“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 AND EXTRACTING THE FLAT BET ADVANTAGE
Beginner’s luck occurs automatically at the third of a series of three random events. It is the natural outcome of a player naturally and necessarily (however and usually unwittingly) placing initial bets on the third of three diameter (or “pi-angle”) poles.
As discussed throughout, all that is randomly measured or “rotating” in any random series of anything are the three poles of a diameter. Therefore, the third pole –or proportion thereof– will necessarily tend to be a .33333…. geometric probability at the third trial. When the third pole occurs in at the third of three random trials, traditional random theory expects and pays off as though it was a quadrant pole –or proportion thereof– with a .25 possibility. The prediction of the third trial being the third pole of a three pole diameter, automatically includes a “finesse” of the second trial. However, since the expectation of the second event is a zero sum expectation, it is irrelevant (except for any possible “house advantage” if the random series is a casino game).
Beginner’s luck ends if a fourth bet (and each successive bet) is made without the geometric finesse.
These matters are dimensional. Gravity only pulls on one dimension. It has been said we live in parallel dimensions. Perhaps more accurately, we live in overlapping dimensions. One dimension is gravity’s straight line pull. This automatically is along and identifies the diameter of a randomly measure field. We “measure” a random series by the use of averages. The identifies a relative cross diameter. Since an average is just a mathematical perception, it may be fairly said we live in overlapping dimensions. The diameter dimension is gravitationally real. The relative cross diameter dimension is only a perception.
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 random 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 cause or 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 geometric probability is found with the original Needle. Its length provides the universal random unit of measure.
Relativity, along with “action at a distance” and the original Needle, 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 the 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 and Rudjer Boskovic’s use of the same.
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 is always on the diameter of the field or object or game. Every diameter has three poles. The relativity connection is between the poles. It is found with a series of random measurements using a geometric finesse to eliminate the middle pole from statistical consideration.
If the middle pole (or “Center of Rotation”) is not eliminated, it will randomly tend to averagely appear once for each random appearance of an end pole. That gives each pole a .25 algebraic expectation. Like a circle of 4 poles.
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. This matches our perceptions …but doesn’t match what gravity is delivering.
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 deliver traditional random theory. There is no meaningful relativity in traditional random theory. Everything is, like Einstein’s theory, equally relative.
(Einstein is famously quoted that the “only way to win money at roulette was to steal chips when the dealer wasn’t looking.”)
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 the geometric probability of relativity …statistically impossible.
The relativity connection is found by using the geometric finesse to find the random statistical connection between the end poles of a 3 pole diameter. That relativity connection allows the third pole (the “other end”) to statistically appear 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 Needle’s universal random average: 1/4 C. Its relativity is meaningless since all possibilities are equally possible (all roulette pockets are equal).
The key to the lock is the original Needle’s universal random average: relative 1/4 pi. Its relativity leads to the values of the COR as pi relative to the cross diameter dimension …and .50 relative to the diameter dimension.
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. It is just a mathematical average. Since an average is just a perception, it may fairly be said: …relative to the geometric randomness of gravity, we and our perceptions and measurements and statistics and algebra are all 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 that we identify as “relative” to the circle of our perceptions of two or more dimensions. However, the random truth of gravity’s relativity is, thanks to the original Needle, described by gravity itself. Gravity’s randomness is relative to gravity’s straight line pull along the diameter of any field, object, circle or game.
The original Needle proves its length of 1/4 C is also 1/4 pi.
As 1/4 C, it is the mathematical average distance around a circle between one random measurement and the next. Since 1/4 C is already a part of the circle “C”, its relativity to “C” is meaningless.
As relative 1/4 pi, relative to the diameter, 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. The COR is mathematically comprised of the algebra of two dimensions and four end poles. To get a clear picture of geometric probability, the algebra of the COR’s possibilities must be cleared away. This is what the geometric finesse does. It eliminates the COR from consideration. This effectively eliminates ourselves and our perceptions and measurements from a 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 is 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 algebra of the averages tends 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 on a zero sum game.
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 the 4th pole of a circle. As the fourth poles on a circle, there is no meaningful relativity since each of the four poles of a circle is already part of a circle of four poles.
True relativity takes form as the unexpected opposing 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 an opposing pole with 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 true geometric probability. This 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 (see: Cracking Random)
The unexpected geometric connection between diameter end poles 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 finesse of “action at a distance” on a cube, 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 in the finesse 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 tumble of the cube effectively releases each of the six radii from the statistics of a hard structure. It is an effectively identical process as with an RNG. The only difference is the COR of a cube has six radii instead of the four radii of an RNG. Similarly, each radius must be allowed to happen with two possible directions On a cube, that is twelve possibilities. Therefore, as a matter of geometric probability, the thirteenth trial must necessarily deliver the relative pi-angle pole …and the flat bet advantage.
The pi-odds study includes now includes over 10,000 trials. Casino quality dice were mainly used, but 6 ordinary game dice were also tested for approximately 1,500 trials.
The ordinary dice gave a flat bet advantage of over .05+ %. They were tested for imbalance by spinning them in salt water. If they are unbalanced, one facet will tend to appear more than the others. Of the six ordinary dice, three consistently came up with the same facet and three refused to float at all.
Two types of casino quality dice were used: Feather Edge and Razor Edge. The Feather Edge delivered a flat bet advantage just under the expected .16666…. .
A Feather Edge is a Razor Edge that has had the edges evenly smoothed over.
The Razor Edge have an automatic built in mechanical imperfection. They are cut from a long molded composite bar that measures 5/8″ by 5/8″. A machine cuts them at 5/8″. The facets that are cut has have four Razor Edges each. The remaining four facets have two edges that are molded and two edges that are cut. That is a 2 -1 difference. That is a .33333 imperfection. The cubes are then randomly numbered and balanced. However, the mechanical imperfections appear to remain. The statistical results of thousands of throws of the twelve Razor Edges averaged just a hair under .11111…. . That is .33333 less than the expected .16666…. .
The Nevada State Gaming Commission mandates that casinos only use Razor Edges.
It is worth noting that a pair of “Laser Perfect” dice were tested. They are board game dice that are cut with a laser. They performed worst of all dice. That would indicate that while they may have been cut with a laser, nothing is said of the standards or calibration or balance.
There is no fixed “Center of Rotation” in a suit or deck of cards. In a deck of four suits, the “COR” is replaced by two suits. This results in the relative pi-angle pole of a suit [the third pole of a three pole diameter] necessarily tending to appear at the fourth relative trial. There are also at least two relative pi-angle poles. They are each on their own “circle of cards.” Each example given here is the result of “flat bet” testing over 2,700 trials. The first advantage is the circle of cards with the pi-angle pole appearing: A-7, 2-8, 3-9, 4-10, 5-J, 6-Q, 7-K, 8-A, 9-2. 10-3, j-4, Q-5, K-6. That is, in a well shuffled deck, the random appearance of an “Ace” will tend to be followed at the fourth trial by the random appearance of a “7.” The random appearance of a “2” will tend to be followed at the fourth trial by an “8.” The other circle of cards is: A-Q, 2-K, 3-A, 4-2, 5-3, 6-4, 7-5, 8-6, 9-7, 10-8, J-9, Q-10, K-J.
A short study of just over 1,000 trials of two and a half “8 deck” shoes delivered an extraordinary advantage of .24830…. at each fourth trial with a circle of cards: A-K, 2-A, 3-2, 4-3, 5-4, 6-5, 7-6, 8-7, 9-8, 10-9, J-10, Q-J, K-Q.
There are, of course, other geometric advantages with cards.
RANDOM NUMBER GENERATORS
There are two fundamentally different types of random number generators (RNGs): True and Psuedo. Each is driven by an algorithm through which the input/output is filtered. The field used in this study consists simple of 12 numbers, in natural sequence, organized like a roulette wheel. In traditional random theory each field is considered a zero sum game in which it is considered impossible to predict a random outcome. Where to look for the advantage and how deep a finesse to take will very with the algorithm. In each case a flat bet advantage is sought: .16666…. .
True RNGs may receive their input from a variety of random sources such as radio waves from outer space or atmospheric noise or radioactive decay.
Pseudo RNGs receive their input from a non random “seed” number around which the subsequent numbers occur. There is a reason they are called “pseudo”: they are not random. They have an initial appearance of randomness which is lost as the algorithm inevitably repeats itself. This is study is not concerned with pseudo randomness. Nevertheless, pseudo RNG’s have been cracked as well.
While traditional random theory calls for millions of trials to prove a point, geometric probability requires far less. The matter is dimensional. The key number of trials in which random geometry usually settles in appears to be twelve cubed. That is: 1,728. This is the number of all possible permutations, over three random measurements, of the three dimensional gravitational poles of a relative pi-angle …and the four perceived quadrant poles of a circle or “game.”
The quantum RNG tested here may be found online at www.Randomnumbers.info. It fires light photons at a semi transparent mirror. Half go through, half are reflected. From the random binary results (1 / 0) random numbers are obtained. The “0” is automatically used to start the random series. This appears to perhaps not be a true “number” but rather a default from the binary dynamic: “0” or “1”. That is, a twelve pocket “wheel” is now numbered “0” through “11.”
The .16666…. flat bet advantage cannot be destroyed if all is random. However each algorithm delivers it slightly differently.
The quantum RNG at Randomnumbers.info delivered an advantage just over .15…. .
The Mersenne Twister is perhaps the world’s most widely used pseudo RNG. Each session (except for the last) was of 17 sets of 100 trials each. Two sessions of 1,728 each (3,456 trials total) delivered a flat bet advantage: .11458…. .
Appzaza.com offers a cryptographically secure RNG. With 1,728 trials, it delivered a flat bet advantage just over .13…. . Such secure RNGs are used for critical matters such as secret codes, passwords and financial transactions.
Random.org uses a true random number generator. The advantage with 1,728 trials was just over .13
It should be noted that there is more than one predictable flat bet advantage in every random series.
As well, there is a predictable serial flat bet disadvantage Less than zero sum.
More. Within the predictable flat bet disadvantage there are two predictable flat bet advantages!!
RANDOM PSYCHOLOGY: ANTI SOCIAL BEHAVIOR
Two separate studies of psychology have each delivered fascinating results. The first concerns anti social behavior. The second concerns the stock market.
There is a stretch of highway outside Santa Barbara has long been 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 liberalism 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.
RANDOM MASS PSYCHOLOGY: STOCK MARKET
In 1007, 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. A slight variation was necessary to accommodate the intermittent presence of the listed stocks. 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 this.
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. With data input, without a geometric finesse, it will also reflect the algebra and quadrature of the stock market. However, 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 of the stock market as is already known.
Recently, Wall St. investment firms have looked to quantum computers for their incredible speed in transmitting data. The use of the light photon quantum experiment is now being worked with. It is mind numbing that these major companies are completely missing what quantum science is all about in the first instance: a predictable flat bet advantage over randomness!
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 .27777 flat bet advantage is not found in the stock market despite whatever RNG is used to analyze it. It is only found in the RNG itself.
The stock market has its own geometric probability and flat bet advantage regardless of what RNG (or no RNG at all) is used to analyze it.
It is ironic that the Quants (quantum computer specialists) of Wall Street are looking at quantum science for speedily getting the usual ordinary data almost as fast as light …while completely missing the far more salient point. It is the pure methodology itself (which even comes from quantum science but doesn’t need a quantum computer) that delivers far more meaningful data analysis ….complete with a significant flat bet advantage!