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DECONSTRUCTING PI

Written by G. T. Hushion. Posted in Exploring Random

"You can't calculate probabilities with just algebra. The geometry must be taken into account."

Comte George Buffon, Essay on Moral Arithmetic

 

DECONSTRUCTING PI

Since the geometry of a diameter has random gravitational dominance over the algebra of a circle, and since the ratio between them is pi, the geometry will remain dominant and intact regardless of what system of mathematics is used to describe the algebra of pi.

Our common description of the ratio between a circle and diameter is in terms of pi. Pi is always expressed as a percent. That is: in parts of hundreds that are constructed with the tenths of the decimal system. It is an arbitrary system.

If a different system of measurement, other than the decimal system, was used to describe pi, the algebraic description would be different ...but the geometric ratio would remain the same.

The formula for the gravity bet may be reduced to a string of fractions. If each element of the formula is reduced to its fundamental structure of relative 1/4 pi, the result is a string of 81 fractions.

In a series of random statistics, using the gravity bet ("action at a distance") and its geometric finesse to find geometric probabilities (rather than using simple Monte Carlo methodology to find the algebraic possibilities) what is delivered is the answer to Einstein's own paradoxical inferences in his EPR. That is, a complete statement of physical reality (or at least the mechanics of gravity).

The paradoxical problem for Einstein was that the values of the methodology ("action at a distance") used by Quantum Mechanics that he was questioning ...held the very grail he was seeking elsewhere. At the same time, Einstein was asking the right question. Essentially, he was asking: "...Even if Quantum Mechanics is right, what about everything else that isn't part of the geometric probability with its flat bet advantage: .08333.... ?"

The answer to Einstein's valid EPR question in 1935 ...was delivered by deduction and inference in the original Needle in 1733. That is, relative to the randomness of gravity (by the Needle or comet's orbit or particle spin or roulette with a dealer's random release) the nature of "everything else" other than gravity's straight line pull may be expressed as no more than relative 1/4 pi.

Gravity is identified by its straight line pull on a field, object or game's diameter (or "pi-angle"). It is demonstrated by the .08333 flat bet advantage based on the express proof of the original Needle. That is, relative to a series of random measurements, gravity has a value: "1." ...and,relative to gravity, everything else is just so much pi in rotation with relative 1/4 pi as the unit of measure, relative to the diameter. That is, relative to gravity, everything else is just a mathematical perception of relative 1/4 pi in rotation.

Einstein's EPR question about Quantum Theory not being a complete description of physical reality was answered in 1733. Relative to the geometric probability of a series of random measurements, everything other than the geometric probability is just so much relative pi in rotation, relative to the diameter (or "pi-angle').

Since relative 1/4 pi is only a percentage of a gravity field’s diameter ...and since a diameter is randomly proven by the original Needle as having a relative geometric value of “1.” ...the component parts of a “percent” must necessarily be expected to appear when the complete string of the pi-odds formula --Einstein's own but misunderstood inferential definition of a complete description of physical reality-- is factored back into the gravity to which it is relative!

And so it is!

In other words, there is a geometric point in a stream of random events where there is a perfect convergence of random matters of the geometric probability of gravity ...and the algebra of our perceptions and games.

That point of convergence is not a point of equality. It appears as a Cardinal pole with 90 degrees of arc relative to the circle or "game," but is also a point of relative geometric probability, of 60 degrees of arc on the "circle" or game. The 60 degrees of arc are the geometric probability of a diameter end pole as a .33333.... geometric probability (as 1/3 of a circle of 360 degrees: 120 degrees) factored by the algebra of two possible directions. That is: 120 / 2 = 60.

Although the Cardinal pole has a larger algebraic description, the geometry of the diameter's smaller relative pi-angle pole gravitationally dominates with a flat bet .16666 geometric probability. The relative pi-angle pole of the diameter is a .33333 geometric probability, factored by two directions. That is: 2 (.08333) = .16666.... . That is: 90 - 60 = 30. Next: 30 / 90 = .33333 . Next: .33333 / 2 directions = .16666 . Randomly, with relativity, this geometric probability dominates over algebraic possibility.

The advantage is only effectuated with the finesse methodology in "action at a distance." Again, this is what spooked Einstein.

The relative pi-angle pole of 60 degrees is surrounded by the Cardinal pole of 90 degrees that contains it. More than just a point of perfect convergence, it is also a point of perfect separation.

The finesse of "action at a distance" separates gravity's delivery of geometric probability on a randomly measured diameter ...from the quadrature of life's perception of the random algebraic possibilities on a circle.

That point of separation only makes mathematical sense when the unit of measurement is relative 1/4 pi. It is only found with the geometric finesse in "action at a distance."

That point of separation tends to statistically contain a random .16666 flat-bet advantage. It is the difference between predicting a relative diameter end pole as a .33333 geometric probability on a diameter of three poles ...and having it expected and pay off under traditional random theory as a Cardinal pole with a .25 algebraic possibility, on a circle of four Cardinal poles. All is factored by the algebraic possibility of two directions with the geometric certainty of one direction.

The core point of the entire matter is that relative 1/4 pi --and only relative 1/4 pi-- is the unit of measure for the bridge between random perception and random gravity. As 1/4C, it is only algebraic in nature and only relative to the circle or game. On the other hand, as relative 1/4 pi, it is both algebraic and geometric in nature relative to the diameter.

The original Needle proved every game was a game of pi and that pi was a percentage of the circle or game or field's diameter.

Since the decimal system is used to describe percentages ...and since percentages are used to describe pi ...and since the original Needle inferentially and deductively proved every game was a game of pi ...and since predicting random particle spin is as equally much a game as predicting random roulette spin ...and since Quantum theory also finds a .08333 advantage in predicting random particle spin ...and since, for the reasons given above and herein, the random measurement of anything is therefore the random measurement of pi in rotation ...there must necessarily be a .08333 flat-bet advantage, doubled by the possibility of two directions --that is: 2 (.08333....) = .16666.... -- at precisely (because "percentages" and "hundredths" are used) the 100th pi-angle relationship between the digits of relative 1/4 pi and the digits of relative 1/2 pi!

Similarly,  the same .16666 advantage is found at precisely the relative 100th pi-angle between the digits of 1/4 pi and the digits of relative 1/6 pi.

Other geometric descriptions, utilizing divisions of pi to describe the relationship between a diameter and a circle, also deliver a .16666 advantage at the relative 100th relationship.

This means that every stream of random events tends to duplicate the streaming geometric relationships within the digits of pi and its geometric components!!

An understanding of the geometry of pi begins with the gravity bet and its string of 81 beads of 1/4 pi each.

When the string of 81 events of relative 1/4 pi is factored into that to which it is relative (gravity's pull along a pi-angle) the ten digits that comprise the DNA of both the decimal system and “percent” precisely appear in that quotient. That is: 1 / 81 = .0123456789....!

The remaining digits after .0123456789 are simply an infinite repeat of 0123456789. They appear at this time to be the geometric infinity of “pi” and/or the infinite possibilities of two directions and/or the infinity of time and/or the infinity of the endless nature of the universe and our perception thereof or any other reasonable explanation that fits life's perceptions in attempts to define pi.

Further evidence that the endless repeat of: 0123456789 is in furtherance of a complete statement of physical reality is that the totality of the numbers add up to: 45 . This is the algebraic total of the decimal system. That is: 0+1+2+3+4+5+6+7+8+9 = 45. When that totality is made relative to the decimal system that generated it (divide 45 by 10) the quotient is 4.5 .

When 4.5 is factored into the gravity to which it is relative, the geometric truth appears as: 1/ 4.5 = .22222.... . Divided by 2 the directions of randomness, this gives: .22222 / 2 = .11111.... .

Gravitationally, .11111 is the statistical value of Centrifugal force (discussed elsewhere in this site). Centrifugal force also describes a radius. A radius is one half a diameter. Therefore, relative to Centrifugal force, a diameter (or pi-angle) has a value .22222 . And so it is.

Centrifugal force is only possible in one direction at time for any random measurement. Since there are always two possibilities (two possible directions) in any series of random measurements ...and since Centrifugal force is from the COR in one direction, such as for example, COR to North ...therefore: .22222 is a complete description of a randomly measured rotating diameter with both opposing centrifugal forces describing a complete diameter. Such as, for example: South, COR, North or, more accurately, pi-angle-base, COR, pi-angle pole.

Since, by the proofs and deductions and inferences of the original Needle, pi is geometrically meaningless relative to randomness and gravity, these numbers are the long sought pattern in pi. Except ....since pi is gravitationally meaningless ...the pattern is in the gravitational relevance of a pi-angle measured by the geometric relationship between relative 1/4 pi and relative 1/2 pi (or equally with relative 1/6 pi). That geometric relationship ---the random relative truth of gravity-- is only found with the geometric finesse of "action at a distance."

Since, by the original Needle, the significance of relative pi is simply the possibility of two relative directions, relative to the totality of gravity (the field's complete diameter) and since gravity is identified by the geometric structure of a rotating pi-angle between relative 1/4 pi and relative 1/2 pi (identifying both relative ends of a gravity field's entire rotating diameter) ...the infinity of pi again appears to be no more than the algebraic and infinite possibility of two possible directions.

Geometrically, since a "circle" is also just the end points of radii extending from the COR, pi also appears as the COR on a rotating diameter of three poles.

Paradoxically, the COR has three mathematical natures. It is algebraic by its nature of two random possibilities: the diameter and cross diameter. It is algebraic in nature relative to pi by its value of 1/2 pi on a cross-diameter of relative pi. It is also geometric in nature with a random value of .50 as the middle pole relative to the diameter.

This is why the geometric finesse is necessary: to bypass or "finesse through" the dual/multiple nature of the COR and pi. The COR is geometric relative to gravity's diameter. The COR is algebraic relative to life's perception of a cross diameter (the "game"). Further studies will undoubtedly be more productive, but here is the mathematical proof of the foregoing.

The ten digits of the decimal system ...and the percentages or "hundredths" they describe ...are the DNA with which, gravitationally and randomly, the percentages between relative 1/4 pi and relative 1/2 pi (or between relative 1/4 pi and relative 1/6 pi) describe random gravity.

That random description is a geometric probability that is describable as a percent (hundredths). It is statistically found by repeatedly predicting relative pi-angle poles (identifiable by the perceived geometric relationship between relative 1/4 pi and relative 1/2 pi). It is only found, however, with a geometric finesse. The finesse delivers the flat bet random gaming advantage of .16666 as a by-product of the unique measurement of "action at a distance." 

The original Needle proves a series of random table gaming outcomes (or any series of random measurements of any field) as only a string of algebraic statements of relative 1/4 pi in the first instance. This allows the third in a random series (also proven by Bell’s Theorem and the Quantum sciences) to tend to be the sum of the first two. That is, using the geometric finesse, the third random measurement in a series of three tends to be a pi-angle pole which is identified by relative 1/2 pi ...and by two measurements of relative 1/4 pi each which add up to relative 1/2 pi. It should be noted that this phenomenon is recognized but not understood in the Quantum sciences. That is, it is recognized that the third of three random measurements tends to be the sum of the first two ...but it is not understood why.

CRACKING PI CRACKING RANDOM herein gives the why of it.

Every stream of random events ...every stream of random Roulette outcomes ...tends to statistically duplicate the relative geometric relationships between the geometric components of pi!

The key of understanding is found in the nature of relativity on a diameter or "pi-angle."

Using the finesse, the flat-bet advantage of .16666 must necessarily appear in the 102nd relative digit of 1/2 pi as a relative pi-angle pole, relative to the first 100 digits of relative 1/4 pi.

By the proof, deductions and inferences of the original Needle, pi itself is the COR. This is because, geometrically, a circle is only a series of the end points of radii extending from the COR. If a circle is pi ...so too, the COR is pi.

Since the original Needle proved a circle is only a mathematical perception of pi, then the COR is also only a mathematical perception and statement of pi. Therefore, relative to gravity, since the geometric finesse is through the COR, the digits of pi are ignored since their relativity is meaningless. Pi only has apparent meaning relative to the algebra of perception. That is: pi is just a series of perceived averages on an algebraic circle comprised of relative 1/4 pi multiplied by 4.

When measured randomly, such an algebraic circle always contains the algebraic possibility of two directions. This is the true nature of randomness in every series of random measurements. That is: randomness is only the possibility of one of two equally possible directions.

The geometry of relative 1/4 pi and relative 1/2 pi are mathematically relative to gravity by virtue of algebraically identifying both ends of a semi-circle ...while simultaneously geometrically identifying both ends of a diameter.

That simultaneous representation, and the geometric difference, inherently contains the .16666 advantage. It is the geometric probability difference between the algebraic end pole of a semi-circle as a Cardinal pole identifying an arc of 90 degrees on the complete circle (or "game") ...and the geometric end pole of a diameter with a geometric probability of 60 degrees. That difference, factored by two directions, is the .16666 flat-bet advantage of the gravity bet.

The reason a diameter end pole is an arc of 60 degrees of geometric probability on a circle instead of the expected 120 degrees of arc (as one of three poles) is because the randomness of two possible directions must always be factored.

For these reasons, the same .16666 flat-bet advantage is found between the digits of relative 1/4 pi as a diameter-base and the relative digits of relative 1/2 pi as the relative pi-angle pole.

• Let the digits that comprise the decimal system (0,1,2,3,4,5,6,7,8,9) be structured as the field of a ten pocket roulette wheel. This is a "decimal wheel" or "percent wheel." More accurately, it is a "decimal/percent" wheel. Hereinafter, it is called a "Decimal" wheel.

• Let the number/pockets on the Decimal wheel appear in their regular order of 1 through 10.

• Let there be a series of three events structured with the methodology of the geometric finesse wherein the third event is predicted relative to the first event.

• Let the geometric finesse be through the digits of pi.

• Let the geometric finesse be repeated 100 times. This matches the structure of the experiment (100 measurements) with the structure of that which is being measured: the 100 parts of a percent.

• Instead of three throws of a roulette ball, let the geometric finesse be through a series of three respective digits of relative 1/4 pi, relative pi, and relative 1/2 pi. This is the structure of a diameter relative to percent.

• Let the diameter of the field be a pi-angle (diameter) between a digit of relative 1/4 pi as a diameter base ...and the respective relative digit of relative pi as the COR ...and the respective relative digit of relative 1/2 pi to be found as the relative pi-angle pole at the third measurement, using the geometric finesse of "action at a distance."

• Let time be factored as a sequential order of the relative digits as follows:

EXAMPLE: the first diameter in the series of 100 diameter measurements is: the first digit of relative 1/4 pi as a diameter-base; the second digit of relative pi as the COR; the third digit of relative 1/2 pi as the relative pi-angle pole, relative to the first digit of relative 1/4 pi.

EXAMPLE: the second diameter in the series of 100 diameters would be: the second digit of relative 1/4 pi as a diameter base; the third digit of relative pi as the COR; the fourth digit of relative 1/2 pi as the relative pi-angle pole, relative to the second digit of relative 1/4 pi.

EXAMPLE: the third diameter in the series of 100 diameters would be: the third digit of relative 1/4 pi as a diameter base; the fourth digit of relative pi as the COR; the fifth digit of relative 1/2 pi as the relative pi-angle pole, relative to the third digit of relative 1/4 pi.

These examples factor time correctly since time could not be factored if the pi-angle diameter was defined simply by the first digit of 1/4 pi and the first digit of pi and the first digit of 1/2 pi. In such a case there would be no "rotation" or movement or serial random measurement. Without the serial nature, time would not exist. The realization of relativity would also be impossible since everything would be static.

TO BE FOUND IN ACCORD WITH THE “ACTION AT DISTANCE” OF THE GRAVITY BET’S GEOMETRIC FINESSE AND THE METHODOLOGIES OF RUDJER BOSKOVIC, QUANTUM MECHANICS AND BELL’S THEOREM:

1: over the span of 100 measurements, of three events each, the sum of the first two measurements will tend to equal the third. That is: relative 1/4 pi plus relative 1/4 pi = relative 1/2 pi. This will be evidenced by a tendency of a relative pi-angle pole to appear with a .16666 geometric probability over all traditional theories of random expectation.

2: This will deliver, by the 102 digit of relative 1/2 pi, a flat-bet advantage of .16666 over all traditional theories of random expectation!

Since the pi-angle to be predicted is a probability statement of .16666, on a probability field of the 10 digits comprising the decimal system, the size of the pi-angle pole must be: .16666 of the field, factored by two directions.

Since, because of the geometric finesse, one probability event (the COR) is necessarily averagely removed from play or geometric consideration (because the geometry is not part of the endless possibilities of algebra) the average size of the field is necessarily and geometrically reduced by one “pocket.”

On a ten pocket "decimal/percent" roulette wheel, that leaves nine pockets in average play in which there is to be predicted a relative pi-angle pole of three pockets. The pi-angle pole may be accessed with the geometric finesse from either of two directions. That is: 2 (( .16666 (9)) = 3 .

• Let the relative pi-angle pole consist of three adjacent pockets.

• Let the only bet possible on this ten pocket "decimal" roulette wheel be the prediction of a complete relative pi-angle pole of three pockets.

• Let each flat-bet prediction be of one unit (or dollar or chip) on each pi-angle pocket. That is: each bet or prediction is a total of three units.

• Let success come whenever a digit of relative 1/2 pi appears in the relative pi-angle pole/pocket. A success pays nine to one (10 for 1) under traditional random theory.

The three relative pi-angle pole/pockets to be found on a 10 pocket "decimal" wheel are: roulette wheel
opposite 0 are 4,5,6.

opposite 1 are 5,6,7

opposite 2 are 6,7,8

opposite 3 are 7,8,9

opposite 4 are 8,9,0

opposite 5 are 9,0,1

opposite 6 are 0,1,2

opposite 7 are 1,2,3

opposite 8 are 2,3,4

opposite 9 are 3,4,5.    

CASE EXAMPLE: 1) The first bet on the ten pocket "decimal" wheel is as follows. The first digit of relative 1/4 pi is: 7. It is a diameter base of the diameter: 7, COR (the second digit of pi), and the relative digit (the third digit) of relative 1/2 pi as the relative pi-angle pocket. On the ten pocket wheel, the relative pi-angle pole to 7 is comprised of the digits: 1,2,3. The bet or prediction is one unit each on the digits: 1,2,3. Three units in all. The success or failure of the bet is found at the third relative digit of relative 1/2 pi. It is relative to the first digit of relative 1/4 pi. That digit of relative 1/2 pi is: 7. It does not appear on the ten pocket wheel in the relative pi-angle pole relative to 7. Therefore, the bet loses.

CASE EXAMPLE: 2) The second bet on the ten pocket wheel is as follows. The second digit of relative 1/4 pi is: 8. It is a diameter base of the diameter: 8, COR (the third digit of pi), and the relative digit (the fourth digit) of relative 1/2 pi as the relative pi-angle pocket. On the ten pocket wheel, the pi-angle pole relative to 8 is comprised of the digits: 2,3,4. Therefore the bet or prediction is one unit each on the digits: 2,3,4. Three units in all. The success or failure of the bet is found at the fourth relative digit of relative 1/2 pi. That digit is: 0. It does not appear on the ten pocket wheel in the relative pi-angle pole relative to 8. Therefore, the bet loses.

CASE EXAMPLE: 3) The third bet on the ten pocket "decimal" wheel is as follows. The third digit of relative 1/4 pi is: 5. It is a diameter base of the diameter: 5, COR, (the fourth digit of pi), and the relative digit (the fifth digit) of relative 1/2 pi as the relative pi-angle pocket. On the ten pocket wheel, the pi-angle pole relative to 5 is comprised of the digits: 9,0,1. Therefore the bet or prediction is one unit each on the digits: 9,0,1. Three units in all. The success or failure of the bet is found at the fifth relative digit of relative 1/2 pi. That digit is 7. It does not appear on the ten pocket wheel in the relative pi-angle pole relative to 5. Therefore, the bet loses.

CASE EXAMPLE: 4) The fourth bet on the ten pocket "decimal" wheel is as follows. The fourth digit of relative 1/4 pi is: 3. It is a diameter base of the diameter: 3, COR (the fifth digit of pi), and the relative digit (the sixth digit) of relative 1/2 pi as the relative pi-angle pocket. On the ten pocket wheel, the pi-angle pole relative to 3 is comprised of the digits: 7,8,9. Therefore the bet or prediction is one unit each on the digits: 7,8,9. Three units in all. The success or failure of the bet is found at the sixth relative digit of relative 1/2 pi. That digit is 9. It appears on the ten pocket wheel in the relative pi-angle pole relative to 3. Therefore, the bet wins.

The process is repeated until the first 102 relative digits of relative 1/2 pi have each been bet or predicted relative to the first 100 digits of relative 1/4 pi.

THE RESULTS

This experiment of 100 measurements was predicated on the fact that pi is a percentage (3.14159....) of a randomly measured field's diameter.

The 100 measurements represented the 100 parts that comprise “percent.”

The pi-angle or "diameter" that was measured was identified by the “distance” between one end of the pi-angle as a diameter base and the "other end" as a pi-angle pole. The diameter base was identified by relative 1/4 pi, relative to the field's diameter. The pi-angle pole was identified by relative 1/2 pi, relative to the field's diameter.

A .16666 advantage was predicted, using the methodology of the gravity bet and the geometric finesse. This is the methodology of “action at a distance” that spooked Einstein. The methodology is identical with the methodology of Rudjer Boskovic for predicting the orbits of comets ...and with the methodology of Quantum Mechanics and Bell’s Theorem for predicting the spin of a particle!

The .16666 advantage was predicted to be found in the geometric relationships between each of the first 100 digits of 1/4 pi and each of the first 102 respective relative digits of relative 1/2 pi when they are structured as the relative end poles of a randomly measured gravity field’s rotating diameter.

The original Buffon Needle Problem was the first random proof of pi. The advantage was predicted with a formula that is an extension of the formula for the original Needle. The extension is the geometric finesse of "action at a distance." This was algebraically factored by two possible directions with the geometric certainty of one direction. The results were identical with the results of the gravity bet for predicting the spin of a table game ...and of the Quantum sciences for predicting the spin of a particle.

Time was factored by a sequential order of the component poles of a rotating pi-angle as discussed above.

Relativity was automatically factored between the first and third measurement as the geometry of the finesse in "action at a distance" was superimposed on the matrix of traditional Monte Carlo methodology.

The geometric finesse was though the digits of pi.

One hundred bets were made. The number of bets matches the numbers in a "percent" that is used to describe pi. Each bet was of three units: one unit on each of the three pockets that constitute a relative pi-angle pole. There was an expenditure of three hundred units.

There were thirty five successes. Each success pays ten units. That is a return of three hundred fifty units. That is a “profit” of fifty units over and above the expenditure and over and above all traditional theories of random expectation. That delivers the predicted .16666 advantage! That is: 50 / 300 = .16666 !

Therein is uncovered the mystery of pi. It is the random bridge, with a .16666 flat bet advantage, between perception and gravity. One end of the bridge is relative 1/4 pi: the length of the original Needle. The other end of the bridge is relative 1/2 pi spookily turning into relative 1/6 pi ...which is the goal of the geometric finesse.

Relative to our random games, we are in the middle of the randomness ...and we and our random measurements are just a game of relative pi.

More! The gravity bet exposes the "game" of pi as having a geometric structure of one sixth of the field or game relative to gravity. Since the original Needle identifies relative 1/4 pi to be only an algebraic perception and since the geometric finesse identifies 1/6 pi to be the true building block of geometric probability relative to gravity, the same .16666 flat bet advantage would be expected between the relative digits of relative 1/4 pi and the relative digits of 1/6 pi.

And so it is.

Since perception is eliminated when relative 1/6 pi is randomly found, but the measurements of geometric probability are still in terms of percent, the relativity would also be expected, with a geometric finesse, at precisely 100 measurements, entirely within the digits of 1/6 pi relative to itself.

And so it is!

• Let the 10 pocket roulette wheel again represent the decimal system that is the basis of "percent."

• Let relativity be found between each sixth digit of 1/6 pi.

• Let the sixth digit of 1/6 pi be predicted or bet or compared to the first digit of 1/6 pi. In this case example, the first digit of 1/6 pi is: 5. On the ten pocket wheel, the pi-angle pole/pockets opposite 5 are: 9,0,1. The sixth digit of 1/6 pi is: 8. Therefore the prediction or bet loses.

The second digit of 1/6 pi is: 2. On the ten pocket wheel, the pi-angle pole/pockets opposite 2 are: 6,7,8.

The seventh digit of 1/6 pi is: 7. Therefore the prediction or bet wins.

The mathematical vehicle of "percent" is the means by which we measure geometric probability. As above, this process is repeated 100 times to make the measurements relative to and, replicate, the 100 parts of "percent."

The results are identical with the relationships between relative 1/4 pi and relative 1/2 pi. That is: 100 predictions or bets with 1 unit on each of the three pockets comprising a pi-angle pole is an expenditure of 300 units.

There are 35 successes. Each success pays ten units. That is a return of 350 units. That is a flat bet advantage of .16666 . That is: 350 - 300 = 50 ...and 50 / 300 = .16666 !

Other combinations; between 1/4 pi, 1/2 pi and 1/6 pi; also deliver a precise .16666 flat bet advantage at the 100th measurement.

In sum: every series of random measurements is statistically revealed as a game of pi. Relative to a series of random gravitational measurements, we the players are an essential part of our games. We and our games are the COR. We are what must be finessed through. We and our games and our random measurements and perceptions are the pi ...and gravity is the relative pi-angle.

To find the gravitational truth of randomness, we have to finesse through pi. Relative to the gravitational truth of randomness ...we and our perceptions are the pi.