimension of gravity's straight line pull along the pi-angle (or "diameter") of any randomly measured field, object or game. From any single measurement of gravity, there is only a straight line pull. The appearance of gravity as a warped field is only the result of several measurements in an ever changing field.
Such probabilities and the flat bet advantage are only found statistically and only with a geometric finesse.
The so called "probabilities" offered by the casino industry and traditional random theory are actually only algebraic possibilities. Their roots are based on the mathematical fraud executed by Simon Laplace in the early 19th century. Laplace also controlled the curriculum of the world's first state run system of modern education. disastrously, it has continued to serve as a model into the 21st century. By Laplace's intent, it does not contain geometric probability. Laplace's malicious conduct is discussed in depth in the history section of this site.
These matters are 8th grade simple concerning the geometry. They are 5th grade simple concerning the algebra.
Question: If the Vatican found "action at a distance" so threatening that it suppressed the concept ...and if it was so important that it was the subject of the longest debate in the history of the Paris Academy of Sciences ...why aren't we studying it today?
Question: If the simple original Buffon Needle Problem provides the geometric matrix for "action at a distance" ...and if the Needle is so powerful that physicists had to throw it to determine the geometric probability of random neutron collision when they built the first atomic reactor ...why aren't we studying it today?
These matters are dimensional in nature. On one hand, we perceive randomness delivered in two or more dimensions. This perception may be idealized by a circle of two dimensions: diameter and cross-diameter. The end poles of the two dimensions are the four quadrant poles often referred to as: North, South, East and West. Each pole is a random .25 possibility. This is quadrature. It is the foundation of traditional random theory. It is completely irrelevant how many possibilities are on the circle (or pockets on a wheel). There are still only two dimensions and 4 poles.
The methodology of "action at a distance" mathematically separates gravity from perception. Gravity forever delivers its random events on one dimension only: the diameter of any randomly measured field, object or game. A diameter has 3 poles: one end, the Center of Rotation, the "other end." The third pole (the relative "other end") on a three pole diameter is obviously a .33333.... geometric probability. The third pole is called a pi-angle pole since the rotation of the diameter end poles describe the perfect arc of a circle of pi.
The flat bet advantage comes from using the geometric finesse of "action at a distance" (see within) to predict and find the third pole (the relative pi-angle pole) as a .33333.... geometric probability that traditional random expects and "pays off" as a .25 algebraic possibility under quadrature. The difference is the flat bet advantage (.33333.... - .25 = .08333....) factored by two possible directions. That is: 2(.08333....) = .16666.... .
Knowledgeable entry into this world of geometric probability requires a mental admission. The ticket is a psychological leap: relative to serial random measurements, we and our perceptions and dimensions and measurements and statistics are all ...just relative pi in rotation.
Cracking Pi Cracking Random resurrects and combines two very old geometries of random probability. These are the original Buffon Needle Problem (1733) and the methodology of “action at a distance.” The methodology was suppressed by the Vatican four centuries ago: (actio in distans). It is a geometric finesse that delivers the random flat bet advantage. The original Needle is a matrix of geometric probability which is foundational and naturally leads to "action at a distance." The original Needle provides the correct unit of measurement to make mathematical sense of "action at a distance" the advantage of geometric probability. That unit of measurement is the original Needle's unchangeable length. It is the universal random average: relative 1/4 pi.
Both geometries have developmental roots traceable to Isaac Newton. Both geometries had a tortuous history throughout the 17th and 18th Century with the Vatican also banning the books of Newton and Buffon. Both geometries were lost in the French Revolution's Terror.
The methodology was only partly recovered in Werner Heisenberg's theory of Quantum Mechanics. The original Needle has never fully recovered until this website. In 1812, Laplace warped the original Needle. Reader's should very carefully note that what is offered in texts and on the web as the "Buffon Needle Problem" is NOT the original Buffon Needle Problem (see Exploring Random: Buffon Needle Problem)!
Only the original Needle supports the mathematical truth of "action at a distance" and the flat bet advantage.
CRACKING PI CRACKING RANDOM extends the methodology of the original Needle (and quantum theory) to every series of random measurements of anything. The original Needle provides its own length as the correct unit of measure: relative 1/4 pi, relative to the object, field or game's pi-angle.
The flat bet advantage is gravitational, simple, random, geometric, contains relativity and is dimensional in nature. The pi-odds formula delivers it with the relativity that eluded Albert Einstein. He didn't believe in "action at a distance" and called it "spooky!"
In its most fundamental form, the flat bet advantage is doubled from quantum theory's .08333.... (because the particle or "field" is split) to .16666.... (because the "field" or circle is not split). In many random games the advantage may be refined to include an additional .11111.... flat bet advantage from centrifugal force.
Of particular fascination, every series of random measurements --of anything-- inevitably tends to duplicate the relative geometric relationships between the digits of geometric divisions of pi. This duplication includes the .16666…. advantage. Indeed, it is in and through these geometric divisions that the advantage appears. It does so with predictable geometric precision. It is found with averages of geometric probability piled on top of averages of geometric probability.
In other words, any random series of anything is already predictable with a flat bet advantage simply by looking at the relative digits of the geometric divisions of pi?!
The inevitable conclusion is that every random series is already a predictable statement of pi in the first instance of gravity and randomness!!
Roulette with a dealer’s random release of the ball was used throughout this study as a near perfect universal model of randomness. Only the frets of a wheel hold back near absolute perfection. These matters have also been thoroughly and successfully tested with dice and cards and True Random Number Generators. So too, this has been lightly but successfully tested with the randomness of the stock market and psychology as well as biological and geological distributions.
Far beyond gaming, the real nest of the gravity bet will be a statistical revolution in the actuarial sciences.
We --and our perceptions and measurements and quadrature-- are the mysterious “hidden variables” of quantum theory.
The inevitable startling mathematical conclusion is that "randomness" is only the possibility of 1 of 2 directions in a matrix of pi.
We cannot see the forest for the trees. The reason is also a philosophical conclusion: relative to serial random measurements of gravity, we and the forest and the trees …including our perceptions and traditional random theories and games and ideas and measurements and statistics and quantum theories and descriptions and conclusions are all ...just so much relative pi in rotation!